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We explore the far-off-equilibrium aspects of the (1+1)-dimensional early-stage evolution of a weakly-coupled quark-gluon plasma using kinetic theory and hydrodynamics. For a large set of far-off-equilibrium initial conditions the system exhibits a peculiar phenomenon where its total equilibrium entropy decreases with time. Using a non-equilibrium definition of entropy based on Boltzmann's H-function, we demonstrate how this apparently anomalous behavior is consistent with the second law of thermodynamics. We also use the H-function to formulate 'maximum-entropy' hydrodynamics, a far-offequilibrium macroscopic theory that can describe both free-streaming and nearequilibrium regimes of quark-gluon plasma in a single framework. [ABSTRACT FROM AUTHOR]

A central question in heavy-ion collisions is how the initial far-from-equilibrium medium evolves and thermalizes while it undergoes a rapid longitudinal expansion. In this work we use the two-particle irreducible (2PI) effective action for the first time to consider this question, focusing on ϕ4 scalar theory truncated at three loops. We calculate the momentum distribution of quasiparticles in the medium and show that isotropization takes place. We furthermore consider the thermal mass of quasiparticles and the importance of number-changing processes. [ABSTRACT FROM AUTHOR]

We present a new general formalism for introducing thermal fluctuations in relativistic hydrodynamics, which incorporates recent developments on the causality and stability of relativistic hydrodynamic theories. Our approach is based on the information current, which measures the net amount of information carried by perturbations around equilibrium in a relativistic many-body system. The resulting noise correlators are guaranteed to be observer-independent for thermodynamically stable models. We obtain an effective action within our formalism and discuss its properties. [ABSTRACT FROM AUTHOR]

We first assemble a full set of the Boltzmann Equation in Diffusion Approximation (BEDA) for studying thermalization/hydrodynamization and quark production in out of equilibrium systems. We then discuss thermalization and the production of three flavors of massless quarks in spatially homogeneous systems initially filled only with gluons. A complete parametric understanding for thermalization and quark production is obtained for both initially very dense or dilute systems, which are complemented by detailed numerical simulations. For initial distributions more relevant for heavy-ion collisions, the complete thermal equilibration is found to be significantly delayed by considering quark production. [ABSTRACT FROM AUTHOR]

We use QCD effective kinetic theory to calculate far-fromequilibrium dynamics on an event-by-event basis within the KøMPøST framework. We present non-equilibrium charge response functions and the dynamical evolution of the conserved charge current pertinent to the early-time dynamics of heavy-ion collisions at the highest energies. The KøMPøST framework with conserved baryon, strangeness, and electric charges can then be readily implemented into a multistage model allowing for the initialization of a nonequilibrium charge current in hydrodynamic simulations. [ABSTRACT FROM AUTHOR]

The polarization of the Λ particle offers the unique opportunity to study the hydrodynamic gradients in the Quark-Gluon Plasma formed in heavyion collisions. However, the theoretical formula commonly used to calculate polarization is only a linear order expansion in thermal vorticity and neglects higher-order corrections. Here, I present an exact calculation to all orders in (constant) thermal vorticity at global equilibrium, obtaining the analytic form of the spin density matrix and the polarization vector for massive particles of any spin. Finally, I extend these results to local equilibrium and assess their phenomenological impact by numerically calculating the polarization vector in a 3+1 hydrodynamic simulation. [ABSTRACT FROM AUTHOR]

We discuss recent theoretical developments in understanding the early pre-equilibrium dynamics and onset of hydrodynamic behavior in high-energy heavy-ion collisions. We highlight possible experimental signatures of the pre-equilibrium phase, and present recent progress in developing a consistent theoretical description of collective flow in small systems. [ABSTRACT FROM AUTHOR]

This paper proposes a non-classical theory of stressed plates. Resolving equations are obtained in terms of longitudinal forces of shear forces and internal moments, and boundary conditions are formulated. The obtained solutions simultaneously satisfy the equilibrium equations and the Beltrami-Mitchell stress compatibility equations. A boundary value problem is formulated for a plate under the action of mutually balanced loads. Some applied problems have been solved. [ABSTRACT FROM AUTHOR]

This research aims to determine the impact of misconceptions about dynamic equilibrium, which can potentially cause misconceptions about chemical equilibrium shifts in concentration factors, and the correlation category between misconceptions in dynamic equilibrium and chemical equilibrium shifts in concentration factors. The method used in this research is the descriptive qualitative method. The instrument used is a worksheet developed based on the representation-metacognitive reinforcement conceptual change model (R-MR CCM). Students who understand the concept of dynamic equilibrium will more easily understand the chemical equilibrium shifts in concentration factors. However, students who have had misconceptions about dynamic equilibrium will tend to have misconceptions about the concept of shifting chemical equilibrium on concentration factors because the idea of dynamic equilibrium is prerequisite material for the concept of shifting chemical equilibrium on concentration factors. Misconceptions in dynamic equilibrium impacting the misconception in chemical equilibrium shifts and misconceptions about the idea of dynamic equilibrium and shifts in chemical equilibrium on concentration factors can be reduced using a worksheet with a representation-metacognitive reinforcement conceptual change model. [ABSTRACT FROM AUTHOR]

In planning to construct the diversion tunnel at Riam Kiwa Dam, a tunnel with a length of 425 meters will be built to change the direction of the water flow. According to the planning report, the stability analysis of the tunnel portal slope has not been conducted. Slope stability analysis is necessary for tunnel construction to guarantee portal stability during construction and use. This study uses the Limit Equilibrium Method (LEM) to evaluate slope stability at the tunnel's inlet and outlet under static and seismic loads. The input material parameters for the slope stability study were acquired from evaluating soil and rock cores, and they included lithology type, level of weathering, rock mass quality based on the Geology Strength Index (GSI), and testing in laboratory results. Based on the observations, the inlet and outlet portal slopes consist of residual soil, lapilli tuff and andesite lava of poor and fair quality with light weathering. The Limit Equilibrium Method (LEM) analysis shows that the slopes of the inlet and outlet portals of the Riam Kiwa dam diversion tunnel are categorised as unstable under static and seismic loads. [ABSTRACT FROM AUTHOR]

An Ellipsoidal-statistical-model-based kinetic equation is proposed for a dense gas. The proposed model has a merit of reproducing appropriate values of the transport coefficients over the previous models by the authors. It has, however, a potential demerit that the H theorem is not fully guaranteed. Related discussions are made and numerical simulations of the phase separation from a uniform equilibrium state are conducted for illustrative purposes. [ABSTRACT FROM AUTHOR]

The energy source known as natural gas can be regarded as the fuel that enables us to transition to a future with lower carbon emissions while meeting the massive demand for energy. There are several attractions to conserving natural gas as hydrates, including the incredible capacity to store multiple volumes in hydrate crystals. Being eco-conscious, non-explosive, and providing a compact method of natural gas storage with a high volumetric storage capacity, clathrate hydrates are a highly advantageous form of natural gas storage. When they develop in oil-gas pipes and obstruct flow, gas hydrates are an industry annoyance that creates problems with flow assurance. It is crucial to forecast the gas hydrate formation conditions to make the most of the potential for storing natural gas as clathrate hydrates and tackle hydrate-related issues in the gas and oil sector. This paper analyzes some of the available empirical correlations from the literature and is then compared using statistical tools to obtain the optimum one to compute the equilibrium state points of methane (CH4) hydrate in pure water for storage applications. The suggested empirical correlations are analyzed for a collection of pressure from 2.641 to 299 MPa and temperatures between 273.2–317.2 K. [ABSTRACT FROM AUTHOR]

The subject of this work is a Holling type-I prey-predator model containing variable prey carrying capacity, prey refuge, and supplemental food for the predator. The goal is to see how varying prey carrying capacity affects the model's stability in the presence of a prey refuge and increased food for the predator. The stability of the system's equilibrium points by sufficient conditions are discussed. The effect of model's parameters linked to extra food, prey refuge, and variable prey carrying capacity on the stability of the suggested model is investigated. Numerical tests are undertaken to ensure the accuracy of theoretical results. [ABSTRACT FROM AUTHOR]

Bogor regency has high susceptibility to landslides disaster. Geotextile reinforcement is an attempt that is appropriate to deal with slope instability. However, the significant slip parameters that guide the reinforcement design are still complicated to study. This research aims to analyze landslide slip surfaces in various circumstances. Landslide analysis was conducted in Limit Equilibrium with GeoStudio. The tensile strength geotextile was of various types: woven (7.1kN/m, 8.4kN/m, and 10kN/m) and nonwoven (32kN/m 44kN/m, and 54kN/m). Moreover, the vertical distances among geotextiles were varied in 0.25m, 0.5m, 0.75m, 1m, 1.25m, and 1.5m. The slip surface position analysis was divided into three models with different landslide beginning and ending coordinates. The result shows that Model 3 has the most significant SF of all the models, while Model 2 has the lowest. The lower the vertical distance of geotextile, the higher SF will be. The slip surface position data indicated that Model 3 is narrower than Models 1 and 2, with having an extensive slip surface position. This result is intended to assist the engineer in calculating the landslide's starting and finishing locations (slip surface) to determine the appropriate geotextile reinforcement and the optimum safety factor. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the multistability of a non-smooth model having infinite number of equilibrium points. The three-dimensional model is in a form of a system of nonlinear ordinary differential equations including a non-smooth function. The influence of initial conditions is considered while observing coexistence of multiple attractors. To obtain such phenomena, the Newton's method is applied to find the initial conditions which lead to a periodic orbit near the chaotic attractor. By perturbing the initial conditions around this point, nearby points are found using the 0-1 test for chaos, for which the system exhibits regular and chaotic behavior. Curiously, isolated grid points of initial conditions are detected, leading to the periodic orbit, remaining isolated under magnification. These are surrounded by initial conditions tending to chaotic attractors. [ABSTRACT FROM AUTHOR]

Here, in this paper, the spatial motions of a boundless collisionless electron Vlasov-Poisson gas were considered in a three-dimensional Cartesian coordinate system. Using the replacing of independent variables in the form of hydrodynamic substitution, a transition was made from the kinetic equations to an infinite system of gas-dynamic equations in the "vortex shallow water" and the Boussinesq approximations. In the process of proving the linear instability for the exact stationary solutions to the Vlasov-Poisson equations, the well-known sufficient Newcomb-Gardner-Rosenbluth condition for stability of these solutions with respect to one incomplete unclosed particular class of small spatial perturbations was reversed. An original linear differential second-order inequality with constant coefficients for the Lyapunov functional was also obtained. When the sufficient conditions found in this paper for the linear practical instability of the exact stationary solutions under research are satisfied, an a priori exponential estimate from below for the growth of small three-dimensional perturbations follows from this inequality. Since the estimate was derived without any additional restrictions on the exact stationary solutions under study, then, in this way, the absolute linear instability for the spatial dynamic equilibrium states of the electron Vlasov-Poisson gas with respect to three-dimensional perturbations was proved. [ABSTRACT FROM AUTHOR]

In this paper, the stability for three-dimensional (3D) states of dynamic equilibrium of the two-component Vlasov-Poisson plasma was studied. Using the direct Lyapunov method, it was proved that the spatial dynamic equilibria of the Vlasov-Poisson plasma with respect to small 3D perturbations are absolutely unstable. For the spatial states of dynamic equilibrium of the two-component Vlasov-Poisson plasma, the sufficient conditions for linear practical instability were obtained. The a priori exponential lower estimate was constructed, and the initial data for small 3D perturbations which are growing with time were characterized. [ABSTRACT FROM AUTHOR]

The environmental feedback loop could be a crucial condition for the specie population resilience. In most cases, such a loop could be determined through the environmental temperature and supply of available resources. Here, we present a resource competition model for species populations with environmental feedback. We find the conditions when the environmental feedback loop in this model may destroy the equilibrium in population; increase species abundances; and lead to biomass loss. [ABSTRACT FROM AUTHOR]

For reactive burn models in hydrocodes, an equilibrium closure assumption is typically made between the unreacted and product equations of state. In the CTH [1] (not an acronym) hydrocode the assumption of density and temperature equilibrium is made by default, while other codes make a pressure and temperature equilibrium assumption. The main reason for this difference is the computational efficiency in making the density and temperature assumption over the pressure and temperature one. With fitting to data, both assumptions can accurately predict reactive flow response using the various models, but the model parameters from one code cannot necessarily be used directly in a different code with a different closure assumption. A new framework is intro-duced in CTH to allow this assumption to be changed independently for each reactive material. Comparisons of the response and computational cost of the History Variable Reactive Burn (HVRB) reactive flow model with the different equilibrium assumptions are presented. [ABSTRACT FROM AUTHOR]

This paper presents a 4D hyperchaotic system with two unstable saddle-foci equilibria which is constructed by combining a 3D chaotic system with a 1D linear system utilizing a coupling control strategy. The proposed system is characterized by one exponential term and consists of eight terms. Some of the dynamic behaviors of this system have been analyzed theoretically and numerically through simulation such as equilibria points, Lyapunov exponents, Kaplan-York dimension, Multistability, chaos control, and chaos synchronization. The proposed controls were implemented theoretically through the Lyapunov stability theorem and the numerical simulation confirmed the accuracy and validity of our theoretical results. [ABSTRACT FROM AUTHOR]

We modify a theory of flow stress introduced in [6,7,8] for a class of polycrystalline materials with equilibrium and quasy-equilibrium defect structure under quasi-static plastic deformations. We suggest Maxwell-like distribution law for defects (within dislocation-disclination mechanism) in the grains of polycrystalline samples with respect to grain's diameter. Polycrystalline aggregates are considered within single-and two-phase models that correspond by the presence of crystalline and grain-boundary (porous) phases. The scalar dislocation density is derived. Analytic and graphic forms of the generalized Hall–Petch relations for yield strength are produced for single-mode samples with BCC (a-Fe), FCC (Cu, Al, Ni) and HCP (a-Ti, Zr) crystal lattices at T=300 K with different values of the grain-boundary phase. We derived new form of the temperature-dimensional effect. The values of extremal grain and maximum of yield strength are decreased with raising the temperature in accordance with experiments up to UFG region. [ABSTRACT FROM AUTHOR]

Non-inductive plasma start-up is required for a spherical tokamak fusion reactor. Start-up using lower-hybrid current drive has been studied at the TST-2 spherical tokamak. Recently, equilibrium reconstruction based on the extended MHD model was developed to describe the fast electron current dominated equilibrium more accurately. The new equilibrium was applied to a coupled ray-tracing and Fokker-Planck solver based current drive simulation. The simulated total plasma current was within a factor of two of the outer-midplane launch experimental result, but overestimated the experiment by a factor of three for the top launch case. The measured x-ray radiation was substantially greater for the top launch case compared to the outer-midplane launch case despite the similar plasma current. This may indicate that current drive is affected appreciably by the rf induced transport that is a finite-orbit effect neglected in the present current drive simulation. [ABSTRACT FROM AUTHOR]

This paper studies the presence of collinear and out of plane equilibrium points in the elliptic restricted four body problem under the influence of radiation pressure and oblateness effects. It also deals with the linear stability of the equilirium points. We have assumed that three primaries are moving in elliptic orbits around their common center of masses which is assumed to be the origin of the coordinate system. Primaries are positioned at the vertices of an equilateral triangle while the fourth body of the system is assumed to be infinitesimally small in size. It was observed that for this system, we have two collinear and two or four out of plane equilibrium points exists which is depend on true anomaly of the orbit. The position of the out of plane equilibrium points obtained on the x-z plane are found to be in symmetrically aligned with respect to x-y plane. It was observed that both the collinear and out of plane equilibrium points are linearly unstable. The fractal Basin for out of plane equilibrium points were studied. [ABSTRACT FROM AUTHOR]

Bar elements pretensioned by unbonded steel reinforcement placed in narrow ducts are considered in this paper. Such elements find one of their main applications in the field of post-tensioned reinforced concrete. One of the main features of the post-tensioned concrete beams is an interaction between pretensioned strand and rest of the construction body which appears like a distributed balancing load. Increasing of the beam deflection leads to tensioning force change in its strands. This affects to the balancing load that in turn differs the subsequent deflection increasing. Analysis of influence of changing balancing load to equilibrium of cross sections of simply supported post-tensioned reinforced concrete beam has been made in the proposed article by methods of applied mechanics of materials. It is shown that increasing deflection of the beam and corresponding growth of balancing load are compensated by bending moment caused by eccentrical compression of the beam. [ABSTRACT FROM AUTHOR]

The paper studies the behavior of a pivotally supported rod, the ends of which are fixed in the longitudinal direction under the action of a compressive load. The stability of a centrally compressed rod with an incompressible axis is considered if transverse reactions occur during buckling that are proportional to its deflections. It is assumed that these reactions are distributed along a vertical axis parallel to the axis of the rod and are determined by the coordinates in three-dimensional space x, y, and z. The equations are used, taking into account which it is possible to study the buckling of the rod in the case when the axis around which the cross sections rotate during the buckling does not shift. The condition is assumed that if the compressive force differs little from the critical load, then the resulting curved form of the rod equilibrium differs little from the rectilinear one, and the usual approximate expressions can be used to express the curvature. It is shown that in this case, the buckling of the rod in the planes of symmetry does not depend on torsion. When studying the stability of the rod under the action of end forces, it is shown that even in the first approximation, the results are close to the exact solution of F. S. Yasinsky. The stability of the supported rod is analyzed when the intensity of the longitudinal compressive load changes according to a linear law. The author believes that buckling occurs at a non-deformable surface. [ABSTRACT FROM AUTHOR]

In carrying out mining activities, many factors must be considered, especially geotechnical factors, one of which is slope stability analysis. Landslide events in a mining area are still often found based on the author's observations in the last one year. The purpose of this study is to determine the prediction of landslide volume and the cost of mitigating the risk of landslides. This study uses the 3-Dimensional limit equilibrium method "Bishop Simplified" with the research variables increasing the radius increment and the number of grid points, to obtain the safety factor and landslide volume. The variables of the radius increment and the number of grid points that are optimal in this research are the radius increment of 30 and the number of grid points 30x30x15. Prediction of landslide risk mitigation can be determined by multiplying the results of the average potential volume of 3D landslides that have been validated with the results of volume calculations in areas that have optimal variables for heavy equipment costs $/Bcm, in this case PT X uses contractor services, so the equipment rental costs covered operational and non-operational costs. From the results of the 3D slope stability analysis, as well as the results of the calculation of the OB volume in the research area, an average of 391,644 m3 was obtained multiplied by the equipment rental fee of 2$/Bcm, with a 90-day mitigation work plan time scheme, and a total of 3 unit of digging equipment and 2 units of conveyance, the total cost of mitigation of landslide risk is 3,916,44 $/Bcm. [ABSTRACT FROM AUTHOR]

The objective of this paper is to establish the existence and uniqueness of the solution of (EP) by generalizing a new class of trifunction equilibrium problems in the setting of Banach space. Furthermore, we consider trifunction as special cases of 퐸푝(훽1, 훽2) and find new conditions under which the equilibrium state holds using βh- monotone subsets and especially in convex and closed subsets (bounded or unbounded). In so doing, we are able to ensure the existence and uniqueness of the solution of (EP), thus improving latest properties in its literature. We are also interested in obtaining optimization as a particular case of 퐸푝(훽1, 훽2). [ABSTRACT FROM AUTHOR]

The problem of the ecological system long-term keeping near the equilibrium position with minimization of control resources is considered. A mathematical formulation of this problem and a method for optimal expenditure control constructing are presented. While deviations from the equilibrium point are very small, its controlled dynamics can be described by linear differential equations with constant coefficients. The control actions are modeled by piecewise-constant unidirectional functions with a finite number of switching points. The choice of this control class is due to the characteristic features of environmental tasks: control actions on living systems are unidirectional and often have a periodic character [3], [5-11]. It can be individuals catching from the population, feeding, watering, thinning, etc. Therefore, the chosen control class takes into account both the unidirectionality and the periodicity of the control actions. Two types of regulation are discussed: adding to the system any substances promoting the population growth (substrates, fertilizers, etc.), and removal of any volumes (catching individuals from the population, thinning, etc.). As a minimizable functional, the expenditure criterion is used, that is proportional in practice to the consumption of resources used for controlling [1], [4]: pesticides, fertilizers, medicines, etc. In some cases, this criterion minimizing, in addition to the economic one, also gives a direct environmental effect. For example, the constructed optimal control allows the pest population to be destroyed with the minimum quantity of toxic chemicals that adversely affect the environment. The method for solving the problem is based on the mechanical systems optimal control problems methods of solution developed by the authors (e.g. [2]). In this paper, taking into account the ecological specifics of the problem, the system of transcendental equations is obtained. Numerical solution of this system allows us to find the control switching points that satisfy the necessary conditions of the expenditure criterion extremum. To find an adequate initial approximation for the standard numerical methods for solving the equations system an original algorithm is presented. [ABSTRACT FROM AUTHOR]

Finding the ‘right’ balance between centralization and decentralization in organizational processes, governance, and IT can be difficult. To navigate this tension field, organizations need to find (de)centralization equilibria that are often dynamic and depend on organizational strategy and context. However, little is known about how organizations should respond once an old equilibrium is punctuated or breaks down. In this paper, we thus conduct an inductive multiple-case study to investigate how organizations sustain and transition between (de)centralization equilibria. We synthesize our insights into a process model that paints the transition as an iterative recalibration process subject to centralization and decentralization tensions. Often, this process will require local and temporary compromises. Our work contributes a muchneeded process perspective to the IS literature on (de)centralization. [ABSTRACT FROM AUTHOR]

The objective of this research is to study Leslie-Gower predator-prey Holling respond function type II models on predator and prey population. In this predator-prey model it is assumed that there are harvesting efforts in both populations. The steps to analyze this models including to looking for equilibrium points, and analyzing the exchange the parameter of permanent harvesting value to know the possibility of bifurcation. Based on analysis obtained four equilibrium points which is the trivial equilibrium point E0, the equilibrium point E1 for the extinction of predator, the equilibrium point E2for the extinction of prey, and the endemic equilibrium point E3. The equilibrium points of E2 and E3 experiencing stability changes when the rate of harvesting parameter on prey population (H1) and predator (H2) is varied so that the system have a bifurcation. The forming of limit cycle on portrait phase around equilibrium points shows that the kind of bifurcation that happen was a Hopf bifurcation. [ABSTRACT FROM AUTHOR]

Latent phase of Coronavirus infection is a period of time in which an infected person is noninfectious and asymptomatic, so that it does not have a high risk of transmission. We construct a mathematical model that describes human inflammatory response system, i.e. interaction between pro-inflammatory and anti-inflammatory cytokine during Coronavirus infection to identify the sufficient condition for global stability of latency equilibria of the model, so that the latency period of an infected person can be maintained and transmission of Coronavirus can be prevented. The model is a three-dimensional differential equation system that has an equilibria that represents the latent phase of Coronavirus infection. The latency equilibria is globally asymptotically stable if the maximum concentration of Coronavirus is less than the ratio between the natural degradation of pro-inflammatory cytokine and the increasing rate of pro-inflammatory cytokine concentration caused by Coronavirus. Fulfillment of the sufficient condition to create a globally asymptotically stable latency equilibria results in Coronavirus infection on the infected person will remain in latent phase, so that Coronavirus transmission can be suppressed. [ABSTRACT FROM AUTHOR]

A two-step perturbation technique is utilized to determine critical buckling loads and post-buckling equilibrium paths of laminated composite plates. The equilibrium, stability, and compatibility equations of laminated plates are derived by using the first-order shear deformation plate theory (FSDT) also Von-Karman-type nonlinearity formulations are the consideration, and through the minimum total potential energy principle. The structure is assumed to be under uniaxial and biaxial compression loads. Effects of different parameters such as biaxial loads, modulus ratio (E1/E2), and aspect ratio (a/h) on critical buckling loads and post-buckling equilibrium paths of graphite/epoxy laminated plates are investigated. Then, the critical buckling loads and post-buckling equilibrium paths of the symmetrically laminated composites are calculated by Mat lab software code. Results are shown in the form of plots presenting the variation in dimensionless buckling load parameters with dimensionless maximum deflection. The results offer that the critical buckling loads and post-buckling equilibrium paths under uniaxial compression load are higher than those under biaxial compression load. [ABSTRACT FROM AUTHOR]

Universal Nuclearspace theory accomplished its present-day significance because of its various applications in the investigation of numerous true problems, specifically equilibrium problems. Equilibrium problems theory saw as hazardous development in applications over a wide class of direct and nonlinear problems being brought up in picture reproduction, clinical imaging, environment, network investigation, elasticity and nonlinear optimization. A classical speculation in this theory for equilibrium problems is convexity supposition and an equilibrium condition. Such sorts of problems are perceived as the classical equilibrium issue. The optimization problems, the variational inequality problems and the fixed point problems, considered as three standard instances of equilibrium problems. Consequently conjointly, equilibrium problems spread a broad scope of applications. [ABSTRACT FROM AUTHOR]

A predator-prey model with proportional prey harvesting and square root functional response in prey has been studied. The existence and the local stability of equilibria of the system has been analyzed. By analysing the model it is observed that the dynamics of the model depends on the parameter values. It is examined the solutions near the interior equilibrium point the system exhibits Hopf bifurcation. The calculation of the Lypunov number shows that the Hopf bifurcation is super-critical. Various numerical simulations are carried out to justify the analytical results. [ABSTRACT FROM AUTHOR]

Unfortunately, the classical formulation of the problem of the theory of elasticity in stresses consists in solving three equilibrium equations when three static boundary conditions are meet. In this paper, based on the correct formulation of the stress problem for six Beltrami-Mitchell equations when three boundary-line equilibrium equations and three static boundary conditions are satisfied, solutions of stress problems in an approximate analytical form are obtaining. The limiting cases of a parallelepiped in the form of a rod and a plate are considered. [ABSTRACT FROM AUTHOR]

Map-based nonlinear neuron model proposed by Chialvo is considered under the influence of random disturbances. In the deterministic case, the model possesses both mono- and bistability regimes with the coexistence of equilibrium and oscillatory modes in a form of quasiperiodic closed invariant curves. Variability of noise-induced transformations in dynamics of this model is demonstrated. Phenomena of noise-induced excitement, stochastic generation of mixed-mode oscillations, and transitions between order and chaos are discussed. [ABSTRACT FROM AUTHOR]

A new mathematical model describing an equilibrium of a thermoelastic heterogeneous Kirchhoff-Love plate is considered. A corresponding variational problem is formulated in a 2D domain with a cut. The cut corresponds to an interfacial crack located on a part of the boundary of a flat rigid inclusion. The flat inclusion is described by a cylindrical surface. Due to presence of the flat rigid inclusion in the plate, restrictions of the functions describing displacements to the corresponding curves satisfy special constraints having a linear form. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. Solvability of the problem is proved. [ABSTRACT FROM AUTHOR]

In the paper, an equilibrium problem for an elastic body with a crack crossing a thin inclusion at some point is analyzed. As a result, the crack divides the inclusion of two parts. One part of the inclusion is a rigid and the other is an elastic. The elastic inclusion is modeled by a Bernoulli – Euler beam. The conjugation conditions of these inclusions at a given point are considered. To exclude a mutual penetration between inclusions, inequality type boundary conditions are imposed. Nonlinear boundary conditions are also considered at the crack faces.The main goal of the paper is to justify a passage to the limit as the rigidity parameter of the thin inclusion goes to infinity. [ABSTRACT FROM AUTHOR]

Variational problems for composite plates with a system of joined rigid inclusions are considered. It is supposed that plate consist of an elastic matrix and cylindrical rigid inclusions. Inclusions are joined at common fibers so that displacements of these joined inclusions coincide at the corresponding points of fibers. Variational approach is used in order to deal with the Signorini-type boundary condition that describes mutual nonpenetration of opposite crack faces. We study two types of equilibrium models that correspond to different types of rigid inclusions. For the first model, we suppose that the plate has a volume rigid inclusion which is described by a corresponding 3D domain, and the second one describes the body containing a set of fastened thin rigid inclusions, each of which corresponds to a cylindrical surface. The crack is defined by the same curve in both models so that crack curve lies on the part of the boundary of the volume inclusion. An optimal control problem is formulated in the framework of the both model, such that a control is specified by the number of thin rigid thin plane inclusions and by the limiting case which as it turned out, fits to the first model. A quality functional is defined by an arbitrary continuous functional in a suitable Sobolev space. The solvability of the optimal control problem is proved. [ABSTRACT FROM AUTHOR]

We formulate a new variational problem on the equilibrium of a thermoelastic Kirchhoff–Love plate with an inclined crack. We assume that angles of inclination are known in each point of the curve of the crack. We assume that a displacement boundary condition describing nonpenetration of opposite crack faces is specified on the crack curve and has the form of inequality. We impose conditions of rigid clamping on the external boundary of plate. Solvability of the problem is proved, an equivalent differential setting is found. [ABSTRACT FROM AUTHOR]

In the present article, we study singular limits of weak energy solutions to non-instantaneous single-and multi-impulsive advection-diffusion-reaction equation as impulsive source terms collapse to time-dependent the Dirac delta-functions, i.e., to instant impulses. We establish that the limiting functions are the solutions of the instantaneous impulsive advection-diffusion-reaction equations. Besides, in the multi-impulsive case we find the effect of transition to an equilibrium as a number of impulses grows infinitely. The results can be applied to further modeling of such processes as frost-quakes in glaciology. [ABSTRACT FROM AUTHOR]

We use an approach based on studying the response functions of each industrial companies to get sufficient conditions for an existence of a market equilibrium in an oligopoly market, shaped by three players. We replace the maximization of the pay off functions from the classical approach to the problem by considering the response functions. Thus we get not only sufficient conditions for the existence of an equilibrium, moreover, we get its uniqueness and stability. Response functions approach makes it also possible to solve the problem, when players do not behave rationally. Their irrational behavior may be due to a lack of information although they may want to maximize their pay off functions. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic variant of the Li-Rinzel model of calcium oscillations. A bifurcation analysis of the model is carried out, parametric zones of equilibrium and oscillatory regimes are described, basins of their attraction and separatrices detaching these basins are constructed. A probabilistic description of the frequency and amplitude characteristics of calcium oscillations under conditions of parametric random disturbances is given. The phenomena of stochastic excitability and generation of oscillations of mixed modes are described. [ABSTRACT FROM AUTHOR]

Sustainable communications form the basis for any viable socio-economic system. These materials deliver the results of the research aimed at investigation of conditions under which a local community tends to be a viable system. Economic communications have been put in the focus of the research. Agent-based technology has been implemented, and the model simulating economic communications has been built. As the result of a series of experiments, it has been revealed that the Leontief's intersectoral equilibrium conditions might become the theoretical basis for local community's viability, but some other factors, such as ways of economic agents' behavior and money volume circulated in the system could also influence it. [ABSTRACT FROM AUTHOR]

In this article, a predator-prey mathematical model with toxicity, harvesting, and strong Allee effect has been developed. The proposed model has been analyzed analytically as well as numerically. We have examined the boundedness and positivity of the solutions for this proposed mathematical model. The parametric conditions for the existence of various feasible equilibrium points have been obtained. The local stability of these feasible equilibrium points is investigated. It has been shown that the proposed model depicts a saddle-node bifurcation. The parametric conditions for the existence of the bionomic equilibrium point has been investigated. Further, the problem of optimum harvesting policy has been investigated by means of the Pontryagins Maximum Principle. The phase portrait diagrams have been sketched to validate the analysis. [ABSTRACT FROM AUTHOR]

The analysis of mutual competition of the growth of plant with particular emphasis on time reliant variations in their densities has been done in our present work. We are proposing a mathematical model of plant population growth with competitive and allelopathic impacts that are stimulating as well as inhibitory on each other. Equilibrium points are calculated and stability analysis is performed about non-zero equilibrium point. Delay parameter destabilizes the system when allelopathic effect is supposed to be of stimulatory in nature. The system shows asymptotic stability when delay parameter having value below the critical point. Hopf bifurcation is observed when the value of delay parameter crosses the critical point. The numerical results are substantiated using MATLAB. [ABSTRACT FROM AUTHOR]

Pricing plays an important role in any market competition, but particularly in those businesses that hold a seat in hyper competitive economic activities such as hotels. This paper analyses a market competition between one corporate social responsibility (CSR) hotel and one for profit (FP) hotel, in which both hotels set room prices. We study three different market behaviors: (i) both hotels take their decisions simultaneously; (ii) the CSR hotel takes the leader position; (iii) the FP hotel takes the leader position. For each situation, by using game theory techniques, we compute the different outcomes of the model at equilibrium. We also describe the effects of CSR on the outcomes. [ABSTRACT FROM AUTHOR]

In this talk, we investigate the collision energy and particle species dependence of kinetic freeze-out properties in relativistic heavy ion collisions from √SNN = 7.7 - 200 GeV $\sqrt {{S_{NN}}} = 7.7 - 200\,{\rm{GeV}}$ S N N = 7.7 − 200   GeV at Relativistic Heavy Ion Collider (RHIC) and 2.76 TeV at the Large Hadron Collider (LHC) with Tsallis Blast-Wave (TBW) model. Strangeness and non-strange particles show a similar radial flow, while the strange hadrons have higher temperature and smaller non-equilibrium degree. Strangeness approaches equilibrium more quickly than non-strange particles from peripheral to central collisions. The kinetic freeze-out temperature of non-strange particles in central collisions decreases from RHIC to LHC energies, while strangeness does not show this behavior. Finally we discuss the system bulk viscosity dependence on collision energy. [ABSTRACT FROM AUTHOR]

The Beam Energy Scan program at the Relativistic Heavy Ion Collider (RHIC) is searching for the QCD critical point. The main signal for the critical point is the kurtosis of the distribution of proton yields obtained on an event by event basis where one expects a peak at the critical point. However, its exact behavior is still an open question due to out-of-equilibrium effects and uncertainty in the equation of state. Here we use a simplistic hydrodynamic model that enforces strangeness-neutrality, selecting trajectories that pass close to the critical point. We vary the initial conditions to estimate the effect of out-of-equilibrium hydrodynamics on the kurtosis signal. [ABSTRACT FROM AUTHOR]

We give a brief overview about theory development of spin polarization in relativistic heavy ion collisions, which includes how the polarization could be generated by single scattering, what the polarization could be in equilibrium, how to address some recent puzzles in spin polarization in heavy ion collisions and how much progress we have made in spin hydrodynamics and spin kinetic theory. We will also discuss the possible helicity polarization in relativistic heavy ion collisions. [ABSTRACT FROM AUTHOR]