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This article is about the following Kirchhoff–Schrödinger–Poisson system with steep potential well 1.1−(a+b∫ℝ3|∇u|2dx)△u+λV(x)u+μϕ(x)u=f(x,u)+h(x)|u|αinℝ3,−△ϕ=u2,inℝ3,$$ \left\{\begin{array}{ll}-\left(a&#x0002B;b{\int}_{{\mathrm{\mathbb{R}}}&#x0005E;3}{\left&#x0007C;\nabla u\right&#x0007C;}&#x0005E;2 dx\right)\triangle u&#x0002B;\lambda V(x)u&#x0002B;\mu \phi (x)u&#x0003D;f\left(x,u\right)&#x0002B;h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{\alpha }& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}&#x0005E;3,\\ {}-\triangle \phi &#x0003D;{u}&#x0005E;2,& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}&#x0005E;3,\end{array}\right. $$where a,b,λ>0$$ a,b,\lambda >0 $$ are constants, μ>0$$ \mu >0 $$, and 0<α<1,f∈C(ℝN×ℝ,ℝ)$$ 0<\alpha <1,f\in C\left({\mathrm{\mathbb{R}}}&#x0005E;N\times \mathrm{\mathbb{R}},\mathrm{\mathbb{R}}\right) $$. By using the variational principle, we overcome the difficulties caused by Poisson's term and obtain system (1.1) that has two nontrivial solutions under certain assumptions. Moreover, we study the concentration of solutions and obtain new conclusions of system (1.1). Finally, we present the case where the solution to system (1.1) does not exist. [ABSTRACT FROM AUTHOR]

In this paper we consider stationary states of the SSH model for infinite polyacetylene chains that are homoclinic or heteroclinic connections between two-periodic dimerized states. We prove that such connections converge exponentially fast to the corresponding asymptotic periodic states. [ABSTRACT FROM AUTHOR]

We consider the moment map m : ℙ V n → i (n) for the action of GL (n) on V n = ⊗ 2 (ℂ n) ∗ ⊗ ℂ n , and study the functional F n = ∥ m ∥ 2 restricted to the projectivizations of the algebraic varieties of all n -dimensional Leibniz algebras L n and all n -dimensional symmetric Leibniz algebras S n , respectively. First, we give a description of the maxima and minima of the functional F n : L n → ℝ , proving that they are actually attained at the symmetric Leibniz algebras. Then, for an arbitrary critical point [ μ ] of F n : S n → ℝ , we characterize the structure of [ μ ] by virtue of the nonnegative rationality. Finally, we classify the critical points of F n : S n → ℝ for n = 2 , 3 , respectively. [ABSTRACT FROM AUTHOR]

As magnetic refrigerants, first-order transition (FOT) and second-order transition (SOT) materials possess distinct advantages and disadvantages. If the phase transition can be tuned to the critical point between FOT and SOT, it may be possible to combine the benefits of both, thereby achieving an outstanding magnetocaloric effect. Here, we demonstrated this approach through phase transition engineering in Er(Co1-xMnx)2 alloys. When x ≤ 0.06, the magnetic phase transition of the samples was FOT, exhibiting a significant magnetic entropy change. However, at x = 0.08, the samples underwent a SOT from ferromagnetic to paramagnetic, leading to a substantial reduction in the magnetocaloric effect. At the critical point of the FOT/SOT border with x = 0.06, the sample exhibited a large magnetic entropy change along with negligible magnetic hysteresis. This work demonstrates that the critical point between FOT and SOT is an effective means of achieving an excellent magnetocaloric effect. [ABSTRACT FROM AUTHOR]

Optimization problems are omnipresent in the mathematical modeling of real world systems and cover a very extensive range of applications becoming apparent in all branches of Economics, Finance, Materials Science, Astronomy, Physics, Structural and Molecular Biology, Engineering, Computer Science, and Medicine. In this paper, we aim to delve deeper into the multiplicity findings concerning a specific class of quasilinear periodic boundary value problems. In fact, as an optimization problem, we look for the critical points of the energy functional related to the problem. Utilizing a corollary derived from Bonanno's local minimum theorem, we investigate the existence of a one solution under certain algebraic conditions on the nonlinear term. Additionally, we explore conditions that lead to the existence of two solutions, incorporating the classical Ambrosetti–Rabinowitz (AR) condition alongside algebraic criteria. Moreover, by employing two critical point theorems one by Averna and Bonanno, and another by Bonanno, we establish the existence of two and three solutions in a particular scenario. To illustrate our findings, we provide an example.

Nowadays, it is relevant to solve the problems of adapting optimal resource- and energy-efficient modes to technologies for processing food raw materials. The work is focused on the analysis of the prerequisites to find similar features in the dehydration of food capillary-porous colloidal materials by means of various methods. The authors have studied the patterns of cephalopods dehydration using the example of octopus and squid under different heat treatment regimes. It has been proved that there is only one critical point characterizing the transition from moisture with a lower binding energy to moisture with a higher one, and an equation has been proposed for finding the critical humidity during dehydration of the objects been studied. A generalized mathematical model has been developed to determine the duration of the process at the current moisture content of the food material based on dimensionless similarity criteria characterizing the phenomena been investigated. The dependences of the moisture removal rate for different heat treatment methods of cephalopods are given according to their initial moisture content, the specific surface area of the material and the operating factors that determine the process. The obtained dependencies and patterns open up unique opportunities for labor-saving design in the food industry using rational operating modes of industrial enterprises, optimization of heat treatment processes in general and the creation of energy-efficient equipment new designs.

Influence of the sulfur doping on the structural, optical, electrical and magnetic properties of ZnMnO thin films fabricated using the ultrasonic spray pyrolysis technique was investigated. Our study reveals that increasing sulfur content leads to a noticeable shift in the band gap energy towards the red spectrum, an indicator of altered electronic states and potential for enhanced spintronic functionalities. The strong reduction in the band gap for the sulfur doped ZnMnO alloys is the result of the upward shift of the valence-band edge. As a result, the room temperature bandgap of ZnMnO1-xSx alloys can be tuned from 3.2 eV to 2.97 eV for x ≤ 0.2. The observed large bowing in the composition dependence of the energy bandgap arises from the anticrossing interactions between the valence-band of ZnO and the localized sulfur level above the ZnMnO valence-band maximum. The doping process significantly modifies the ferromagnetic properties, with an observed increase in Curie temperature correlating with higher sulfur concentrations. These changes are attributed to the increased free holes concentration, which facilitates a more robust exchange interaction between the magnetic ions. Additionally, the structural assessments via scanning electron microscopy confirm the uniform integration of sulfur into the ZnMnO matrix, resulting in distinct nanocrystalline formations. This study contributes to the understanding of doping mechanisms in semiconductor materials, especially for highly mismatched alloys, where the anions are partially substituted with isovalent atoms of considerably different size and/or electronegativity, offering insights into the tunability of their magnetic and electronic properties for potential future applications in spintronic devices. [ABSTRACT FROM AUTHOR]

In this work, the evolution of the morphological properties of the liquid-liquid phase separation process of water-lutidine mixtures in a quasi-2D geometry locally heated by laser absorption is studied at different heating rates by videomicroscopy and complemented by a finite element simulation. Morphological changes of the separated domains are characterised using the fractal dimension and the distribution of domain sizes, capturing the main steps of the process: spinodal decomposition derived from the fluctuations in density at the critical point, separation into a bicontinuous structure, breaking of the structures producing a wide distribution of sizes, and the subsequent growth and coalescence of the demixed regions (domains) to produce a complete separation. A comparison with the simplest case of typical nucleation is made by performing the same analysis at a concentration where critical fluctuations are not present. We conclude that the methodology presented here can be used to characterise the main steps of the phase separation process and distinguish between spinodal decomposition and nucleation. [ABSTRACT FROM AUTHOR]

Global quantum discord (GQD) refers to the number of quantum correlations present in the entire quantum many-body system, rather than just between two subsystems. Here, we utilize GQD to characterize quantum phase transitions in an Ising chain subjected to both transverse and longitudinal magnetic fields. We investigate the effects of the transverse magnetic field h x , longitudinal magnetic field h z , and temperature T on the properties of GQD while keeping the coupling strength J between spins constant. We show that we can perfectly illustrate the critical points of the model by analyzing the singularity of GQD. We find that the GQD exhibits an increase as the system size N increases, regardless of whether the temperature is zero or finite. We present the phase diagram of a mixed Ising model under the combined influence of h x and h z . Moreover, we show that we can use the features of GQD at lower temperatures to identify QPTs in quantum many-body systems and determine their critical points, as achieving absolute zero temperatures is practically impossible. Additionally, we show that GQD both at zero and finite temperatures show a linear behavior of the system size N, i.e., G = k N + b , in which k and b are the fitting parameters. [ABSTRACT FROM AUTHOR]

In this work, we study a singular elliptic Dirichlet problem involving a general elliptic operator. Using the critical point theory, we investigate and give out some new solvability conditions for the existence of at least one nontrivial weak solution. Our framework includes a large class of weighted -Laplacian models, which is a special case of the problem studied in this paper. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Animal Production & Processing Technology / JurnalIlmu Produksi dan Teknologi Hasil Peternakan is the property of IPB University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Considerable evidence supports the existence of many-body localization (MBL) phase transitions, although accurately determining the critical disorder intensity remains challenging due to significant instabilities in system size within the examined parameters. In this study, we employ the global quantum discord (GQD) to investigate MBL phase transitions and identify the critical points of the quantum Ising spin chain subjected to both disordered interacting and disordered external fields. Our analysis of GQD demonstrates its effectiveness in identifying the critical points between the thermal and the MBL phases. We further utilize the temporal evolution of GQD to comprehensively explore the characteristics of MBL phase transitions in the disordered quantum Ising spin chain. Our findings suggest that MBL phase transitions adhere to the same generality category based on the scaling analysis. Additionally, we investigate the effects of these examined parameters on the GQD and its dynamics and use them to estimate the critical points. [ABSTRACT FROM AUTHOR]

This study employs holography within a modified D3/D7 framework to explore the phase diagram of a QCD-like theory. The corresponding dual theory is characterized by a large N, N = 4 gauge theory, integrated with quenched N = 2 quark matter and a novel dilaton profile. The research focuses on how the critical point’s location in the phase diagram is influenced by temperature and chemical potential. Additionally, the study examines the trajectory of these critical points in response to alterations in the dilaton profile’s control parameter, revealing a trend where the critical endpoint shifts to higher temperatures and lower chemical potentials. [ABSTRACT FROM AUTHOR]

Within the framework of inverse problems of photometry, we study questions on reconstruction of the spatial location and luminosity of a Lambertian optical surface from its images obtained with the use of a small number of optical systems. We study causes of ambiguity in reconstruction of the location of such a surface. We suggest criteria for existence of a unique solution of the inverse problem on reconstruction of a luminous surface from three images for general weight functions and apply the results to specific classes of weight functions that model the degree of transparency of the medium (including its absorption or scattering). [ABSTRACT FROM AUTHOR]

We develop a theory of the critical point of the ferromagnetic Ising model, whose basic objects are the ergodic (pure) states of the infinite system. It proves the existence of anomalous critical fluctuations, for dimension ν = 2 and, under a standard assumption, for ν = 3 , for the model with nearest-neighbor interaction, in a way which is consistent with the probabilistic approach of Cassandro, Jona-Lasinio, and several others, reviewed in Jona-Lasinio's article in Phys. Rep. 352,439 (2001). We propose to single out the state at the critical temperature T c , among the ergodic thermal states associated to temperatures 0 ≤ T ≤ T c , by a condition of non-summable clustering of the connected two-point function. The analogous condition on the connected (2r)- point functions, for r ≥ 2 , together with a scaling hypothesis, natural within our framework, proves that the (macroscopic) fluctuation state is quasi-free, after a proper rescaling, also at the critical temperature, in agreement with a theorem by Cassandro and Jona-Lasinio, whose proof is, however, shown to be incomplete. Other subjects treated include topics relating to universality, including spontaneous breaking of continuous symmetries and violations of universality in problems of energetic and dynamic stability. [ABSTRACT FROM AUTHOR]

We explore a class of nonlocal Schrödinger equations that include not only fractional Schrödinger equations but also other nonlocal Schrödinger equations studied in the literature. We prove the existence of least energy solutions to this class of equations by the variational method, which extends the results obtained by Gu et al. (2018) and Xiang et al. (2019). [ABSTRACT FROM AUTHOR]

The problem of constructing n-linear (n ≥ 2) plane vector fields with an isolated critical point and given separatrices of prescribed types is considered. Such constructions are based on the use of vector algebra, the qualitative theory of second-order dynamic systems and classical methods for investigating their critical points. This problem is essentially an inverse problem of the qualitative theory of ordinary differential equations, and its solution can be used to synthesize mathematical models of controlled dynamical systems of various physical nature. [ABSTRACT FROM AUTHOR]

The classical thermoacoustic refrigeration adopts gases with ideal-gas properties as working fluids. Herein, the thermoacoustic refrigeration using a compressible liquid as the working fluid is investigated for the first time. Two models are utilized parallelly: a highly-simplified short refrigerator model and a far-more realistic full-scale thermoacoustic refrigerator model. The results from the short refrigerator model show that, ideally, the coefficient of performance can reach above 70% of the Carnot limit. In the full-scale system discussion, the coefficient of performance of the system can reach as high as 4.1 in a typical working condition for air conditioning (pumping heat from 285 K to 310 K), with respect to 36% of the Carnot limit. When pumping heat from 332 K to 357 K, the coefficient of performance can reach 44% of the Carnot limit. These results indicate that the efficiency of the thermoacoustic refrigeration with a compressible liquid as the working fluid is potentially high, but with a much smaller displacement amplitude of the fluid. As a result, both the acoustic source (the linear motor, for instance) and the heat exchanger can be much more compact, so that the mass and the volume of the system can be greatly reduced, as well as the cost. • Both an idealized and a full-size refrigerator using liquid are modeled. • The liquid thermoacoustic refrigeration may be as efficient as the gas system. • Both the linear motor and the heat exchanger can be much more compact. [ABSTRACT FROM AUTHOR]

We generalize the theory of homotopic deviation of square complex matrices to regular matrix pencils. To this end, we study the existence and the analyticity of the resolvent of the matrix pencils whose matrices are under homotopic deviation with the deviation parameter $ t \in \mathbb {C} $ t ∈ C . Moreover, we investigate and identify the limits of both the resolvent and the spectrum of the deviated matrix pencils, as $ | t | \to \infty $ | t | → ∞. We also study the special cases where t tends to the eigenvalues of the related matrix pairs. We use the notions and the results of the generalized homotopic deviation theory to analyze the Weierstrass structure of the deviated matrix pencils under two different assumptions, in particular, either the eigenvalues of the deviated matrix pencils are independent parameters, or the deviation parameter t is an independent parameter. Numerical examples illustrate and support the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, by employing the variational method, we show that a boundary value problem of sixth order has infinitely many solutions. In fact, via a critical point theorem, we will present sufficient conditions such that the problem has a sequence of solutions in a suitable function space. Specific cases and an example of results are also stated. [ABSTRACT FROM AUTHOR]

In this paper, we study the following non-local problem in fractional Orlicz–Sobolev spaces: (− Δ Φ) s u + V (x) a (| u |) u = f (x , u) ,   x ∈ R N , where (− Δ Φ) s (s ∈ (0 , 1)) denotes the non-local and maybe non-homogeneous operator, the so-called fractional Φ -Laplacian. Without assuming the Ambrosetti–Rabinowitz type and the Nehari type conditions on the non-linearity f, we obtain the existence of ground state solutions for the above problem with periodic potential function V (x) . The proof is based on a variant version of the mountain pass theorem and a Lions' type result in fractional Orlicz–Sobolev spaces. [ABSTRACT FROM AUTHOR]

An equation of state that predicts the critical thermodynamic behavior of n-butane is formulated. This equation takes into account the global behavior that includes the singular thermodynamic behavior asymptotically close to the critical point and the crossover to the regular thermodynamic behavior far away from the critical point. The formulated equation is based on the transformation of a truncated classical Landau expansion and represents the thermodynamic properties of n-butane in a wide range of temperatures and densities around the critical point. A comparison of the pressure P–ρ–T data measured by Beattie and co-workers and those calculated with the crossover EOS is made. Finally, the specific heat at constant volume, Cv, for n-butane along the critical density within a restricted temperature interval around the critical point is presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of infinitely many periodic solutions for second-order perturbed Hamiltonian systems. By using variational methods, we obtain new criteria to guarantee the existence of infinitely many periodic solutions using Bolle's perturbation method. Our results improve upon those presented in the existing literature. [ABSTRACT FROM AUTHOR]

We report the first measurements of cumulants, up to 4th order, of deuteron number distributions and proton-deuteron correlations in Au+Au collisions recorded by the STAR experiment in phase-I of Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider. Deuteron cumulants, their ratios, and proton-deuteron mixed cumulants are presented for different collision centralities covering a range of center-of-mass energy per nucleon pair sNN=7.7 to 200 GeV. It is found that the cumulant ratios at lower collision energies favor a canonical ensemble over a grand canonical ensemble in thermal models. An anti-correlation between proton and deuteron multiplicity is observed across all collision energies and centralities, consistent with the expectation from global baryon number conservation. The UrQMD model coupled with a phase-space coalescence mechanism qualitatively reproduces the collision-energy dependence of cumulant ratios and proton-deuteron correlations.

Acetate ester compounds find widespread use in various applications such as surface coatings, ink formulations, pharmaceuticals, and adhesives. It is essential to investigate the phase transition behavior of amyl acetate, amyl acetoacetate, and isoamyl acetoacetate in high-pressure supercritical CO2 (SC-CO2). The vapor-liquid equilibria (VLE) of the SC-CO2 + amyl acetate, SC-CO2 + amyl acetoacetate, and SC-CO2 + isoamyl acetoacetate systems were examined at different temperatures (313.2 ≤ T ≤ 393.2 K) and pressures (1.67 ≤ P ≤ 20.76 MPa). The solubility curve of these systems shows Type-I phase behavior, and the critical points of these binary mixtures were observed between the critical properties of the pure components involved in the systems. The solubility of amyl acetate, amyl acetoacetate, and isoamyl acetoacetate in the SC-CO2 + amyl acetate, SC-CO2 + amyl acetoacetate, and SC-CO2 + isoamyl acetoacetate systems increases with increasing temperature at constant pressure. The two-parameter model of Peng-Robinson equation of state along with a mixing rule, accurately correlated the phase transition behavior and critical mixtures curves for all three systems. The binary interaction parameters (BIPs) were adjusted, and the minimum root mean square deviation percentage was identified for all three systems. The calculated error% was found to be within reasonable limits, with values of 4.95 %, 3.93 %, and 4.18 % for SC-CO2 + amyl acetate, SC-CO2 + amyl acetoacetate, and SC-CO2 + isoamyl acetoacetate systems, respectively. Furthermore, the interaction parameters for the SC-CO2 + amyl acetoacetate mixture was found to be temperature-dependent, and the tested linear regression correlation coefficient for the BIPs parameters of (kij) and (ηij) are 0.98533 and 0.99083, respectively. This is the first research study on the phase behavior of acetate ester compounds in SC-CO2 solvents, and the results have a significant impact on industries at different operating conditions.

Abstract In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we prove that the problem has at least two positive solutions for the parameter λ ∈ ( 0 , Λ ) $\lambda \in (0,\Lambda )$ , one positive solution for λ = Λ $\lambda =\Lambda $ , and no positive solution for λ > Λ $\lambda >\Lambda $ , where Λ > 0 $\Lambda >0$ is a constant.

We report the complex dielectric function ε = ε1 + iε2 of MoS2/WS2 and WS2/MoS2 heterostructures and their constituent monolayers MoS2 and WS2 for an energy range from 1.5 to 6.0 eV and temperatures from 39 to 300 K. Comparisons between the optical properties of the heterostructures and their monolayers were conducted. Critical-point (CP) energies of the heterostructures were traced back to their origins in the monolayers. Low-temperature measurements confirmed the existence of only three excitonic CPs from 1.5 to 2.5 eV due to the overlap of trion B− of the MoS2 monolayer and exciton A0 of the WS2 monolayer. Due to the dielectric screening effect, most CPs exhibit red shifts in the heterostructures compared to their monolayer counterparts.

Temperature and field dependences of dielectric permittivity ε and unipolar electric field-induced strain S of the 0.675Pb(Mg1/3Nb2/3)O3−0.325PbTiO3 ceramics have been studied in the 25...200 °C range. Temperature dependences of both dielectric permittivity and converse piezoelectric modulus d*33 show anomalies corresponding to phase transitions between rhombohedral (monoclinic), tetragonal, and cubic phases. Based on the data of dielectric and field-induced strain studies, the E,T-phase diagram is plotted. The possible critical behavior of converse piezoelectric modulus d*33 and its correlation with the position of the known critical point in the E,T-phase diagram of PMN-xPT system are discussed. [ABSTRACT FROM AUTHOR]

Temperature and field dependences of dielectric permittivity ε and unipolar electric field-induced strain S of the 0.675Pb(Mg1/3Nb2/3)O3−0.325PbTiO3 ceramics have been studied in the 25...200 °C range. Temperature dependences of both dielectric permittivity and converse piezoelectric modulus d*33 show anomalies corresponding to phase transitions between rhombohedral (monoclinic), tetragonal, and cubic phases. Based on the data of dielectric and field-induced strain studies, the E,T-phase diagram is plotted. The possible critical behavior of converse piezoelectric modulus d*33 and its correlation with the position of the known critical point in the E,T-phase diagram of PMN-xPT system are discussed. [ABSTRACT FROM AUTHOR]

Copyright of Petroleum Refinery Engineering is the property of Petroleum Refinery Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Results are presented from an experimental study of the phase equilibrium (PTxy dependence) of an n-octadecane–propane/n-butane system for three isotherms (403.15, 423.15, 443.15 K) in the 0.89–7.24 MPa range of pressures using a high-pressure optical cell. The PTxy data are used to determine critical parameters of a mixture with identical concentrations of the two phases (x = y at fixed P and T). [ABSTRACT FROM AUTHOR]

A global path-planning algorithm for robots is proposed based on the critical-node diffusion binary tree (CDBT), which solves the problems of large memory consumption, long computing time, and many path inflection points of the traditional methods. First of all, the concept of Quad-connected, Tri-connected, Bi-connected nodes, and critical nodes are defined, and the mathematical models of diverse types of nodes are established. Second, the CDBT algorithm is proposed, in which different planning directions are determined due to the critical node as the diffusion object. Furthermore, the optimization indices of several types of nodes are evaluated in real-time. Third, a path optimization algorithm based on reverse searching is designed, in which the redundant nodes are eliminated, and the constraints of the robot are considered to provide the final optimized path. Finally, on one hand, the proposed algorithm is compared with the A* and RRT methods in the ROS system, in which four types of indicators in the eight maps are analysed. On the other hand, an experiment with an actual robot is conducted based on the proposed algorithm. The simulation and experiment verify that the new method can reduce the number of nodes in the path and the planning time and is suitable for the motion constraints of an actual robot. [ABSTRACT FROM AUTHOR]

We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau--de Gennes framework. There are two geometry-dependent variables: the edge length of the square cross-section, λ and the parameter h, which is a measure of the cuboid height. Theoretically, we prove the existence and uniqueness of the global minimizer with a small enough cuboid size. We develop a new numerical scheme for the high-index saddle dynamics to deal with the surface energies. We report on a plethora of (meta)stable states, and their dependence on h and λ, and in particular how the 3D states are connected with their two-dimensional counterparts on squares and rectangles. Notably, we find families of almost uniaxial stable states constructed from the topological classification of tangent unit-vector fields and study transition pathways between them. We also provide a phase diagram of competing (meta)stable states as a function of λ and h. [ABSTRACT FROM AUTHOR]

In this short communication, following a brief introduction, we undertake a comprehensive analytical study of the weighted Simpson index. Our primary emphasis concerns the precise determination of the optimal point (minimizer) coordinates and of the minimum value of the index, a differentiable convex function, which is related to the harmonic mean concept. Furthermore, we address and solve the inversion problem and show the tight connection between both approaches. Last, we give some insights and final remarks on this subject. [ABSTRACT FROM AUTHOR]

Femtoscopy is a unique tool to investigate the space-time geometry of the matter created in ultra-relativistic collisions. If the probability density distribution of hadron emission is parametrized, then the dependence of its parameters on particle momentum, collision energy, and collision geometry can be given. In recent years, several measurements came to light that indicated the adequacy of assuming a Lévy-stable shape for the mentioned distribution. In parallel, several new phenomenological developments appeared, aiding the interpretation of the experimental results or providing tools for the measurements. In this paper, we discuss important aspects of femtoscopy with Lévy sources in light of some of these advances, including phenomenological and experimental ones. [ABSTRACT FROM AUTHOR]

We theoretically study the generic mechanisms that could establish critical behavior in nematic liquid crystals (NLCs). The corresponding free energy density terms should exhibit linear coupling with the nematic order parameter and, via this coupling, enhance the nematic order. We consider both temperature- and pressure-driven, order–disorder phase transitions. We derive a scaled effective free energy expression that describes how qualitatively different mechanisms enforce critical behavior. Our main focus is on the impact of nanoparticles (NPs) in homogeneous NP-NLC mixtures. We illustrate that in the case of pressure-driven phase changes, lower concentrations are needed to impose critical point conditions in comparison with pure temperature variations. [ABSTRACT FROM AUTHOR]

We investigate a particular type of damped vibration systems that incorporate impulsive effects. The objective is to establish the existence and multiplicity of -rotating periodic solutions. To achieve this, the variational method and the fountain theorem, as presented by Bartsch, are used. The research builds upon recent findings and extends them by introducing notable enhancements. [ABSTRACT FROM AUTHOR]

Tripartite interactions play a fundamental role in the quantum information processing and quantum technology. However, it is generally difficult to realize strong tripartite coupling. We investigate the estimation of a tripartite coupling strength in a hybrid setup composed of a single nitrogen-vacancy (NV) center and a micromagnet. A time-independent parametric drive can be utilized to increase the estimation precision of the tripartite coupling strength. By calculating the quantum Fisher information (QFI), we can obtain the optimal estimation precision by measuring the eigenstate of the tripartite system. At the critical position, the QFI is divergent due to that the preparation time of the eigenstate is divergent. When the system is subjected to a dissipation, the QFI near the critical point of the driven-dissipation phase transition is analytically obtained. The direct intensity measurement is the optimal measurement near the dissipation phase transition point. In addition, we quantify the robustness of an imperfect measurement operator by the measurement noise susceptibility based on the error propagation formula. We find that the direct intensity measurement is robust enough against small measurement disturbance from a coherent drive. But it can be disturbed by the nonlinear anti-harmonic measurement noise, especially near the critical point.

Supercritical CO2 (sCO2) stands out for concentrating solar power (CSP) due to its superior thermophysical and chemical properties, promising higher cycle efficiency compared to superheated or supercritical steam. Leveraging the waste heat from sCO2 cycles through the organic Rankine cycle (ORC) as a low-grade energy source enhances overall thermal efficiency. This research explores advanced sCO2 power cycles and introduces a novel approach by integrating machine learning and genetic algorithms for optimizing cycle performance. Utilizing a thermodynamic model-derived dataset, various machine learning algorithms, including Random Forest, XGBoost, and Artificial Neural Network are employed for prediction, evaluation and optimization. This innovative integration enables a comprehensive understanding of the complex dynamics of sCO2 power cycles. Subsequently, the study employs multi-objective optimization for the systematic evaluation and optimization of the combined power cycles, incorporating multiple bottoming cycles to maximize efficiency. The findings not only showcase the superiority of the unified sCO2ORC cycle but also emphasize the impact of integrating advanced computational methods in achieving optimal performance. The sCO2 cycle is explored in recompression, partial cooling, and main compression intercooling configurations. Recompression cycles utilize a single cooling system, while partial cooling and main compression intercooling layouts integrate a pair of ORCs at two precoolers. The ORC cycle enhances the recompression cycle through heat recuperation, extracting enhanced power originating from the bottom cycle. Critical parameters are taken into consideration to carry out optimization and performance evaluations. such as cycle temperatures, recuperator effectiveness, bottoming cycle pressure ratio, and condensation temperature. Results indicate that the combined partial cooling sCO2ORC cycle yields the optimal net output power of 7994.541 kW and thermal efficiency of 53.365 %. The findings highlight the capacity to propel and promote the utilization of waste heat recovery in energy technologies through enhanced and optimized power cycle designs, contributing to their advancement and widespread adoption.

To each isolated critical point of a smooth function on a 3-manifold we put in correspondence a tree (graph without cycles). We will prove that functions are topologically equivalent in the neighbourhoods of critical points if and only if the corresponding trees are isomorphic. A complete topological invariant of functions with fore critical points, on a closed 3-manifold, was constructed. A criterion for the topological equivalence of functions with a finite number of critical points on 3-manifolds is given.