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In this paper, a frequency domain simulation method of magneto-acousto-electrical tomography (MAET) was proposed. This method is based on discrete Fourier transform. With this approach, the solving degrees of freedom of the simulation model can be significantly reduced. It can greatly reduce the requirements of computer hardware and improve efficiency. At the same time, the interaction between fluid and biological tissues was considered, which makes the simulation model closer to the real model. In this paper, an MAET simulation model of acoustic–solid–electromagnetic multi-physical field coupling corresponding to the actual physical world was established. It is more reasonable to adopt the fully coupled method. However, the fully coupled method needs more computational memory. To further study the memory and time required for calculation, the segregated method was used to calculate the simulation model without affecting the accuracy and tolerance in this paper. The results show that using the segregated method can significantly reduce the memory requirement of the MAET model, but the solution time will increase accordingly. Therefore, the appropriate solution method can be selected according to the simulation computer configuration and the desired solution time. We, finally, built an experimental platform to conduct MAET experiments and verified the theoretical and simulation analyses. [ABSTRACT FROM AUTHOR]

Quantum dynamics simulation and computational spectroscopy serve as indispensable tools for the theoretical understanding of various fundamental physical and chemical processes, ranging from charge transfer to photochemical reactions. When simulating realistic systems, the primary challenge stems from the overwhelming number of degrees of freedom and the pronounced many-body correlations. Here, we present Kylin-V, an innovative quantum dynamics package designed for accurate and efficient simulations of dynamics and spectroscopic properties of vibronic Hamiltonians for molecular systems and their aggregates. Kylin-V supports various quantum dynamics and computational spectroscopy methods, such as time-dependent density matrix renormalization group and our recently proposed single-site and hierarchical mapping approaches, as well as vibrational heat-bath configuration interaction. In this paper, we introduce the methodologies implemented in Kylin-V and illustrate their performances through a diverse collection of numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we present a combined experimental and theoretical study that explored the initial sticking of water on cooled surfaces. Specifically, these ultra-high vacuum gas–surface scattering experiments utilized supersonic molecular beam techniques in conjunction with a cryogenically cooled highly oriented pyrolytic graphite crystal, giving control over incident kinematic conditions. The D2O translational energy spanning 300–750 meV, the relative D2O flux, and the incident angle could all be varied independently. Three different experimental measurements were made. One involved measuring the total amount of D2O scattering as a function of surface temperature to determine the onset of sticking under non-equilibrium gas–surface collision conditions. Another measurement used He specular scattering to assess structural and coverage information for the interface during D2O adsorption. Finally, we used time-of-flight (TOF) measurements of the scattered D2O to determine how energy is exchanged with the graphite surface at surface temperatures above and near the conditions needed for gaseous condensation. For comparison and elaboration of the roles that internal degrees of freedom play in this process, we also did similar TOF measurements using another mass 20 incident particle, atomic neon. Enriching this study are precise molecular dynamics simulations that elaborate on gas–surface energy transfer and the roles of molecular degrees of freedom in gas–surface collisional energy exchange processes. This study furthers our fundamental understanding of energy exchange and the onset of sticking and ultimately gaseous condensation for gas–surface encounters occurring under high-velocity flows. [ABSTRACT FROM AUTHOR]

Coarse-grained (CG) molecular models greatly reduce the computational cost of simulations allowing for longer and larger simulations, but come with an artificially increased acceleration of the dynamics when compared to the parent atomistic (AA) simulation. This impedes their use for the quantitative study of dynamical properties. During coarse-graining, grouping several atoms into one CG bead not only reduces the number of degrees of freedom but also reduces the roughness on the molecular surfaces, leading to the acceleration of dynamics. The RoughMob approach [M. K. Meinel and F. Müller-Plathe, J. Phys. Chem. B 126(20), 3737–3747 (2022)] quantifies this change in geometry and correlates it to the acceleration by making use of four so-called roughness volumes. This method was developed using simple one-bead CG models of a set of hydrocarbon liquids. Potentials for pure components are derived by the structure-based iterative Boltzmann inversion. In this paper, we find that, for binary mixtures of simple hydrocarbons, it is sufficient to use simple averaging rules to calculate the roughness volumes in mixtures from the roughness volumes of pure components and add a correction term quadratic in the concentration without the need to perform any calculation on AA or CG trajectories of the mixtures themselves. The acceleration factors of binary diffusion coefficients and both self-diffusion coefficients show a large dependence on the overall acceleration of the system and can be predicted a priori without the need for any AA simulations within a percentage error margin, which is comparable to routine measurement accuracies. Only if a qualitatively accurate description of the concentration dependence of the binary diffusion coefficient is desired, very few additional simulations of the pure components and the equimolar mixture are required. [ABSTRACT FROM AUTHOR]

We present the computational methodology, which for the first time allows rigorous twelve-dimensional (12D) quantum calculations of the coupled intramolecular and intermolecular vibrational states of hydrogen-bonded trimers of flexible diatomic molecules. Its starting point is the approach that we introduced recently for fully coupled 9D quantum calculations of the intermolecular vibrational states of noncovalently bound trimers comprised of diatomics treated as rigid. In this paper, it is extended to include the intramolecular stretching coordinates of the three diatomic monomers. The cornerstone of our 12D methodology is the partitioning of the full vibrational Hamiltonian of the trimer into two reduced-dimension Hamiltonians, one in 9D for the intermolecular degrees of freedom (DOFs) and another in 3D for the intramolecular vibrations of the trimer, and a remainder term. These two Hamiltonians are diagonalized separately, and a fraction of their respective 9D and 3D eigenstates is included in the 12D product contracted basis for both the intra- and intermolecular DOFs, in which the matrix of the full 12D vibrational Hamiltonian of the trimer is diagonalized. This methodology is implemented in the 12D quantum calculations of the coupled intra- and intermolecular vibrational states of the hydrogen-bonded HF trimer on an ab initio calculated potential energy surface (PES). The calculations encompass the one- and two-quanta intramolecular HF-stretch excited vibrational states of the trimer and low-energy intermolecular vibrational states in the intramolecular vibrational manifolds of interest. They reveal several interesting manifestations of significant coupling between the intra- and intermolecular vibrational modes of (HF)3. The 12D calculations also show that the frequencies of the v = 1, 2 HF stretching states of the HF trimer are strongly redshifted in comparison to those of the isolated HF monomer. Moreover, the magnitudes of these trimer redshifts are much larger than that of the redshift for the stretching fundamental of the donor-HF moiety in (HF)2, most likely due to the cooperative hydrogen bonding in (HF)3. The agreement between the 12D results and the limited spectroscopic data for the HF trimer, while satisfactory, leaves room for improvement and points to the need for a more accurate PES. [ABSTRACT FROM AUTHOR]

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics. [ABSTRACT FROM AUTHOR]

The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna–Matthews–Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model. [ABSTRACT FROM AUTHOR]

We introduce a generalized micro–macro Markov chain Monte Carlo (mM-MCMC) method with pseudo-marginal approximation to the free energy that is able to accelerate sampling of the microscopic Gibbs distributions when there is a time-scale separation between the macroscopic dynamics of a reaction coordinate and the remaining microscopic degrees of freedom. The mM-MCMC method attains this efficiency by iterating four steps: (i) propose a new value of the reaction coordinate, (ii) accept or reject the macroscopic sample, (iii) run a biased simulation that creates a microscopic molecular instance that lies close to the newly sampled macroscopic reaction coordinate value, and (iv) microscopic accept/reject step for the new microscopic sample. In the present paper, we eliminate the main computational bottleneck of earlier versions of this method: the necessity to have an accurate approximation of free energy. We show that the introduction of a pseudo-marginal approximation significantly reduces the computational cost of the microscopic accept/reject step while still providing unbiased samples. We illustrate the method's behavior on several molecular systems with low-dimensional reaction coordinates. [ABSTRACT FROM AUTHOR]

The network structure within polymers significantly influences their mechanical properties, including their strength, toughness, and fatigue resistance. All-atom molecular dynamics (AAMD) simulations offer a method to investigate the energy dissipation mechanism within polymers during deformation and fracture; Such an approach is, however, computationally inefficient when used to analyze polymers with complex network structures, such as the common chemically double-networked hydrogels. Alternatively, coarse-grained molecular dynamics (CGMD) models, which reduce the computational degrees of freedom by concentrating a set of adjacent atoms into a coarse-grained bead, can be employed. In CGMD simulations, a coarse-grained force field (CGFF) is a critical factor affecting the simulation accuracy. In this paper, we proposed a data-based method for predicting the CGFF parameters to improve the simulation efficiency of complex cross-linked network in polymers. Here, we utilized a typical chemically double-networked hydrogel as an example. An artificial neural network was selected, and it was trained with the tensile stress–strain data from the CGMD simulations using different CGFF parameters. The CGMD simulations using the predicted CGFF parameters show good agreement with the AAMD simulations and are almost fifty times faster. The data-inspired CGMD model presented here broadens the applicability of molecular dynamics simulations to cross-linked polymers and has the potential to provide insights that will aid the design of polymers with desirable mechanical properties. [ABSTRACT FROM AUTHOR]

Ytterbium monohydroxide is a promising molecule in the search for new physics. It is well known that levels of opposite parity, separated by energy split, the so-called l-doublets, define the experimental electric field strength required for molecule polarization. In addition, in our previous paper [Phys. Rev. A 105, L050801 (2022)], we have shown that the value of l-doubling directly influences the sensitivity of linear triatomic molecules toward the P , T -odd effects. In our work [J. Chem. Phys. 155, 164301 (2021)], we have calculated the value of l-doubling for YbOH molecules with the approximation of fixed O–H bond length. Taking the importance of this property into account, in the present study, we consider the additional degree of freedom corresponding to ligand (OH) deformation. [ABSTRACT FROM AUTHOR]

The control of the excitation force of pump-jets is of great significance for the stealth performance of submarines. In a previous study, the authors found that the sinusoidal unevenly spaced rotor blades (SUSR) can control the excitation force of the rotor, but the suppression effect is limited by the low degree of freedom. This paper proposes random unevenly spaced rotor blades (RUSR) with higher degrees of freedom, achieving twice the suppression effect of the SUSR. A method for batch generation of RUSRs is proposed in this paper, and a large number of RUSRs are generated. The numerical simulation study was carried out by selecting the RUSRs with better suppression effects through theoretical methods, and the numerical simulation method used was improved based on the previous study. The RUSR also has an impact on the excitation force of the duct. The conclusion of this paper has guiding significance for the low excitation design of pump-jets and has the potential to promote the use of unevenly spaced rotor blades in the field of pump-jets. [ABSTRACT FROM AUTHOR]

In this paper, we discuss extending the sub-system embedding sub-algebra coupled cluster formalism and the double unitary coupled cluster (DUCC) ansatz to the time domain. An important part of the analysis is associated with proving the exactness of the DUCC ansatz based on the general many-body form of anti-Hermitian cluster operators defining external and internal excitations. Using these formalisms, it is possible to calculate the energy of the entire system as an eigenvalue of downfolded/effective Hamiltonian in the active space, which is identifiable with the sub-system of the composite system. It can also be shown that downfolded Hamiltonians integrate out Fermionic degrees of freedom that do not correspond to the physics encapsulated by the active space. In this paper, we extend these results to the time-dependent Schrödinger equation, showing that a similar construct is possible to partition a system into a sub-system that varies slowly in time and a remaining sub-system that corresponds to fast oscillations. This time-dependent formalism allows coupled cluster quantum dynamics to be extended to larger systems and for the formulation of novel quantum algorithms based on the quantum Lanczos approach, which has recently been considered in the literature. [ABSTRACT FROM AUTHOR]

As the novel suspension bearing, Magnetic-Liquid Double Suspension Bearing (MLDSB) is mainly supported by magnetic suspension and supplemented by a liquid hydrostatic bearing. Due to its great bearing capacity and stiffness, rapid response, great active control, and so on, MLDSB is suitable for medium speed heavy loads and has a large carrying capacity and high operating stability. In addition, the radial inertia coupling and gyroscopic coupling between radial 4-DOF control channels can reduce control precision, operation stability, and reliability of MLDSB. Therefore, a mathematical model of radial 4-DOF rotor-dynamics of MLDSB is established in this paper, and the inherent coupling mechanism is explored. Taking inertial coupling, gyroscopic coupling, and external disturbance loads as lumped disturbances, a decoupled controller based on Generalized Extended State Observer (GESO) is established. The influence of the GESO controller on the decoupling and control performance of radial 4-DOF control channels is simulated. The results indicate that the decoupling effect of the GESO controller is great. Under the action of step signal, the steady displacement, maximum displacement, adjustment time, and peak time of the rotor after decoupling are all reduced, among which the steady displacement and maximum displacement are the most obvious. Under the sinusoidal signal, the steady displacement and maximum displacement are reduced by 90%, which can effectively avoid the "gap-impact" fault. Under the pulse signal, the steady displacement, maximum displacement, adjustment time, and peak time are all reduced, among which the maximum displacement is the most obvious. The research in this paper can provide a theoretical reference for the stable support and decoupling control of MLDSB. [ABSTRACT FROM AUTHOR]

The investigation of interior spacetimes sourced by stationary cylindrical anisotropic fluids is pursued and specialized here to rigidly rotating fluids with an azimuthally directed pressure. Based on the occurrence of an extra degree of freedom in the equations, two general methods for constructing different classes of exact solutions to the field equations are proposed. Exemplifying such recipes, a bunch of solutions are constructed. Axisymmetry and regularity conditions on the axis are examined, and the spacetimes are properly matched to a vacuum exterior. A number of classes and subclasses are thus studied, and an analysis of their features leads to sorting out three classes whose appropriate mathematical and physical properties are discussed. This work is part of a larger study of the influence of anisotropic pressure in general relativity, using cylindrical symmetry as a simplifying assumption, and considering, in turn, each principal stress direction. It has been initiated in companion Papers I and II, where the pressure was assumed to be axially directed, and is followed by Paper IV considering radial pressure and Paper V contrasting the previous results with the corresponding dust and perfect fluid solutions. [ABSTRACT FROM AUTHOR]

Chemical and photochemical reactivity, as well as supramolecular organization and several other molecular properties, can be modified by strong interactions between light and matter. Theoretical studies of these phenomena require the separation of the Schrödinger equation into different degrees of freedom as in the Born–Oppenheimer approximation. In this paper, we analyze the electron–photon Hamiltonian within the cavity Born–Oppenheimer approximation (CBOA), where the electronic problem is solved for fixed nuclear positions and photonic parameters. In particular, we focus on intermolecular interactions in representative dimer complexes. The CBOA potential energy surfaces are compared with those obtained using a polaritonic approach, where the photonic and electronic degrees of freedom are treated at the same level. This allows us to assess the role of electron–photon correlation and the accuracy of CBOA. [ABSTRACT FROM AUTHOR]

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom. [ABSTRACT FROM AUTHOR]

As the main merits, self-stabilization and no magnetic resistance make the high-temperature superconducting (HTS) magnetic levitation technology a crucial area for high-speed magnetic levitation development. To guarantee a stable operation of superconducting magnetic levitation systems, the dynamic characteristics of superconducting bulk materials occupy a significant place. However, in the previous research, there is still a lack of a simulation method that can describe 6 degree of freedom (DOF) motion of the superconductor. In this paper, an electromagnetic–thermal–dynamic coupling calculation model was established first. Then, the damping characteristics of 5-DOF superconducting levitation were experimentally tested, and the response analysis of the superconductor under 1–20 Hz excitation was carried out to explore the coupled motion relationship between the various degrees of freedom of the superconductor. In addition to the above, the operating conditions and primary resonance intervals that should be avoided by the HTS maglev system were identified. Additionally, a numerical simulation was conducted to investigate the dynamic response of the HTS maglev system under impact loads. All in all, this study explored the temperature rise conditions of superconducting bulk materials under excitation force through magnetic-thermal-force multi-physics coupling research. This 6-DOF model can provide a comprehensive simulation method for superconducting maglev systems in superconductor's motion behavior, attitude, and thermal state monitoring. [ABSTRACT FROM AUTHOR]

Mechanical properties of nucleic acids play an important role in many biological processes that often involve physical deformations of these molecules. At sufficiently long length scales (say, above ∼ 20 − 30 base pairs), the mechanics of DNA and RNA double helices is described by a homogeneous Twistable Wormlike Chain (TWLC), a semiflexible polymer model characterized by twist and bending stiffnesses. At shorter scales, this model breaks down for two reasons: the elastic properties become sequence-dependent and the mechanical deformations at distal sites get coupled. We discuss in this paper the origin of the latter effect using the framework of a non-local Twistable Wormlike Chain (nlTWLC). We show, by comparing all-atom simulations data for DNA and RNA double helices, that the non-local couplings are of very similar nature in these two molecules: couplings between distal sites are strong for tilt and twist degrees of freedom and weak for roll. We introduce and analyze a simple double-stranded polymer model that clarifies the origin of this universal distal couplings behavior. In this model, referred to as the ladder model, a nlTWLC description emerges from the coarsening of local (atomic) degrees of freedom into angular variables that describe the twist and bending of the molecule. Different from its local counterpart, the nlTWLC is characterized by a length-scale-dependent elasticity. Our analysis predicts that nucleic acids are mechanically softer at the scale of a few base pairs and are asymptotically stiffer at longer length scales, a behavior that matches experimental data. [ABSTRACT FROM AUTHOR]

Water molecules trapped in rare gas matrices exhibit conspicuous shifts in their far-infrared (FIR), rotranslational spectral features compared with the corresponding transitions observed in the gas phase. These confinement-induced perturbations have been related not only to the quantization of translational motion but also to the coupling between the orientational and positional degrees of freedom: the rotation–translation coupling (RTC). As the propensity displayed by the nuclear spin isomers (NSI) of water to undergo interconversion in confinement is intimately related to how its nuclear spin degrees of freedom are coupled with those for intra- and intermolecular motions, confinement-induced RTC should also strongly impact the NSI interconversion mechanisms and rates. Insight into the rotranslational dynamics for H 2 16 O , H 2 17 O , and H 2 18 O , confined in argon and krypton matrices, is provided here based on the evolution of rotranslational spectra induced by NSI interconversion while a definitive assignment is provided from the transition energies and intensities calculated using the confined rotor model [Paper I, Wespiser et al., J. Chem. Phys. 156, 074304 (2021)]. In order to build a complete rotranslational energy diagram of confined water, which is fundamental to understand the NSI interconversion rates, the energy difference between the ground ortho and para rotranslational states is derived from the temperature dependence of the intensity ratio of mid-infrared lines emerging from these states. These investigations should provide deeper insight of the factors that control NSI interconversion of water isotopologues under extreme confinement. [ABSTRACT FROM AUTHOR]

By extending an earlier study [Gianturco et al., J. Chem. Phys. 154, 054311 (2021)] on the purely rotational excitation of HeH+ by He atoms, we report in this paper integral cross sections and rate coefficients for rovibrational excitation and de-excitation processes in HeH+ due to collisions with He. The data were obtained using a new ab initio potential energy surface that includes the vibrational degree of freedom. The results are compared with those computed using the earlier potential energy surface by Panda and Sathyamurthy [J. Phys. Chem. A 107, 7125 (2003)] that additionally accounts for the proton-exchange reaction between HeH+ and He. It is shown that the exchange channel contributes nearly as much as the inelastic channel to the vibrational excitation and de-excitation processes and that the total rate constants pertaining to the purely inelastic processes are largely of the same magnitude as those obtained when both inelastic and reactive channels are included in the dynamics. The inelastic rovibrational rate coefficients involving this astrophysical cation are also found to be much larger than those obtained for anions present in similar interstellar environments. [ABSTRACT FROM AUTHOR]

Micromagnetic simulations require the numerically challenging preservation of the Euclidean norm during the whole simulation. This can be accomplished by applying a priori length preserving methods, renormalization algorithms, or penalization strategies. The latter one includes both the penalty method and the Lagrangian multiplier. The penalty method requires the definition of a penalty parameter during the initiation of the simulation which, depending on its size, can lead to an unsatisfied constraint or stiff and difficult to solve systems of equations. The Lagrange multiplier always penalizes in problem-dependent intensity, hence, an additional degree of freedom is added to the system of equations to the drawback of higher computational costs. This paper proposes a method that utilizes a perturbed Lagrangian multiplier and an element level static condensation to condensate the additional degree of freedom. This guarantees fast simulations, and no parameter fitting in advance. Suitable numerical examples are conducted to prove the workability of the outlined scheme and to highlight the efficiency compared to the non-condensed formulation. [ABSTRACT FROM AUTHOR]

This paper introduces a new numerical approach that integrates local randomized neural networks (LRNNs) and the hybridized discontinuous Petrov–Galerkin (HDPG) method for solving coupled fluid flow problems. The proposed method partitions the domain of interest into several subdomains and constructs an LRNN on each subdomain. Then, the HDPG scheme is used to couple the LRNNs to approximate the unknown functions. We develop local randomized neural networks with hybridized discontinuous Petrov–Galerkin (LRNN-HDPG) methods based on velocity-stress formulation to solve two types of problems: Stokes–Darcy problems and Brinkman equations, which model the flow in porous media and free flow. We devise a simple and effective way to deal with the interface conditions in the Stokes–Darcy problems without adding extra terms to the numerical scheme. We conduct extensive numerical experiments to demonstrate the stability, efficiency, and robustness of the proposed method. The numerical results show that the LRNN-HDPG method can achieve high accuracy with a small number of degrees of freedom. [ABSTRACT FROM AUTHOR]

In this paper, a transmission model of power-exponential Airy vortex beams in plasma turbulence is established based on the random phase screen theory, and the information transmission characteristics of Airy vortex beams are compared under the OOK, BPSK, and DPSK modulation modes in free-space optical communication systems. Bit error rates (BERs) were calculated for different power indices (n), undulation variances (<Δn2>), transmission distances, and anisotropy parameters. In addition, the orbital angular momentum multiplexing of Airy vortex beams in the Line-of-Sight multiple input multiple output system under a plasma turbulence environment is investigated. The spectral efficiency (SE) is analyzed for different signal-to-noise ratio (SNR) and radii of the emitting surface, and the effects of the variation in the system's numerical aperture and the power exponent on the SE and the effective degrees of freedom in space are analyzed. The results show that the Airy beam has better turbulence resistance than the Laguerre–Gaussian beam. The power-exponential Airy beam has better transmission performance than the conventional Airy beam. By increasing the anisotropy parameter, the BER of the system decreases. When the <Δn2> and the transmission distance increase, the BER increases. Increasing the SNR, the radius of the launching surface and the choice of power-exponential Airy beams can improve the channel capacity. These findings provide a theoretical basis for the problem of optical signal propagation in plasma turbulence. [ABSTRACT FROM AUTHOR]

Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward–backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei—a result that is in perfect accordance with the principle of the indistinguishability of identical particles. [ABSTRACT FROM AUTHOR]

The effective design of dyes optimized for thermally activated delayed fluorescence (TADF) requires the precise control of two tiny energies: the singlet–triplet gap, which has to be maintained within thermal energy, and the strength of spin–orbit coupling. A subtle interplay among low-energy excited states having dominant charge-transfer and local character then governs TADF efficiency, making models for environmental effects both crucial and challenging. The main message of this paper is a warning to the community of chemists, physicists, and material scientists working in the field: the adiabatic approximation implicitly imposed to the treatment of fast environmental degrees of freedom in quantum–classical and continuum solvation models leads to uncontrolled results. Several approximation schemes were proposed to mitigate the issue, but we underline that the adiabatic approximation to fast solvation is inadequate and cannot be improved; rather, it must be abandoned in favor of an antiadiabatic approach. [ABSTRACT FROM AUTHOR]

To control mechanical waves and structural vibrations, an important method is to design metamaterials with tailored elastic constants, but it is very difficult. In this paper, a simple and universal metamaterial design method is proposed. This orthotropic metamaterial is composed of elements arrayed periodically in space. The element includes two cuboid structures. The first structure is the basic structure of the element, and the second structure is the transformation of the first structure of the element. The first structure of the element is a cuboid structure composed of 24 bars connected by 8 nodes, and the second structure of the element is a cuboid structure composed of 36 bars connected by 14 nodes. This metamaterial has six independent elastic constants, so there is a large degree of freedom in the material design. Therefore, it has great application value in the fields of mechanical metamaterials, elastic wave metamaterials, acoustic metamaterials, and seismic metamaterials, and has also laid the foundation for realizing the dream of controlling mechanical waves and structural vibrations. [ABSTRACT FROM AUTHOR]

In this paper, electromagnetic force on two degrees of freedom vortex-induced vibration (VIV) of an elastically mounted sphere for vibration suppression is numerically achieved at Re = 300. The relations between the wake structures, velocity and pressure distributions, force coefficients, and sphere displacement are investigated by varying the interaction parameter (N) of electromagnetic force. With the increase in N, the momentum of the fluid near the sphere is enhanced to control the flow separation. Therefore, both the rotation radii of the rear stagnation point (RSP) and the separation line (SL) decrease, causing the spiral vortices to become thinner. This leads to a reduction in the fluctuation amplitude of the lift coefficient and mitigates the VIV. As N exceeds 0.5, the periodic spiral vortices transform into a steady double-thread wake due to the stopping of RSP and SL rotation. Therefore, a constant lift is generated in the z-direction due to the asymmetric flow field in the x–z plane, which is accompanied by the VIV fully suppressed. Moreover, the effect of electromagnetic locations (θm) on vibration suppression is examined. With the increase of θm, the vibration suppression efficiency increases first and then decreases, which achieves the maximum vibration suppression efficiency at θm = 125°. The reason is that the electromagnetic force covers the location of the half-circle-shaped SL, which has a significant effect on the control of the flow separation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel two degree of freedom large range coarse–fine parallel dual-actuation flexure micropositioner (CFPDFM) with low interference behavior. First, the structure and working principle of the CFPDFM are introduced. Then, based on the stiffness matrix method, the analytical models of the motion range, input stiffness, and amplification ratio of the mechanism are established. Subsequently, the accuracy of the analytical model is verified by finite element analysis and experiments. Moreover, the dual-servo cooperative drive control strategy is designed to improve the closed-loop positioning ability of the CFPDFM. Finally, the CFPDFM experimental system is built to verify the plane trajectory tracking performance. The results reveal that the micropositioner can achieve a total range of 3.02 × 3.11 mm2, a resolution of ≤40 nm, low interference performance of coarse and fine actuators, good cross-axis decoupling, and planar complex trajectory tracking performance, while possessing a compact structure. It can be used in many plane positioning situations requiring large range and high precision. [ABSTRACT FROM AUTHOR]

We present two major improvements over the Compressible High-ORder Unstructured Spectral difference (CHORUS) code published in Wang et al., "A compressible high-order unstructured spectral difference code for stratified convection in rotating spherical shells," J. Comput. Phys. 290, 90–111 (2015). The new code is named CHORUS++ in this paper. Subsequently, we perform a series of efficient simulations for rotationally constrained convection (RCC) in spherical shells. The first improvement lies in the integration of the high-order spectral difference method with a boundary-conforming transfinite mapping on cubed-sphere grids, thus ensuring exact geometric representations of spherical surfaces on arbitrary sparse grids. The second improvement is on the adoption of higher-order elements (sixth-order) in CHORUS++ vs third-order elements for the original CHORUS code. CHORUS++ enables high-fidelity RCC simulations using sixth-order elements on very coarse grids. To test the accuracy and efficiency of using elements of different orders, CHORUS++ is applied to a laminar solar benchmark, which is characterized by columnar banana-shaped convective cells. By fixing the total number of solution degrees of freedom, the computational cost per time step remains unchanged. Nevertheless, using higher-order elements in CHORUS++ resolves components of the radial energy flux much better than using third-order elements. To obtain converged predictions, using sixth-order elements is 8.7 times faster than using third-order elements. This significant speedup allows global-scale fully compressible RCC simulations to reach equilibration of the energy fluxes on a small cluster of just 40 cores. In contrast, CHORUS simulations were performed by Wang et al. on supercomputers using approximately 10 000 cores. Using sixth-order elements in CHORUS++, we further carry out global-scale solar convection simulations with decreased rotational velocities. Interconnected networks of downflow lanes emerge and surround broader and weaker regions of upflow fields. A strong inward kinetic energy flux compensated by an enhanced outward enthalpy flux appears. These observations are all consistent with those published in the literature. Furthermore, CHORUS++ can be extended to magnetohydrodynamic simulations with potential applications to the hydromagnetic dynamo processes in the interiors of stars and planets. [ABSTRACT FROM AUTHOR]

The Direct Dynamics variational Multi-Configurational Gaussian (DD-vMCG) method provides a fully quantum mechanical solution to the time-dependent Schrödinger equation for the time evolution of nuclei with potential surfaces calculated on-the-fly using a quantum chemistry program. Initial studies have shown its potential for flexible and accurate simulations of non-adiabatic excited-state molecular dynamics. In this paper, we present developments to the DD-vMCG algorithm that improve both its accuracy and efficiency. First, a new, efficient parallel algorithm to control the DD-vMCG database of quantum chemistry points is presented along with improvements to the Shepard interpolation scheme. Second, the use of symmetry in describing the potential surfaces is introduced along with a new phase convention in the propagation diabatization. Benchmark calculations on the allene radical cation including all degrees of freedom then show that the new scheme is able to produce a consistent non-adiabatic coupling vector field. This new DD-vMCG version thus opens the route for effectively and accurately treating complex chemical systems using quantum dynamics simulations. [ABSTRACT FROM AUTHOR]

Experimental measurements of electron transport properties of molecular junctions are often performed in solvents. Solvent–molecule coupling and physical properties of the solvent can be used as the external stimulus to control the electric current through a molecule. In this paper, we propose a model that includes dynamical effects of solvent–molecule interaction in non-equilibrium Green's function calculations of the electric current. The solvent is considered as a macroscopic dipole moment that reorients stochastically and interacts with the electrons tunneling through the molecular junction. The Keldysh–Kadanoff–Baym equations for electronic Green's functions are solved in the time domain with subsequent averaging over random realizations of rotational variables using the Furutsu–Novikov method for the exact closure of infinite hierarchy of stochastic correlation functions. The developed theory requires the use of wideband approximation as well as classical treatment of solvent degrees of freedom. The theory is applied to a model molecular junction. It is demonstrated that not only electrostatic interaction between molecular junction and solvent but also solvent viscosity can be used to control electrical properties of the junction. Alignment of the rotating dipole moment breaks the particle–hole symmetry of the transmission favoring either hole or electron transport channels depending upon the aligning potential. [ABSTRACT FROM AUTHOR]

In this paper, an amplitude and phase gradient-modulated surface is introduced to design a low cost and simple radar cross section (RCS) reducer metasurface. The simultaneous gradual amplitude and phase differences between adjacent unit cells achieve more degrees of freedom in the design approach, which leads to bandwidth enhancement of RCS reduction. A dual-layer stacked patch unit cell analyzed with a transmission line method is proposed to design the different required unit cells. The sinusoidal modulation applied on top and bottom layers of two stacked FR-4 substrates is used to realize the unit cells with gradual amplitude and phase variations. Finally, an ultrawideband dual-layer stacked modulated surface composed of 26 x 26 unit cells is fabricated to demonstrate the idea. This surface achieves more than 10 dB RCS reduction from 9 GHz to 40.7 GHz (128%) for normal incident waves. Moreover, this surface has more than 118% and 88% RCS reduction bandwidths for transverse magnetic and transverse-electric obliquely polarized waves, respectively. Low profile, low cost, lightweight, and a simple assembling procedure are the main specifications of the proposed structure rather the state-of-the-art references, which candidate it as an ultra-wideband monostatic RCS reduction surface in practical applications. [ABSTRACT FROM AUTHOR]

We investigate different approaches to derive the proper Floquet-based quantum–classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis and then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form that is similar to the usual QCLE with two modifications: (1) The electronic degrees of freedom are expanded to infinite dimension and (2) the nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a fictitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., [J. Chem. Phys. 140, 084104 (2014)] who found that transforming to the adiabatic representation must always be the last operation applied, although now we have extended this result to a time-dependent Hamiltonian. This paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the explicit role of resonant nuclear/vibrational modes in mediating energy transport among chlorophylls in the Light-harvesting Complex II (LHCII), the major light-harvesting complex in green plants. The vibrational modes are considered to be resonant/quasi-resonant with the energy gap between electronic excitons. These resonant vibrations, along with the remaining nuclear degrees of freedom, constitute the environment/bath to the electronically excited system and contribute to two major phenomena: (a) decoherence and (b) incoherent phonon-mediated population relaxation. In this work, we explore the subtle interplay among the electronic excitation, the resonant vibrations, and the environment in dictating environment assisted quantum transport in light-harvesting complexes. We conclusively show that resonant vibrations are capable of boosting the incoherent population relaxation pathways and cause rapid decoherence. [ABSTRACT FROM AUTHOR]

We have developed an algorithm to detect holes in multi-dimensional real-valued surfaces—such as the potential energy surfaces (PESs) that describe the nuclear motion of molecules in the context of the Born–Oppenheimer approximation. For our purposes, a PES "hole" is defined as an unphysical saddle point, beyond which the potential energy drops (typically) without limit to negative infinity. PES holes are numerical artifacts that can arise when fitting PES functional forms to discrete ab initio data—even when the data is of high quality, and/or for comparatively few degrees of freedom (DOF). Often undetected, PES holes can have devastating effects on subsequent dynamical calculations, especially if they occur at low energies. In this paper, we present a highly efficient algorithm designed to systematically identify hole configurations and energies. The method is applied to a variety of molecular PESs ranging up to 30 DOF. A number of evidently previously undetected PES holes are reported here—surprisingly, even for PESs that have been available for decades. The code itself (Crystal) is presented together with a user manual. These tools may be of great benefit for PES developers, who can use the information they provide to fix holes, once identified. More generally, the methodology can be applied in any context involving multi-dimensional surfaces. [ABSTRACT FROM AUTHOR]

As a fundamental degree of freedom, phonon chirality is expected to promote the development of quantum information technology just like electron spin. Currently, central to this area is the realization of efficient transmission and control of chiral information. In this paper, we propose an approach by integrating topological theory, leveraging topologically invariant Chern numbers, to encode hexagonal lattice systems. Our investigation reveals the presence of topologically protected chiral interface states within the shared band gaps of both trivial and non-trivial system units. By precisely modulating the magnetic field distribution within the encoding system, we can effectively manipulate the topological pathways. Building upon this framework, we design and implement a chiral phonon three-port device. Through dynamic calculations, we demonstrate the transmission process of chiral information, showcasing the chiral phonon switching effect and logical OR operation. Our findings not only establish a fundamental mechanism for the manipulation and control of phonon chiral information but also provide a promising direction for research in harnessing chirality degrees of freedom in practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we give an explicit nondegeneracy condition for the existence of Kolmogorov-Arnold-Moser (KAM) tori of an N-point vortex system on the plane by using the method of reduction via generalized Jacobi coordinates and matrix theory. Furthermore, by constructing a series of canonical transformations to reduce the degree of freedom of the Hamiltonian, we obtain a new simplified Hamiltonian system. Finally, we give the equivalent relationship between the relative equilibrium point of the original system and the equilibrium point of the new system. [ABSTRACT FROM AUTHOR]

The nonequilibrium Fermi's golden rule describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state, when the nuclear degrees of freedom start out in a nonequilibrium state. In a previous paper [X. Sun and E. Geva, J. Chem. Theory Comput. 12, 2926 (2016)], we proposed a new expression for the nonequilibrium Fermi's golden rule within the framework of the linearized semiclassical approximation and based on the Condon approximation, according to which the electronic coupling between donor and acceptor is assumed constant. In this paper we propose a more general expression, which is applicable to the case of non-Condon electronic coupling. We test the accuracy of the new non-Condon nonequilibrium Fermi's golden rule linearized semiclassical expression on a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering the following: (1) A modified Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary-mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions, in both normal and inverted regions, and over a wide range of initial nonequilibrium states, temperatures, and frictions. [ABSTRACT FROM AUTHOR]

Control of oscillations in mechanical systems in the start-up and passage through resonance modes is studied. In both cases, the control algorithm is based on the speed-gradient method with energy-based goal functions. It is shown that for Hamiltonian 1-degree of freedom (DOF) systems, it is generically possible to move the system from any initial state to any final state by means of a controlling force of arbitrarily small intensity. Controlled passage through resonance is studied for a 5-DOF vibration machine taking friction into account. It is shown by simulation that applying feedback control makes passage through lower resonance feasible with smaller control intensity compared with passage through resonance under constant control torque. The specific feature of this paper is consideration of the case when constant control torques do not allow the rotors even to start rotation. Applying feedback control allows rotors to overcome gravity and to start rotation. Another key novelty of this paper is comparison of the results obtained from the simulation with the experimental results obtained from the two-rotor laboratory mechatronic stand. It appears that most results are qualitatively the same, which confirms the adequacy of the model. [ABSTRACT FROM AUTHOR]

The discontinuous Galerkin (DG) method has been widely adopted due to its excellent properties. However, the problem of designing a class of high-order limiter that takes into account accuracy, compactness, efficiency, and robustness has long been an open question in simulating compressible flow with strong discontinuities. In this paper, a high-order multi-resolution weighted essentially non-oscillatory (MR-WENO) limiter is designed for the DG method on a parallel adaptive Cartesian grid, based directly on the weak solution to a polynomial obtained by the DG method. It can gradually be reduced to first-order accuracy in the vicinity of discontinuities while maintaining the excellent features of the DG method. Thus, it essentially has non-oscillatory characteristics in non-smooth regions with respect to the adaptive Cartesian grids. An improved shock detection technique is adopted as an indicator to identify troubled cells, which forms a high-order limiting procedure. A high-order MR-WENO limiter is used for both two- and three-dimensional cases to reconstruct different degrees of freedom on adaptive Cartesian grids. If the mesh is refined or coarsened, the details of the implementation algorithm are presented to determine how the hanging nodes are modulated and how the numerical solutions are redefined on such adaptive Cartesian grids. The parallelization of this method can be achieved by linking to the octree-based adaptive mesh refinement library called p4est. Finally, the low dissipation, shock capture ability, and load balancing of the high-order DG method with an MR-WENO limiter may enhance the resolutions of nearby strong discontinuities in adaptive Cartesian grids. [ABSTRACT FROM AUTHOR]

Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction, and elsewhere. In this paper, we apply mathematically rigorous methods to show why this is so. Our stabilization results do not assume a full set of observations and we provide examples where it suffices to observe the model's unstable degrees of freedom. [ABSTRACT FROM AUTHOR]

This paper numerically investigates the effects of rigid coupling and the vibration degrees of freedom on the vortex-induced vibrations (VIV) of two tandem circular cylinders for a spacing ratio L/D = 4 at a Reynolds number of 150. Two (translational vibration) and three (translational and rotational vibration) degrees of freedom (RC-2DOF and RC-3DOF, respectively) cases are considered and compared with the case of two freely vibrating cylinders (FC). The dynamic response characteristics, flow structures, and vortex dynamics are analyzed. The results show that the rigid coupling has a significant effect on VIV. Compared with FC, the maximum transverse amplitude of the downstream cylinder decreases by 30% for RC-2DOF and approximately 15% for RC-3DOF. The lock-in region narrows by 40% for RC-2DOF, while it widens by 80% for RC-3DOF. Reattachment and co-shedding regions are observed for FC and RC-3DOF, whereas only the co-shedding region exists for RC-2DOF. We further explore flow forces and fluid–structure-interaction mechanisms in the lock-in region for RC-3DOF. The rotation of the twin-cylinder system triggers some unique vibration characteristics, such as two transverse amplitude peaks of the upstream cylinder and a prominent streamwise amplitude at Vr = 7–9. The vortex-to-vortex and vortex-to-cylinder interactions are complicated and changeable with reduced velocity for RC-3DOF. [ABSTRACT FROM AUTHOR]

In a recent paper of Mitsopoulos and Tsamparlis [J. Geom. Phys. 170, 104383 (2021)], a general theorem is given, which provides an algorithmic method for the computation of first integrals (FIs) of autonomous dynamical systems in terms of the symmetries of the kinetic metric defined by the dynamical equations of the system. In the present work, we apply this theorem to compute the cubic FIs of autonomous conservative Newtonian dynamical systems with two degrees of freedom. We show that the known results on this topic, which have been obtained by means of various divertive methods, and the additional ones derived in this work can be obtained by the single algorithmic method provided by this theorem. The results are collected in Tables I–IV, which can be used as an updated reference for these types of integrable and superintegrable potentials. The results we find are for special values of free parameters; therefore, using the methods developed here, other researchers by a different suitable choice of the parameters will be able to find new integrable and superintegrable potentials. [ABSTRACT FROM AUTHOR]

Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing mimetic dark matter models. Recently, it has been shown that many more transformations of this type, if not virtually all of them when the coefficients depend on the scalar kinetic term, can produce new solutions with mimetic properties. The aim of this paper is to explain how it works at the level of the variational principle, and to express some worries about the viability of these models. [ABSTRACT FROM AUTHOR]

This paper selects China's renewable energy enterprises as a research sample and analyzes the impacts of equity balance and executive stock ownership on these companies' innovation efficiency from 2009 to 2018. The results show that equity balance has significant and positive impacts on innovation efficiency, while there is a significant nonlinear, inverted U-shaped relationship between the executive stock ownership and innovation efficiency. In addition, with changes in the shareholding ratio of the largest shareholder, equity balance and executive stock ownership are substitutive in terms of their impacts on innovation efficiency. Therefore, this paper proposes the following recommendations. The shareholding ratio of the largest shareholder should be controlled within a reasonable range to help force executives and outside blockholders to make decisions in the company's interests. When implementing an equity balance, companies should avoid shareholders' oversupervision of executives, which may restrict executives' enthusiasm for innovation investment. A moderate degree of freedom for management executives should be appropriate. [ABSTRACT FROM AUTHOR]

The generalized quantum master equation (GQME) provides a powerful framework for simulating electronically nonadiabatic molecular dynamics. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. In this paper, we consider two different procedures for calculating the memory kernel of the GQME from projection-free inputs obtained via the combination of the mapping Hamiltonian (MH) approach and the linearized semiclassical (LSC) approximation. The accuracy and feasibility of the two procedures are demonstrated on the spin-boson model. We find that although simulating the electronic dynamics by direct application of the two LSC-based procedures leads to qualitatively different results that become increasingly less accurate with increasing time, restricting their use to calculating the memory kernel leads to an accurate description of the electronic dynamics. Comparison with a previously proposed procedure for calculating the memory kernel via the Ehrenfest method reveals that MH/LSC methods produce memory kernels that are better behaved at long times and lead to more accurate electronic dynamics. [ABSTRACT FROM AUTHOR]

In Paper I [Polimeno et al., J. Chem. Phys. 150, 184107 (2019)], we proposed a general approach for interpreting relaxation properties of a macromolecule in solution, derived from an atomistic description. A simple scheme (the semiflexible Brownian, SFB, model) has been defined for the case of limited internal flexibility, but retaining full coupling with external degrees of freedom, inclusion of all of the momenta, and dissipation. Here we discuss the application of the SFB model to the practical evaluation of orientation spectral densities, based on two complementary computational treatments. [ABSTRACT FROM AUTHOR]

This paper presents the systematic classical consideration of a statistical averaging procedure that permits the calculation of partition function, equilibrium constant, and some observables for polyatomic dimers composed of weakly interacting rigid monomers. It was shown that the number of independent internal coordinates in a body-fixed frame is a crucial parameter that largely determines the temperature dependence of the partition function irrespective of the kinematic coupling within various degrees of freedom. The kinetic energy was derived for the molecular pair of arbitrary complexity in the body-fixed frame. Rigorous expression was obtained for the partition function over a pre-selected domain in the phase space. A similar expression was applicable to perform statistical averaging of some observables. Taking a linear molecule–atom as an example, it was shown how the suggested general approach permits the calculation of the equilibrium constant for true bound dimer formation or zeroth spectral moment of a collision-induced absorption band. [ABSTRACT FROM AUTHOR]

McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium sta-tistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the sol-vent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentra-tion, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {NA, μB, V, T}, to those rele-vant to the experiment, i.e., fixed {NA, NB, V, T}, where ß denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature. [ABSTRACT FROM AUTHOR]

Large-capacity optical storage materials have reached a stage of relative maturity, but progress in the design of optical pickup actuators is currently slow. To improve the reading and writing capabilities of optical recording systems, we propose a design for a four-sided magnetic circuit for an optical pickup actuator for multilayer high-density optical disks that make full use of the space around the actuator. The basic magnetic circuit model in this design, which is derived by the equivalent magnetic charge method, can be applied to the design of all such actuators. The static and dynamic magnetic circuit evaluation parameters established in this paper can be used conveniently and directly to improve the magnetic circuit performance of the actuator. The design was verified by finite element simulation, and linear working ranges of ±2.6 mm, ±0.6 mm, and ± 16 ° were found in the focusing, tracking, and tilting degrees of freedom. This is sufficient to compensate for errors in phase-change optical disks with more than 50 layers in high-speed rotation. The theoretical servo accuracy of the actuator can reach tens of nanometers. This can be used with a dual-objective-lens layout that can support layer-skip reading and writing of optical disks with an effective working bandwidth greater than 10 000 Hz. [ABSTRACT FROM AUTHOR]