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A revision of the mechanism of mechanical-to-vibrational energy transfer in crystals of energetic materials undergone impact loading is proposed. The new approach takes into account previous inaccuracies of normalization of the number of couplings between phonon overtones and conformational vibrational fundamentals (ζ), which is critical for comparison of molecules that differ greatly in the number of atoms. Moreover, it introduces two very important damping factors, namely a and b. The a factor allows differentiation of the phonon overtones by their coupling strength; the lower the overtone interacts, the stronger the coupling is. Meanwhile, the b factor is aimed to distinguish the coupling strength itself. This factor is the denominator in the exponent of a Gaussian-type function and determines the rate at which the coupling strength decays with the rise of difference between the interacting phonon overtones and conformational vibrational fundamentals. After a careful regression analysis of ζ against impact sensitivities (h50) of 30 common nitroexplosives, we have determined the numerical values of these damping factors as a = 2.5 and b = 40 cm–1. The proposed approach is extrapolated on the vibrational spectra of 21 crystalline energetic materials with Z' ≥ 1 and a general applicability along with limitations of the method are discussed for the family of nitroexplosives and nitrogen-rich (cyclo-pentazolate and 5,5′-bitetrazole) energetic salts as an example.

This paper presents a design method of cylindrical uniform field coil based on quasi-elliptic function fitting (EFF method with multiple optimizations. EFF method is a type of discrete wire techniques aiming at simplifying the coil structure. Combing with particle swarm optimization (PSO algorithm, the optimized parameters of EFF coil are obtained for high uniform magnetic field. And to further improve the uniformity of magnetic field in the central space, a new regional points selection optimization method is proposed. The calculation results show that after PSO optimization the absolute maximum relative error in the target region is optimized to 0.098% by EFF coil comparing with modified single saddle coil (3.08%, nest coil (2.4% and target field method (TFM coil (0.11% . And after regional points selection optimization, the volume proportion of absolute magnetic field relative error less than 110-4 increases from 35.24% to 54.38% by EFF coil comparing with TFM coil. In addition, the simple EFF coil structure is verified to be easy to process and keep high performance through experiments. As the EFF coil's high uniformity and simple structure, the new method has important significance for miniaturization of atomic sensors.

The bifurcation structure of the oscillations of ultrasound contrast agents (UCAs) was studied as a function of the driving pressure for excitation frequencies that were determined using the UCAs pressure-dependent resonances $$(f_\mathrm{s})$$ . It was shown that when excited by the $$(f_\mathrm{s})$$ , the UCA can undergo a saddle-node bifurcation (SNB) to higher amplitude oscillations. The driving pressure at which the SNB occurs is controllable and depends on the $$(f_\mathrm{s})$$ magnitude. Utilizing the appropriate $$(f_\mathrm{s})$$ , the scattering cross section of the UCAs can significantly be enhanced (e.g., $$\sim $$ ninefold) while at the same time avoiding potential UCA destruction (by limiting the radial expansion ratio $$

This paper aims to present a new method for obtaining an analytical solution for the Kaniadakis Doppler broadening (KDB) function. Also, in this work, we report the computational efficiencies of this solution compared with the numerical one. The solution of the differential equation achieved in this paper is free of approximations and is, consequently, a more robust methodology for obtaining an analytical representation of ψ k . Moreover, the results show an improvement in efficiency using the analytical approximation, indicating that it may be helpful in different applications that require the calculation of the deformed Doppler broadening function.

A cooperative molecular communication (CMC) system is considered inside a cylindrical-shaped channel where a few cooperative nodes (CNs) are intermediately placed between a transmitter (TX) and a fusion center (FC). The expressions for the maximum achievable rate and probability of error at the FC considering AND and OR rules are derived. Furthermore, the performance of the CMC system in a cylindrical channel is compared with the direct and CN-assisted systems. The CMC system with randomly-placed CNs is also analyzed and compared with the uniformly-placed CNs, and it is found that a lower probability of error is obtained in the case of uniform placement\ud of CNs. Furthermore, the system performance as a function of radial displacement of TX and FC under constant flow is compared with that under laminar flow and a higher probability of error is observed under laminar flow. The increased probability of error under laminar flow occurs due to the fact that the drift velocity decreases towards the walls of the cylindrical channel. The analytical expressions are verified using Monte-Carlo simulations.

Static random access memories (SRAMs) are prone to a single-event upset (SEU), also known as soft errors, due to transient noise caused by a single strike of radiation. Beam testing has been extensively used to measure the SEU cross section of SRAMs as a function of the linear energy transfer (LET) of charged particle radiation. The evolution of the cross section as a function of LET is called the cross section curve, which plays a vital role in upset rate analysis for hardness assurance. Various analytical models have been developed to describe SRAM SEU cross-section curves, and they have proven to be useful in reducing the cost of beam testing as well as revealing the physics behind test results. However, they involve arbitrary parameters, which make it challenging to predict cross-section curves without any beam results. Moreover, the current method of analyzing cross-section curves or the LET dependence of cross sections relies on a model different from that is used in the analysis of power-supply-voltage dependence, which is becoming increasingly important because of the demand for low-power operation. To overcome these problems, this paper proposes a unified equation that describes both LET and the power-supply-voltage dependence of SRAM SEU cross sections. It comprises only parameters that are physically clear and familiar to SEU researchers. As well as giving possible constraints, comparisons with data from the literature suggest it can be applied to SRAMs fabricated in bulk and silicon-on-insulator (SOI) processes across generations from the early 1000-nm-scale to the current 10-nm-scale technology nodes.

We demonstrate analytically and numerically that the transverse spatial coherence (the spectral degree of coherence) of the field radiated by two partially correlated electromagnetic sources oscillates as a function of propagation distance in free space. In particular, it is possible for its magnitude to completely collapse to zero on propagation, and then return again to unity at a further distance. Our results are a direct demonstration of the wave character of the optical correlation functions. A similar oscillatory effect occurs for the degree of polarization.

This paper proposes a rotor design method suitable for double-layer interior permanent magnet synchronous motor (DIPMSM), which can reduce electromagnetic torque ripple and at the same time reduce the electromagnetic noise of the motor. In previous studies, the inverse cosine function (ICF) was used to modify the rotor shape for making the air gap flux density distribution sinusoidal under no-load conditions, which can reduce the torque ripple. However, conventional ICF can only be used in a single-layer interior rotor structure. Consequently, this paper proposes a piecewise inverse cosine function (PICF) based on ICF, which can be applied to DIPMSM. To verify the improvement of the proposed method in the electromagnetic and noise aspects of the motor, the electromagnetic model and a noise prediction model of the 36-slot/8-pole motor are established by the finite element method. The PICF model is compared with the prototype in the aspects of electromagnetic performance and noise. The torque ripple is reduced by 54.16%, from ± 2.4 Nm to ± 1.1 Nm, and the electromagnetic noise is reduced by about 4.9 dB. Finally, the accuracy of the noise prediction model is verified by the noise test of the prototype.

Viscous drainage of a second grade fluid down inclined porous surface is examined. A constant tangential force F expressed in context of Heaviside’s function. This acts over the system for fixed interval of time. The bounding surface has been rotated at stratified distinct angles of inclination. For sake of brevity the gravitational force is taken into account.

Forced oscillation is challenging power system stability. Most previous research was based on linear models, so analysis of nonlinear characteristics for forced oscillation in power system is missing. Thus, this letter aims to theoretically reveal the effect of the quadratic nonlinearity on forced oscillation. A multi-scale technique is employed, by which the amplitude-frequency function of the steady response and the approximated first-order analytical expression of the dynamic response are derived for nonlinear forced oscillation. Interesting phenomena of frequency deviation and jumping caused by nonlinearity are found and explained. Above expressions and phenomena are verified by numerical simulation. Although revealing all characteristics of nonlinear forced oscillation in power system is difficult, the analysis results in this letter could offer insights.

A new approximation algorithm is developed to compute the electromagnetic (EM) tensor Green's function in the biaxial anisotropic media based on the Fourier series expansion. First, a rectangular region is chosen as the computation region, in which the EM field can be expressed as a 2-D Fourier series. The Fourier coefficients can be regarded as the EM field in discrete wavenumber domain. We further obtain the EM solution in the spatial domain in the form of Fourier series. Then, we use the finite terms of the Fourier series to approximate the EM field for enhancement of computation efficiency. Because the new method avoids the numerical integration in the infinite wavenumber domain, it is more convenient to implement than other methods based on integral transform. Finally, the spatial distribution of the tensor Green's function for a transversely isotropic medium is presented to verify the proposed approach. The agreements between the results obtained by the present method and the analytic solution demonstrate the validity and the robustness of our algorithm.

In this paper we discuss the model of fractional oscillator where the inertial and restoring force terms maintains their usual expression but the damping term involves a fractional derivative of Caputo type, the so called fractional Kelvin-Voigt oscillator. The transient solution of this model is given in terms of the so called bivariate Mittag-Leffler function, while the steady-state solution in response to a sinusoidal force involves a 4-variate Mittag-Leffler function. We give numerical examples comparing the solutions for different values of the order α of the fractional derivative (0

The helicity asymmetry parameter τ in the Cameron decomposition indicates the degree to which a scatterer deviates from being an ideal symmetric scatterer. However, the solving procedure of τ can only be expressed in terms of single-look Sinclair scattering matrix. In this paper, we extend the helicity τ to a generalized helicity parameter τg, which is appropriate for both the single-look and multi-look PolSAR data. For single-look data, the generalized helicity τg is equivalent to the previous helicity τ. In addition, we investigate the relationships among the classical helix/helicity definitions, including the Cameron helicity, the Krogager helix component, and the Yamaguchi helix component. To achieve this, we represent the Cameron and Krogager decompositions in terms of the unified CTD model in the format of coherency matrix and revise the expression of Krogager decomposition contributions in function of Huynen parameters. Results show that essentially the Cameron helicity and Krogager helix are two kinds of representation of reflection asymmetry under the same decomposition model, and the Yamaguchi helix contribution is always larger than the Krogager helix contribution. Single-look PolSAR data from L-band ESAR is used for demonstration in this paper. Several multi-look datasets are generated by 1×3, 3×3, 3×5, 5×5, 5×7, 7×7, 7×9, and 9×9 boxcar average. Two techniques are taken to mitigate reflection symmetry assumption based on helix component and helicity angle respectively. It will be shown that the technique with the generalized helicity τg performs best in terms of efficiency and stability.

The convergence and stability of the fully nonlinear simulation in a three-dimensional potential numerical wave tank is vulnerable along the time marching algorithm of the free surface, as integrating the boundary element's solution into the high-order time integration of the free surface can trigger the numerical instability in the material node approach. Although this matter was identified in some of the prior studies on three-dimensional wave tanks, the approximation of the velocity components plays a crucial role in the sustainability of a simulation. Therefore, a methodology for deriving the Cartesian components of the fluid particles’ velocity over the exact free surface is proposed in this paper. Various circumstances come across while determining the velocity components of fluid particles, which are the function of the location of the free surface nodal points. Since plenty of prior techniques have been based on the tangential derivatives of the free surface boundary value from the previous iteration, the disruption in the convergence of the model occurs most often. Hence, achieving a generic algorithm that merely depends on the boundary element solutions, is a highly important achievement for retaining the stability and simultaneously the convergence of the solution.

International audience; Graphene Nanoribbons (GN), being an important class of next-generation carbon materials, are of immense interest and find innumerable applications in diverse fields. A variation of the generalized Lambert W function, called the Offset Logarithm function, has been found to have important applications in fields such as physics, engineering and nanotechnology. We study the electronic properties of zigzag GN and use the generalized Lambert W function to study the eigenvalue equations of the massless Dirac equation applied to zigzag GN. We have studied the effects of nanoribbon width and determined the parameters that significantly affect the obtained solutions.

We present three analyses that explore the behavior of the Cramer-Rao lower bounds (CRBs) on estimating a target's relaxation frequency response from frequency-domain electromagnetic induction (EMI) data. In the first analysis, we show that the CRB on a given relaxation frequency is independent of the amplitudes of the other relaxations present in the target's relaxation frequency response. In the second, we show that the presence of a second relaxation frequency closer than one decade in frequency greatly increases the CRB on that relaxation frequency. Finally, we illustrate the behavior of the minimum root-mean-square error (RMSE) per relaxation frequency as a function of the number of relaxation frequencies present in the target's relaxation frequency response.

The fast-inertial-relaxation engine (FIRE) has proven to efficiently find local minima of potential energies or related penalty functions although its implementation requires only few, additional lines of code in a molecular-dynamics or steepest-descent program. So far, FIRE has been predominantly applied to particle-based or low-dimensional problems. In this work, we demonstrate that it can also benefit the solution of boundary-value problems. Towards this end, we study the mechanical contact between an elastic body and a rigid indenter of varying complexity by augmenting Green's function molecular dynamics (GFMD) with FIRE. We find a rather remarkable speedup, which can be further enhanced when choosing the masses associated with the eigenmodes of the free elastic solid appropriately. For the investigated adhesive and randomly rough indenter with typical system size, 100 mass-weighted FIRE-GFMD iterations suffice to relax the excess energy to ${10}^{\ensuremath{-}3}$ of its original value. The standard GFMD method needs 25 times more iterations. For the investigated problems, FIRE-GFMD even appears to slightly outperform conjugate-gradient based optimization.

In this work, we explore wormhole geometries in a recently proposed modified gravity theory arising from a non-conservative gravitational theory, tentatively denoted action-dependent Lagrangian theories. The generalized gravitational field equation essentially depends on a background four-vector $\lambda^\mu$, that plays the role of a coupling parameter associated with the dependence of the gravitational Lagrangian upon the action, and may generically depend on the spacetime coordinates. Considering wormhole configurations, by using "Buchdahl coordinates", we find that the four-vector is given by $\lambda_{\mu}=\left(0,0,\lambda_{\theta},0\right)$, and that the spacetime geometry is severely restricted by the condition $g_{tt}g_{uu}=-1$, where $u$ is the radial coordinate. We find a plethora of specific asymptotically flat, symmetric and asymmetric, solutions with power law choices for the function $\lambda$, by generalizing the Ellis-Bronnikov solutions and the recently proposed black bounce geometries, amongst others. We show that these compact objects possess a far richer geometrical structure than their general relativistic counterparts., Comment: 11 pages, 5 figures, V2: version accepted for publication in PRD

Given a stochastic process (V t ) t≥0 having trajectories with bounded variation and a sufficiently regular function f, it is possible to define the integral of Z t = f(V t ) with respect to dV t as follows $$ \int_0^t {Z_s dV_s = \int_0^t {f\left( {V_s } \right)dV_s } } , $$ (5.1) i.e. in the sense of a Riemann-Stieltjes integral.

Given a probability space (Ω, \( \mathcal{F} \), P), where Ω denotes a non-empty set, \( \mathcal{F} \) a σ-algebra and P a probability measure on Ω: A random variable (r.v.) is a function X : Ω → ℝ such that {ω ∈ Ω : X (ω) ∈ A} ∈ F for any Borel set A in ℝ. A stochastic process is a family (X t ) t≥0 of random variables defined on (Ω, \( \mathcal{F} \), P). The stochastic process (X t ) t≥0 is said to be a discrete-time stochastic process if t takes values in ℕ and a continuous-time stochastic process if t takes values in ℝ+. A filtration on Ω is a family \( \left( {\mathcal{F}_t } \right)_{t \geqslant 0} \) of σ-algebras on Ω such that \( \mathcal{F}_u \subseteq \mathcal{F}_v \) for any u ≤ v.

In this paper, we investigate the movement of an inverted pendulum, the suspension point of which performs high-frequency oscillations along a line making a small angle with the vertical. We prove that under certain conditions on the function describing the oscillations of the suspension point of the pendulum, a periodic motion of the pendulum arises, and it is asymptotically stable.

An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overheads of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS towards fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the triplet over the quintet spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.

We present the approach that unifies the analytical description and a new model of the cylindrical plasma produced and sustained by а weakly damped surface-wave. This approach includes the use of a fixed-point magnetic-current model. An analytical expression is reported for the normalized power of a surface plasma wave, Q ˜ . This power is determined as a function of the normalized wavenumber X. We show that the absorbance of the power has a clear maximum at around X ∼ 3 – for the parameters used; the magnitude of the maximum depends on dielectric losses such that Q ˜ generally increases with the increase of t g δ . Analysis of the formula for normalized power of surface electron plasma wave has shown the necessity for evaluating the dispersion relation. Since this equation is very complex and implicit, the calculations are not clearly seen. In this paper, an attempt has been made in order to overcome the difficulties, by applying the fixed convergent iteration algorithm. We show in this paper that the fixed-point method is efficient and can be adapted for computations performed here.

A new approximation for the Green's function of a grounded anisotropic dielectric slab is proposed to obtain closed-form analytical expressions for the maximum radiated power of a short printed dipole on an anisotropic substrate. The corresponding surface wave power can also be accurately estimated as a root of a cubic polynomial which makes it possible to compute radiation efficiency due to surface wave loss analytically.

This paper presents a fast analytical model for estimating the components of the PM flux density distribution in the air-gap for a number of interior permanent magnet synchronous machines (IPMSMs). Deriving the two-dimensional (2-D) analytical model for IPMSMs is more challenging compared to that of surface-mounted permanent magnet synchronous machines (SPMSMs) due to the inconsistent geometry of the rotor in polar coordinates. IPMSMs are usually modeled by using 0-D or 1-D methods such as the magnetic equivalent circuit (MEC); however, the MEC method is unable to take into account the tangential component of the magnetic flux density vector. In this paper, a 2-D analytical no-load electromagnetic model for five rotor topologies of IPMSMs is proposed. The effects of the stator slots on the radial component of the PM flux density distribution in the air-gap are then included by defining an air-gap function. The effects of the stator slots on the tangential components of the PM flux density distribution in the air-gap are also considered by injecting virtual surface currents (VSCs) or virtual permanent magnets (VPMs). For verification purposes, the analytical results are compared with those of the finite element method (FEM) and the experimental results of one of the cases.

This letter provides a new mapping function which allows us to carry out the dual extracted-pole synthesis in inline fully canonical dual-band filters for the first time. To do this, it is a necessary condition that the reflection coefficient phase takes exactly the same value at the position of the two prescribed transmission zeros (TZs), one belonging to one band and the other to the second band, involved at simultaneous extraction. This is achieved by applying an antisymmetric or odd symmetry mapping function. Two different filters, one with asymmetric and the other with symmetric prescribed TZs at each of the passbands have been synthesized which validates the proposed approach.

In this work we present derivations of the formula listed in entry 4.113 in the sixth edition of Gradshteyn and Rhyzik's table of integrals. We evaluate two definite integrals of the form $ \begin{equation*} \int_{0}^{\infty}\frac{e^{-iay}(-iy+\log(z))^k+e^{iay}(iy+\log(z))^k}{\cosh(by)}dy \end{equation*} $ and $ \begin{equation*} \int_{0}^{\infty}\frac{e^{iay}(iy+\log(z))^k-e^{-iay}(-iy+\log(z))^k}{\sinh(b y)}dy \end{equation*} $ in terms of the Lerch function where $ k $, $ a $, $ z $ and $ b $ are arbitrary complex numbers. The entries in the table(s) are obtained as special cases in the paper below.

A new perspective on the ubiquity of classical harmonic oscillators is presented based on the two-variable Taylor expansion of a perturbed system's total energy E(q,q), where q(t) is the system displacement as a function of time t and q(t)=dq/dt. This generalised approach permits derivation of the lossless oscillator equation from energy arguments only, yielding a universal equation for the oscillation frequency ω=(∂2E/∂q2)/(∂2E/∂q2) which may be applied to arbitrary systems without the need to form system-specific linearised models. As illustrated by a range of examples, this perspective gives a unifying explanation for the prevalence of harmonic oscillators in classical physics, can be extended to include damping effects and driving forces, and is a powerful tool for simplifying the analyses of perturbed systems.

A new fractional mapping method based on a generalized fractional auxiliary equation is proposed and applied to solve the space-time fractional perturbed Gerdjikov-Ivanov equation. The main feature of this approach is to obtain more accurate solutions by means of an auxiliary equation. Some exact fractional nonlinear wave solutions, including bright soliton, periodical wave and singularity soliton solutions are constructed by Mittag–Leffler function. Some deformations appear in those fractional nonlinear wave solutions, and those deformations become more obvious with the increase of the fractional order parameter. In addition, the coefficient of group velocity dispersion and the self-steepening for short pulses also affect the intensity of the soliton when the fractional order parameter remains unchanged. The effect of fractional order is explained by the graphical representation of a series of solutions and their physical meanings.

PURPOSE Scintillators and photoconductors used in energy integrating detectors (EIDs) have inherent variations in their imaging response to single-detected X-rays due to variations in X-ray energy deposition and secondary quanta generation and transport, which degrades DQE(f). The imaging response of X-ray scintillators to single X-rays may be recorded and studied using single X-ray imaging (SXI) experiments; however, no method currently exists for relating SXI experimental results to EID DQE(f). This work proposes a general analytical framework for computing and analyzing the DQE(f) performance of EIDs from single X-ray image ensembles using a spatial frequency-dependent pulse-height spectrum. METHODS A spatial frequency (f)-dependent gain, g∼(f) , is defined as the Fourier transform of the imaging response of an EID to a single-detected X-ray. A f-dependent pulse-height spectrum, Pr[g∼(f)] , is defined as the 2D probability density function of g∼(f) over the complex plane. Pr[g∼(f)] is used to define a f-dependent Swank factor, AS (f), which fully characterizes the DQE(f) degradation due to single X-ray noise. AS (f) is analyzed in terms of its degradation due to Swank noise, variations in the frequency-dependent attenuation of |g∼(f)| , and noise in argg∼(f) which occurs due to variations in the asymmetry in each single X-ray's imaging response. Three example imaging systems are simulated to demonstrate the impact of depth-dependent variation in g∼(f) , remote energy deposition, and a finite number of secondary quanta, on Pr[g∼(f)] , AS (f), MTF(f), and NPS(f)/NPS(0), which are computed from ensembles of single X-ray images. The same is also demonstrated by simulating a realistic imaging system; that is, a Gd2 O2 S-based EID. Using the latter imaging system, the convergence of AS (f) estimates is investigated as a function of the number of detected X-rays per ensemble. RESULTS Depth-dependent g∼(f) variation resulted in AS (f) degradation exclusively due to depth-dependent optical Swank noise and the Lubberts effect. Conversely, the majority of AS (f) degradation caused by remote energy deposition and finite secondary quanta occurred due to variations in argg∼(f) . When using input X-ray energies below the K-edge of Gd, variations in the frequency-dependent attenuation of |g∼(f)| accounted for the majority of AS (f) degradation in the GOS-based EID, and very little Swank noise and variations in argg∼(f) were observed. Above the K-edge, however, AS (f) degradation due to Swank noise and variations in argg∼(f) greatly increased. The convergence of AS (f) was limited by variation in argg∼(f) ; imaging systems with more variation in argg∼(f) required more detected X-rays per ensemble. CONCLUSIONS An analytical framework is proposed that generalizes the pulse-height spectrum and Swank factor to arbitrary f. The impact of single X-ray noise sources, such as the Lubberts effect, remote energy deposition, and finite secondary quanta on detector performance, may be represented using Pr[g∼(f)] , and quantified using AS (f). The approach may be used to compute MTF(f), NPS(f), and DQE(f) from ensembles of single X-ray images and provides an additional tool to analyze proposed EID designs.

We establish the following Helly-type theorems: Let $${\mathcal {K}}$$ be a family of sets in $${\mathbb {R}}^3$$ , and let j be a fixed integer, $$0 \le j \le 3$$ . For every countable subfamily of $${\mathcal {K}}$$ , assume that the corresponding intersection is consistent relative to staircase paths, is staircase convex, and contains a convex set of dimension at least j. Then $$\cap \{K \, : \, K \text { in } {\mathcal {K}} \}$$ has these properties as well. For d a fixed integer, $$d \ge 1$$ , define a function f on $$\{0,1\}$$ by $$f(0)=d+1$$ , $$f(1)=2d$$ . Let $${\mathcal {K}}$$ be a finite family of orthogonal polytopes in $${\mathbb {R}}^d$$ . For j fixed in $$\{ 0,1\}$$ , assume that every f(j) members of $${\mathcal {K}}$$ intersect in a set that is staircase convex and contains a convex subset of dimension at least j. Then $$\cap \{K : K \text { in } {\mathcal {K}} \}$$ has these properties, too. The number f(j) is best possible for $$j=0$$ and for $$j=1$$ . There is no analogous Helly number for $$2 \le j \le d$$ .

PurposeGear transmissions are widely utilized in practice. This paper aims to uncouple the crack feature from the cracked time-varying mesh stiffness (TVMS) and investigate the effects of the crack on the nonlinear dynamics of a spur gear pair.Design/methodology/approachAn approximate method to simulate the cracked TVMS is proposed by using an amplitude modulation function. The ratio of mesh stiffness loss is introduced to estimate the TVMS with different crack depths and angles. The dynamic responses are obtained by solving a torsional model which takes the non-loaded static transmission error, the backlash and the cracked TVMS into account. By using the bifurcation diagram, the largest Lyapunov exponent (LLE) and dynamic mesh force, the influences of crack on nonlinear behaviors are examined. The dynamic characteristics are identified from the phase diagram, Poincaré map, dynamic mesh force, time series and FFT spectra.FindingsThe comparison between the healthy and cracked gear pairs indicates that the crack affects the system motions, such as the obvious changes of impact force and unpredictable instability. Besides, the additive and difference combination frequencies can be found in periodic-1 and -2 motions, but they are covered in periodic-3 and chaotic motions. Deeper crack is an important determinant of the nonlinear behaviors at a higher speed.Originality/valueThe research provides an interesting perspective on cracked TVMS and reveals the connection between crack and nonlinear behaviors of the gear pairs.

Various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular phase separation and elucidate the dominant physicochemical driving forces. Here we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino acid sequence. The model is parameterized from both atomistic simulations and bioinformatics data and accounts for the dominant role of π–π and hybrid cation–π/π–π interactions and the much stronger attractive contacts established by arginines than lysines. We provide a comprehensive set of benchmarks for Mpipi and seven other residue-level coarse-grained models against experimental radii of gyration and quantitative in vitro phase diagrams, demonstrating that Mpipi predictions agree well with experiments on both fronts. Moreover, Mpipi can account for protein–RNA interactions, correctly predicts the multiphase behavior of a charge-matched poly-arginine/poly-lysine/RNA system, and recapitulates experimental liquid–liquid phase separation trends for sequence mutations on FUS, DDX4 and LAF-1 proteins. Combining bioinformatics data and atomistic simulations, this study develops a sequence-dependent coarse-grained model for biomolecular phase separation. This model achieves a quantitative agreement with experimental observations. Extensive benchmarks exemplify its performance.

In this paper, we consider the initial-boundary value problem of determining the stationary right-hand side function in the anomalous diffusion equation with a Caputo fractional derivative with res...

We provide the exact analytical ground state solution of one-dimensional H $$_2^+$$ molecule with soft Coulomb potential using our recently developed technique for solving Schrodinger equations. We show that the electronic wave function has similar structure with the ground state wave function of the 1D hydrogen, and we can still identify a power prefactor, an exponentially decaying term and a modulator function on the exponential. However, the behavior of the modulator function for 1D H $$_2^+$$ critically depends on the nuclear separation R. In particular, it differs qualitatively for small and large R, reflecting the different nature of the solution as a compact molecule for small R and two dissociation fragments for large R. This might inspire new strategies of density functional approximations for correctly describing molecular dissociation. The exactly solvable model obtained by our new technique could also be useful for systematically generating error-free training sets for machine-learning based quantum chemistry methods.

The deformed soliton solutions of the (2+1)-dimensional nonlinear Schrodinger Maxwell–Bloch (NLS-MB) equations are investigated by the n-fold Darboux transformation method based on the seed function $$q=p=v=0,\,\eta =1$$ . New soliton solutions, including order-1 and order-2 types, are obtained and analyzed in detail. For the order-1 solutions, polynomial, trigonometric, and hyperbolic solutions are discussed. Especially, the analytical formulas of $$|q^{[1]}|$$ and soliton trajectories are obtained, which are involved by an arbitrary smooth function $$f(y+2\lambda t)$$ . For the order-2 solutions, besides the polynomial, trigonometric, and hyperbolic types, the mixed-type solutions are also derived and exhibited through several typical examples.

In this paper, we have generalized fractal calculus on fractal Cantor cubes. The mass function on fractal Cantor cubes is defined. Then, we use the mass function to define integral staircase function on fractal Cantor cubes. Using the integral staircase function, the fractal derivatives and integrals for a function with fractal Cantor cubes are defined. Fractal Laplace equations are suggested and their solutions are plotted to show more details. As application, Casimir effect is modeled by fractal Laplace equation.

In this paper, we have derived the formula for calculating the mutual inductance between filaments of arbitrary position and square and hexagonal coils. Mutual inductance is an important factor in calculating the exact inductance value of the coils. The studies show that the mutual inductance depends on many factors, such as the type and thickness of the conductors, the distance between the conductors, and the geometric shape. When factors such as the number of turns and the number of sides increase for polygonal shapes, the calculation of inductance becomes more complex. The formulas for square and hexagonal coils are established as a function of the number of turns, the side length of the outermost polygon, and the distance between the coils. We believe that the proposed method is simple, straightforward, accurate, and practical for engineering applications that use inductance calculations. The values of mutual inductance calculated by the proposed method were checked using Grover’s formulas, Neumann integral, and COMSOL.

The Earth's natural pulse electromagnetic field (ENPEMF) signal, is generally considered to be a nonlinear or nonstationary signal received from our instrument, placed on the surface near the source area. To obtain latent information on the ENPEMF signal, this paper employs the time–frequency analysis (TFA) method to get the instantaneous frequency (IF) of the signal. The traditional Data-driven time–frequency analysis (DDTFA) requires to know the initial phase function (IPF) set of the signal, to accomplish the signal decomposition and its IFA. However, it's difficult to observe directly the IPF set of the ENPEMF signal. To acquire accurate time–frequency distribution, an improved DDTFA method was proposed, which adopts differential evolution (DE) to calculate multiple IPF of multi-component non-stationary signals. In this paper, the ENPEMF signal received from the Lushan $${M}_{w}$$ 6.6 earthquake on April 20, 2013, was taken as an example, and the improved method, DE-DDTFA, was used to decompose the signal into multiple intrinsic mode function (IMF) components, and obtained the IF of each IMF. It is demonstrated by the experimental that the number of IMF is 200% more than usual time, and the energy of the signal had grown by approximately 10–20 times, or even more compared with usual in just one week before the earthquake. The experimental result illustrates that the amount of IMF and the energy of the ENPEMF signal show an overall upward trend, which is a distinct trait before the earthquake, and DDTFA is a good reference for studying the time–frequency distribution and energy spectrum variation characteristics of electromagnetic signals before earthquakes.

We make the most precise determination to date of the number density of extragalactic 21-cm radio sources as a function of their spectral line widths - the HI velocity width function (HIWF) - based on 21827 sources from the final 7000 deg$^2$ data release of the Arecibo Legacy Fast ALFA (ALFALFA) survey. The number density of sources as a function of their neutral hydrogen masses - the HI mass function (HIMF) - has previously been reported to have a significantly different low-mass slope and 'knee mass' in the two sky regions surveyed during ALFALFA. In contrast with this, we find that the shape of the HIWF in the same two sky regions is remarkably similar, consistent with being identical within the confidence intervals implied by the data (but the overall normalisation differs). The spatial uniformity of the HIWF implies that it is likely a stable tracer of the mass function of dark matter haloes, in spite of the environmental processes to which the measured variation in the HIMF are attributed, at least for galaxies containing enough neutral hydrogen to be detected. This insensitivity of the HIWF to galaxy formation and evolution can be exploited to turn it into a powerful constraint on cosmological models as future surveys yield increasingly precise measurements. We also report on the possible influence of a previously overlooked systematic error affecting the HIWF, which may plausibly see its low-velocity slope steepen by $\sim$40 per cent in analyses of future, deeper surveys. Finally, we provide an updated estimate of the ALFALFA completeness limit., Comment: 13 pages, 4 figures, 1 table, +appendices. MNRAS, accepted version

While scholars are aware of the suction force of particles (FDn) in gas-solid flow, until recently, most researchers have considered the drag force (FD) to be FDn, and there are few application functions for the calculation of FDn; this will affect the design of air-suction seeders, check valves, or other machines based on particle absorption. Therefore, it is necessary to re-build an applicable function of FDn and verify the equivalence between FDn and FD. In the present study, the empirical formula of FDn, which includes the suction hole diameter (D), particle diameter (dp), distance from the particle center to the suction hole (Lp), pressure difference (ΔP), gas density (ρg), and gas viscosity (μg), is established via dimensional analysis, and the application scope is 0.571 ≤ D/dp ≤ 1, 0.5 ≤ L/dp ≤ 0.634, and 3000 Pa ≤ ΔP ≤ 5000 Pa. Some conjectures are provided based on the comparison of the results of CFD simulations and experiments. For instance, FDn may be a combination of multiple forces, one of which is the dominant force FD. This research introduces a new method and device for measuring FDn for use by other researchers, and contributes to the existing research on particle absorption.

The amplitudes of the first Shapiro steps for an external signal with frequencies of 72 and 265 GHz are measured as function of the temperature from 20 to 80 K for a 6 μm Josephson grain boundary junction fabricated by YBaCuO film deposition on an yttria-stabilized zirconia bicrystal substrate. Non-monotonic dependences of step heights for different external signal frequencies were found in the limit of a weak driving signal, with the maxima occurring at different points as function of the temperature. The step heights are in agreement with the calculations based on the resistively–capacitively shunted junction model and Bessel theory. The emergence of the receiving optima is explained by the mutual influence of the varying critical current and the characteristic frequency.

The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the $$ \mathcal{N} $$ N = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions.

Consider a channel whose the input alphabet set $\mathbb {X}=\{x_{1},x_{2}, {\dots },x_{K}\}$ contains $K$ discrete symbols modeled as a discrete random variable $X$ having a probability mass function $\mathbf {p}(\mathbf {x}) = [p(x_{1}), p(x_{2}), {\dots }, p(x_{K})]$ and the received signal $Y$ being a continuous random variable. $Y$ is a distorted version of $X$ caused by a channel distortion, characterized by the conditional densities $p(y|x_{i})=\phi _{i}(y)$ , $i=1,2, {\dots },K$ . To recover $X$ , a quantizer $Q$ is used to quantize $Y$ back to a discrete output $\mathbb {Z} =\{z_{1}, z_{2}, {\dots }, z_{N}\}$ corresponding to a random variable $Z$ with a probability mass function $\mathbf {p}(\mathbf {z}) = [p(z_{1}), p(z_{2}), {\dots }, p(z_{N})]$ such that the mutual information $I(X;Z)$ is maximized subject to an arbitrary constraint on $\mathbf {p}(\mathbf {z})$ . Formally, we are interested in designing an optimal quantizer $Q^{*}$ that maximizes $\beta I(X;Z) - C(Z)$ where $\beta $ is a positive number that controls the trade-off between maximizing $I(X;Z)$ and minimizing an arbitrary cost function $C(Z)$ . Let $\mathbf {p}(\mathbf {x}|y)=[p(x_{1}|y),p(x_{2}|y), {\dots },p(x_{K}|y)]$ be the posterior distribution of $X$ for a given value of $y$ , we show that for any arbitrary cost function $C(.)$ , the optimal quantizer $Q^{*}$ separates the vectors $\mathbf {p}(\mathbf {x}|y)$ into convex regions. Using this result, a method is proposed to determine an upper bound on the number of thresholds (decision variables on $y$ ) which is used to speed up the algorithm for finding an optimal quantizer. Numerical results are presented to validate the findings.

The virtual equivalent line method for the axial-flux permanent magnet eddy current coupler is proposed in this paper to solve the problem of the difference in the length of the magnetic flux path between the inner radius and outer radius of the axial section of the radial centerline of the magnetic pole. Different from the average radius equivalent method, the virtual equivalent line method adopts the function of variable pole radius instead of the fixed average radius, which establishes a uniform analytical expression of the air gap flux density and can accurately calculate the magnetic flux density at any magnetic pole radius. Furthermore, the end-effect compensation function is obtained. In order to investigate the effectiveness of the proposed method, the results calculated by the analytical method are compared with the finite element method. It is shown that the novel method proposed in this paper is highly consistent with the air gap flux density calculated by the finite element method.

For many years, we have devoted our research to the study of the thermodynamic properties of hydrophobic hydration processes in water, and we have proposed the Ergodic Algorithmic Model (EAM) for maintaining the thermodynamic properties of any hydrophobic hydration reaction at a constant pressure from the experimental determination of an equilibrium constant (or other potential functions) as a function of temperature. The model has been successfully validated by the statistical analysis of the information elements provided by the EAM model for about fifty compounds. The binding functions are convoluted functions, RlnKeq = {f(1/T)* g(T)} and RTlnKeq = {f(T)* g(lnT)}, where the primary linear functions f(1/T) and f(T) are modified and transformed into parabolic curves by the secondary functions g(T) and g(lnT), respectively. Convoluted functions are consistent with biphasic dual-structure partition function, {DS-PF} = {M-PF} ∙ {T-PF} ∙ {ζw}, composed by ({M-PF} (Density Entropy), {T-PF}) (Intensity Entropy), and {ζw} (implicit solvent). In the present paper, after recalling the essential aspects of the model, we outline the importance of considering the solvent as “implicit” in chemical and biochemical reactions. Moreover, we compare the information obtained by computer simulations using the models till now proposed with “explicit” solvent, showing the mess of information lost without considering the experimental approach of the EAM model.