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We derive an analytic expression of the non-equilibrium Fermi's golden rule (NE-FGR) expression for a Holstein–Tavis–Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi's golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant. [ABSTRACT FROM AUTHOR]

In this paper, we develop an integrodifference equation model that incorporates spatial memory and learning so that each year, a fraction of the population use the same dispersal kernel as the previous year, and the remaining individuals return to where they bred or were born. In temporally static environments, the equilibrium of the system corresponds to an ideal free dispersal strategy, which is evolutionarily stable. We prove local stability of this equilibrium in a special case, and we observe convergence towards this equilibrium in numerical computations. When there are periodic or stochastic temporal changes in the environment, the population is less able to match the environment, but is able to do so to some extent depending on the parameters. Overall, the mechanism proposed in this model shows a possible way for the dispersal kernel of a population to evolve towards an ideal free dispersal kernel. [ABSTRACT FROM AUTHOR]

In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a nonvacuum equilibrium in Rn (n = 2, 3). Zero retardation results in zero dissipation in the velocity equation, which is the main difficulty that prevents us from obtaining the long time well-posedness of solutions. Through dedicated analysis, we find that the linearized equations of this model have damping effects, which ensure the global-in-time existence of small data solutions. However, the nonlinear quadratic terms have one more order derivative than the linear part and no good structure is discovered to overcome this derivative loss problem. So we can only build the result in the analytical energy space rather than Sobolev space with finite order derivatives. [ABSTRACT FROM AUTHOR]

In this paper, we examine how finite time disentanglement can be manipulated for the quantum system out of thermal equilibrium. To this aim, we employ the Markovian master equation approach to find the rate equations and Wootter's concurrence to analyze out of thermal equilibrium entanglement dynamics for Dicke bases. The effect of super- and sub-radiant rates on entanglement sudden death is examined for different classes of X-states. It is found that the shorter dark period is achieved at a higher transition rate of a super-radiant state. This approach allows us to analyze the further applications of quantum information technologies. [ABSTRACT FROM AUTHOR]

To explore the effect of the photoperiod on the accumulation and distribution of dry matter in potato, a pot experiment was carried out in 2021 and 2022 with two varieties (Atlantic and Hezuo 88). The varieties were used as the main plot, and light treatments (short-day and long-day) were used as the subplot. The results showed that extended hours of light delayed tuber formation in Hezuo 88, however, the effect was not obvious for the Atlantic. Comprehensive analyses were carried out using the potato developmental process, dynamic equation fitting of the tuber and whole-plant dry matter accumulation, and the dry matter accumulation and distribution rate of each organ of the two varieties under two photoperiods. The two photoperiods had different effects on the parameters of rapid tuber and whole-plant dry matter accumulation: the starting point of the period of the rapid dry matter accumulation (t1), the duration period of the rapid dry matter accumulation (Δt), and the average growth rate of the period of the rapid dry matter accumulation (Vmean). According to comprehensive analysis, tuber dry matter accumulation in Atlantic was the highest under the short-day condition, while Hezuo 88 showed the lowest tuber dry matter accumulation under the long-day condition and was the latest to enter the rapid tuber dry matter accumulation period. The whole-plant dry matter accumulation in Atlantic was the highest under the long-day condition and lowest in Hezuo 88; meanwhile, Hezuo 88 was the latest to enter the rapid whole-plant dry matter accumulation period. In terms of the dry matter accumulation and dry matter partitioning ratio of various organs, Hezuo 88 had the lowest mean tuber dry matter accumulation and partitioning ratio under the long-day condition but the highest mean stem, leaf, root, underground stem, and stolon dry matter partitioning ratio. On the contrary, Atlantic had the highest mean tuber dry matter accumulation and portioning ratio under the short-day condition but the lowest mean stem, leaf, root, underground stem, and stolon dry matter partitioning ratio. It was concluded that different varieties of potato respond differently to the photoperiod. In the case of Hezuo 88, prolonging the photoperiod affected the dynamics and distribution of dry matter accumulation; increased the stem, leaf, root, and underground stem dry matter partitioning ratio; and decreased the tuber dry matter partitioning ratio, which resulted in a decrease in tuber dry matter accumulation and consequently delayed the emergence of the equilibrium period between the aboveground and underground dry matter. [ABSTRACT FROM AUTHOR]

Inthis paper, we consider the reducibility of a class of nonlinear almost periodic Hamiltonian systems. Under suitable hypothesis of analyticity, non-resonant conditions and non-degeneracy conditions, by using KAM iteration, it is shown that the considered Hamiltonian system is reducible to an almost periodic Hamiltonian system with zero equilibrium points for most small enough parameters. As an example, we discuss the reducibility and stability of an almost periodic Hill's equation. [ABSTRACT FROM AUTHOR]

We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels. [ABSTRACT FROM AUTHOR]

In this paper, we shall investigate the large-time behavior of solutions to the Cauchy problem for the three-dimensional bipolar isentropic Euler–Poisson equations with time-dependent damping effects $ -\frac {\mu }{(1+t)^{\lambda }}n_iu_i(i=1, 2) $ − μ (1 + t) λ n i u i (i = 1 , 2) for $ -1 − 1 < λ < 1 , μ > 0. Here, we consider a more general case that the two pressure functions are different and the doping profile is non-zero. Under the assumption that the initial data are close to the constant equilibrium states, we show that the smooth solutions to the Cauchy problem exist uniquely and globally. The algebraic time-decay rates of the solutions toward the constant equilibrium states are also obtained. The main ingredient of the proof is the time-weighted energy method with artfully chosen time-weighted functions. [ABSTRACT FROM AUTHOR]

In this paper, we justify the hydrodynamic limit of the self-organized kinetic (SOK) model with density-dependent parameters. Amic Frouvelle [10] derived this SOK model and formally deduced its hydrodynamic limit to get a self-organized hydrodynamic (SOH) model. Firstly, the local existence of the classical solution of the SOH equations is proved. Then we use Hilbert expansion method and generalized collision invariants (GCIs) hypothesis to construct the solutions of the SOK equations. Finally, we verify that the equilibrium related to the solution of the SOH equations is the limit of solutions of the SOK equations as ϵ → 0. [ABSTRACT FROM AUTHOR]

This paper analyses the stability of cycles within a heteroclinic network formed by six cycles lying in a three-dimensional manifold, for a one-parameter model developed in the context of polymatrix replicator equations. We show the asymptotic stability of the network for a range of parameter values compatible with the existence of an interior equilibrium and we describe an asymptotic technique to decide which cycle (within the network) is visible in numerics. The technique consists of reducing the relevant dynamics to a suitable one-dimensional map, the so-called projective map. The stability of the fixed points of the projective map determines the stability of the associated cycles. The description of this new asymptotic approach is applicable to more general types of networks and is potentially useful in computational dynamics. [ABSTRACT FROM AUTHOR]

We study the one‐dimensional KPZ equation on a large torus, started at equilibrium. The main results are optimal variance bounds in the super‐relaxation regime and part of the relaxation regime. [ABSTRACT FROM AUTHOR]

The ability to accurately predict the shape of a transversely loaded hollow annular membrane is essential to the design of bending-free hollow annular shells of revolution, which requires a further improvement in the hollow annular membrane solution to meet the needs of this accurate prediction. In this paper, the large deflection problem of a transversely loaded hollow annular membrane is reformulated by simultaneously modifying the out-of-plane equilibrium equation and radial geometric equation, and a newer and more refined power series solution is derived. The reason why the classical radial geometry equation induces errors is revealed. The convergence and asymptotic behavior of the power series solution obtained is analyzed numerically. The newly derived solution is compared with the two previously derived solutions graphically, showing that the newly derived solution performs basically as well as expected. In addition, the anticipated use of the hollow and not-hollow annular membrane solutions for the design application of bending-free annular shells of revolution is discussed. [ABSTRACT FROM AUTHOR]

Large values and gradients of stress and strain, triggering concentrated stress and strain, arise in angular areas of a structure. The strain action, leading to the finite loss of contact between structural elements, also triggers concentrated stress. The loss of contact reaches an irregular point and a line on the boundary. The theoretical analysis of the stress–strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous strain is reduced to the study of singular solutions to the homogeneous problem of elasticity theory with power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the area located near the vertex of an angular cutout in the boundary features substantial strain and rotations, and it corresponds to higher values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighborhood of an irregular boundary point. As far as these areas are concerned, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of strain, to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equilibrium equation in the polar system of coordinates for a V-shaped area under the action of temperature-induced strain, taking into account geometric non-linearity and physical linearity. [ABSTRACT FROM AUTHOR]

In the existing literature, there are only two in-plane equilibrium equations for membrane problems; one does not take into account the contribution of deflection to in-plane equilibrium at all, and the other only partly takes it into account. In this paper, a new and exact in-plane equilibrium equation is established by fully taking into account the contribution of deflection to in-plane equilibrium, and it is used for the analytical solution to the well-known Föppl-Hencky membrane problem. The power series solutions of the problem are given, but in the form of the Taylor series, so as to overcome the difficulty in convergence. The superiority of using Taylor series expansion over using Maclaurin series expansion is numerically demonstrated. Under the same conditions, the newly established in-plane equilibrium equation is compared numerically with the existing two in-plane equilibrium equations, showing that the new in-plane equilibrium equation has obvious superiority over the existing two. A new finding is obtained from this study, namely, that the power series method of using Taylor series expansion is essentially different from that of using Maclaurin series expansion; therefore, the recurrence formulas for power series coefficients of using Maclaurin series expansion cannot be derived directly from that of using Taylor series expansion. [ABSTRACT FROM AUTHOR]

The aim of this work is defined by the study of the plane deformation for micropolar isotropic materials in equilibrium theory, where, in addition to displacement and absolute temperature, the particles of the mentioned materials have pores and microrotations. The determined solution to the field equations helps us to study the effect of heat sources and pores on the deformation of the body, which deformation is studied later. [ABSTRACT FROM AUTHOR]

We prove here that the height function associated to non-simple exclusion processes with arbitrary jump-length converges to the solution of the Kardar–Parisi–Zhang SPDE under suitable scaling and renormalization. This extends the work of Dembo and Tsai (Commun Math Phys 341(1):219–261, 2016) for arbitrary jump-length and Goncalves and Jara (Stoch Process Appl 127(12):4029–4052, 2017) for the non-stationary regime. Thus we answer a "Big Picture Question" from the AIM workshop on KPZ and also expand on the almost empty set of non-integrable and non-stationary particle systems for which weak KPZ universality is proven. We use an approximate microscopic Cole-Hopf transform like in Dembo and Tsai (2016) but we develop tools to analyze local statistics of the particle system via local equilibrium and work of Goncalves and Jara (2017). Local equilibrium is done via the one-block step in Guo et al. (Commun Math Phys 118:31, 1988) for path-space/dynamic statistics. [ABSTRACT FROM AUTHOR]

The present study proposes the further validation of a simple mathematical procedure recently proposed by the authors to describe contact and wear evolution in line and point contacts. The procedure assumed that the maximum contact pressure could be determined using Hertz equations and a parabolic pressure profile. The contact half-width was obtained using the equilibrium equation and the Archard wear law. Several cases were selected from the literature, reporting experimental data or Finite Element simulations, and the results were compared to those obtained with the proposed approach. This paper confirms the reliability and potentialities of the proposed analytical procedure, which is capable of providing accurate solutions in case of frictional contacts and at the borders of the contact area, where the main discrepancies were found in the previous study. [ABSTRACT FROM AUTHOR]

Important progress has been made on the standard Laplacian case with mixed partial dissipation and diffusion. The stability problem of the 3D incompressible magnetohydrodynamic (MHD) equations without vertical dissipation but with the fractional velocity dissipation (-Δ)αu and magnetic diαusion (-Δ)βb is unfortunately not often well understood for many ranges of fractional powers. This paper discovers that there are new phenomena with the case α; β ≤ 1. We establish that, if an initial datum (u0; b0) in the Sobolev space H3(R3) is close enough to the equilibrium state, and we replace the terms (-Δ)αu and (-Δ)βb by (-Δh)αu and (-Δh)βb, respectively, the resulting equations with α; β 2 (1 2; 1] then always lead to a steady solution, where Δh = @2x1 + @2x2. [ABSTRACT FROM AUTHOR]

Even for large nonequilibrium systems, local equilibrium subsystems in the presence of strong inhomogeneities may be very small. Such situations typically arise either in the presence of large gradients of temperature, velocity or pressure, or in transition zones between different phases. For small thermodynamic systems, the Euler equation of macroscopic thermodynamics does not hold. One less equation implies one additional degree of freedom, which is the hallmark of small thermodynamic systems. I would like to offer some remarks on the description and role of small local equilibrium subsystems in nonequilibrium thermodynamics. [ABSTRACT FROM AUTHOR]

We investigate exact solutions and the asymptotic dynamics for the Friedmann–Lemaître–Robertson–Walker universe with nonzero spatial curvature in the fourth‐order modified teleparallel gravitational theory known as f(T,B)$$ f\left(T,B\right) $$ theory. We show that the field equations admit a minisuperspace description, and they can reproduce any exact form of the scale factor. Moreover, we calculate the equilibrium points and analyze their stability. We show that Milne and Milne‐like solutions are supported, and the de Sitter universe is provided. To complete our analysis, we use Poincaré variables to investigate the dynamics at infinity. [ABSTRACT FROM AUTHOR]

Some natural phenomena that arise in nonlinear sciences can be sometimes discussed using discrete-time systems. In this work, we investigate the periodicity, boundedness, oscillation, stability, and some exact solutions of nonlinear difference equations with generalized order. Exact solutions are extracted using the traditional iteration and the modulus operator. The stability of the equilibrium points is examined using some well-known theorems. Some numerical examples are also introduced to confirm the validity of the theoretical work. We use MATLAB to implement the numerical part. The used technique can be easily utilized to deal with other rational recursive problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general single species model in a heterogeneous environment of n patches (n ≥ 2), where each patch follows a generalized logistic law. First, we prove the global stability of the model. Second, in the case of perfect mixing, i.e. when the migration rate tends to infinity, the total population follows a generalized logistic law with a carrying capacity which in general is different from the sum of the n carrying capacities. Next, we give some properties of the total equilibrium population and we compute its derivative at no dispersal. In some particular cases, we determine the conditions under which fragmentation and migration can lead to a total equilibrium population which might be greater or smaller than the sum of the n carrying capacities. Finally, we study an example of two-patch model where the first patch follows a logistic law and the second a Richard's law, we give a complete classification of the model parameter space as to whether dispersal is beneficial or detrimental to the sumof two carrying capacities. [ABSTRACT FROM AUTHOR]

We study how a general steady configuration of finitely many point vortices, with Newtonian interaction or generalized surface quasi-geostrophic interactions, can be desingularized into a steady configuration of vortex patches. The configurations can be uniformly rotating, uniformly translating, or completely stationary. Using a technique first introduced by Hmidi and Mateu [Comm. Math. Phys., 350 (2017), pp. 699-747] for vortex pairs, we reformulate the problem for the patch boundaries so that it no longer appears singular in the point vortex limit. Provided the point vortex equilibrium is nondegenerate in a natural sense, solutions can then be constructed directly using the implicit function theorem, yielding asymptotics for the shape of the patch boundaries. As an application, we construct new families of asymmetric translating and rotating pairs, as well as stationary tripoles. We also show how the techniques can be adapted for highly symmetric configurations such as regular polygons, body-centered polygons, and nested regular polygons by integrating the appropriate symmetries into the formulation of the problem. [ABSTRACT FROM AUTHOR]

Two new accelerated fixed-time stable dynamic systems are proposed for solving absolute value equations (AVEs): Ax-|x|-b=0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$Ax-|x|-b=0$$\end{document}. Under some mild conditions, the equilibrium point of the proposed dynamic systems is completely equivalent to the solution of the AVEs under consideration. Meanwhile, we have introduced a new relatively tighter global error bound for the AVEs. Leveraging this finding, we have separately established the globally fixed-time stability of the proposed methods, along with providing the conservative settling-time for each method. Compared with some existing state-of-the-art dynamical methods, preliminary numerical experiments show the effectiveness of our methods in solving the AVEs. [ABSTRACT FROM AUTHOR]

The present work deals with the development of a framework dedicated to the construction of constitutive models with non-local internal variables. Such internal variables allow considering the impact of microstructural changes on the current state of a material point. Non-locality is introduced by considering, not only the spatial average, but also the spatial variance of an internal variable in constitutive relations. The proposed framework relies on continuum thermodynamics to construct the set of constitutive equations. Such a framework allows including some information regarding the spatial distribution of internal variables when constructing non-local models for thermomechanical applications. In contrast with gradient-type models, this strategy does not require additional equilibrium equations and boundary conditions. For the purpose of illustration, some numerical examples are presented. According to the numerical results, the proposed framework can be used to circumvent the difficulties associated with excessive spatial localization or to consider size effects. [ABSTRACT FROM AUTHOR]

Essential to the design and development of circular contact mode capacitive pressure sensors is the ability to accurately predict the contact radius, maximum stress, and shape of a laterally loaded circular membrane in frictionless contact with a concentric circular rigid flat plate. In this paper, this plate/membrane contact problem is solved analytically again by simultaneously improving both out-of-plane equilibrium equation and geometric equation, and a new and more refined closed-form solution is given to meet the need of accurate prediction. The new closed-form solution is numerically discussed in convergence and effectiveness and compared with the previous one, showing that it can greatly improve the prediction accuracy of the contact radius, maximum stress, and shape of the circular membrane in frictionless contact with the rigid flat plate. [ABSTRACT FROM AUTHOR]

We study an equation with periodically distributed delay. The dependence of the equilibrium state stability on the parameters is investigated. We show that the stability region can have a complicated shape. For a long delay, we construct the asymptotic approximations of expressions for the stability region boundary in the parameter space. We construct the normal forms and determine the occurring bifurcations in the critical cases. [ABSTRACT FROM AUTHOR]

We review space and time discretizations of the Cahn-Hilliard equation which are energy stable. In many cases, we prove that a solution converges to a steady state as time goes to infinity. The proof is based on Lyapunov theory and on a Lojasiewicz type inequality. In a few cases, the convergence result is only partial and this raises some interesting questions. Numerical simulations in two and three space dimensions illustrate the theoretical results. Several perspectives are discussed. [ABSTRACT FROM AUTHOR]

Difference equations are used to describe the future pattern of the phenomena that they model. Therefore, obtaining the solutions of these equations plays a crucial role in explaining the future behavior of these applications. It is sometimes impossible to find the solutions of some problems. Thus, this paper studies the stability and the boundedness of the equations... where the coeffcients A and B are positive real numbers and the initial conditions xi for all i = -7;-6;...0; are arbitrary non-zero real numbers. This work also aims to extract the solutions of the considered equation and depicts some 2D diagram for some obtained results. [ABSTRACT FROM AUTHOR]

The Alekseev-type annular membranes here refer to annular membranes fixed at outer edges and connected with a movable, weightless, stiff, con-centric, circular thin plate at inner edges, which were proposed originally by Alekseev for bearing centrally concentrated loads. They are used to bear the pressure acting on both membranes and plates, which was proposed originally in our previous work for developing pressure sensors. The pressure is applied onto an Alekseev-type annular membrane, resulting in the parallel movement of the circular thin plate. Such a movement can be used to develop a capacitive pressure sensor using the circular thin plate as a movable electrode plate of a parallel plate capacitor. The pressure applied can be determined by measuring the change in capacitance of the parallel plate capacitor, based on the closed-form solution for the elastic behavior of Alekseev-type annular membranes. However, the previous closed-form solution is unsuitable for annular membranes with too large deflection, which limits the range of pressure operation of the developed sensors. A new and more refined closed-form solution is presented here by improving simultaneously the out-of-plane equilibrium equation and geometric equation, making it possible to develop capacitive pressure sensors with a wide range of pressure operations. The new closed-form solution is numerically discussed in its convergence and effectiveness and compared with the previous one. Additionally, its beneficial effect on developing the proposed capacitive pressure sensors is illustrated. [ABSTRACT FROM AUTHOR]

In a previous work by the same authors, a hollow annular membrane structure loaded transversely and uniformly was proposed, and its closed-form solution was presented; its anticipated use is for designing elastic shells of revolution. Since the height–span ratio of shells of revolution is generally desired to be as large as possible, to meet the need for high interior space, especially for the as-small-as-possible horizontal thrust at the base of shells of revolution, the closed-form solution should be able to cover annular membranes with a large deflection–outer radius ratio. However, the previously presented closed-form solution cannot meet such an ability requirement, because the previous out-of-plane equilibrium equation used the assumption of a small deflection–outer radius ratio. In this study, the out-of-plane equilibrium equation is re-established without the assumption of a small deflection–outer radius ratio, and a new and more refined closed-form solution is presented. The new closed-form solution is numerically discussed regarding its convergence and effectiveness, and compared with the old one. The new and old closed-form solutions agree quite closely for lightly loaded cases but diverge as the load intensifies. Differences in deflections, especially in stresses, are very significant when the deflection–outer radius ratio exceeds 1/4, indicating that, in this case, the new closed-form solution should be adopted in preference to the old one. [ABSTRACT FROM AUTHOR]

This paper is devoted to kinetic equations without confinement. We investigate the large time behaviour induced by collision operators with fat tailed local equilibria. Such operators have an anomalous diffusion limit. In the appropriate scaling, the macroscopic equation involves a fractional diffusion operator so that the optimal decay rate is determined by a fractional Nash type inequality. At kinetic level we develop an L 2 -hypocoercivity approach and establish a rate of decay compatible with the fractional diffusion limit. [ABSTRACT FROM AUTHOR]

We introduce a new class of Wasserstein-type distances specifically designed to tackle questions concerning stability and convergence to equilibria for kinetic equations. Thanks to these new distances, we improve some classical estimates by Loeper (J Math Pures Appl (9) 86(1):68–79, 2006) and Dobrushin (Funktsional Anal i Prilozhen 13:48–58, 1979) on Vlasov-type equations, and we present an application to quasi-neutral limits. [ABSTRACT FROM AUTHOR]

We provide the first quantitative result of convergence to equilibrium in the context of the spatially homogeneous Boltzmann-Fermi-Dirac equation associated with hard potentials interactions under angular cut-off assumption, providing an explicit – algebraic – rate of convergence to Fermi-Dirac steady solutions. This result complements the quantitative convergence result of [15] and is based upon new uniform-in-time-and- ε L ∞ bound on the solutions. [ABSTRACT FROM AUTHOR]

Resisting mechanisms including compressive membrane action (CMA) and tensile membrane action (TMA) are critical for RC beam-slab structures against progressive collapse. However, due to the difficulties in considering the nonlinear behaviors and beam-slab interactions, limited analytical studies are currently available to accurately determine the whole resistance evolution path, let alone a simplified design model. This study presents a unified analytical model and a design-oriented simplified model to predict the whole resistance displacement of RC beam-slab substructures under internal column loss. Both equivalent uniformly distributed load (EUDL) and concentrate load (CL) conditions have been considered. In the analytical model, the beam-slab system is discretized into interior beams and multiple slab strips with consideration of their interaction. The compatibility and equilibrium conditions, curvature equations, and constitutive laws of concrete and reinforcement are incorporated to analyze each beam and slab strip. In the design model, a new strategy is proposed to decompose the structural resistance of membrane effect into summation of two components, CMA and TMA resistances, with explicit expressions. Both developed models are validated through experimental and numerical results and good agreements are achieved. Results of the analytical model show that ignoring the beam-slab interactions can lead to underestimation of structural resistance, especially during the transition from the CMA to TMA. The locations of loading points should be carefully selected to make sure 12-point loading system effective. A rule is also suggested to determine proper locations. The simplified design method gives slightly conservative predictions of structural resistance, and its calculation is easy for engineers to use. • A unified analytical model is developed to evaluate the compressive and tensile membrane actions in RC beam-slab structures. • A design-oriented simplified model is proposed to predict the whole resistance evolution path of RC structures. • Both equivalent uniformly distributed load and concentrate load conditions are considered. • The developed models are validated through experimental and numerical results and good agreements are achieved. [ABSTRACT FROM AUTHOR]

Motivated by the need for greater understanding of systems that involve interfaces between a nematic liquid crystal, a solid substrate and a passive gas that include nematic–substrate–gas three-phase contact lines, we analyse a two-dimensional static ridge of nematic resting on a solid substrate in an atmosphere of passive gas. Specifically, we obtain the first complete theoretical description for this system, including nematic Young and Young–Laplace equations, and then, making the assumption that anchoring breaking occurs in regions adjacent to the contact lines, we use the nematic Young equations to determine the continuous and discontinuous transitions that occur between the equilibrium states of complete wetting, partial wetting and complete dewetting. In particular, in addition to continuous transitions analogous to those that occur in the classical case of an isotropic liquid, we find a variety of discontinuous transitions, as well as contact-angle hysteresis, and regions of parameter space in which there exist multiple partial wetting states that do not occur in the classical case. [ABSTRACT FROM AUTHOR]

We study the generalized Rayleigh-Stokes problem involving a fractional derivative and nonlinear perturbation. Our aim is to analyze some sufficient conditions ensuring the global solvability, regularity and asymptotic stability of solutions. In particular, if the nonlinearity is Lipschitzian then the mild solution of the mentioned problem becomes a classical one and its convergence to equilibrium point is proved. [ABSTRACT FROM AUTHOR]

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering 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.)

Some natural phenomena are sometimes modeled by using recursive equations. Therefore, extracting exact solutions of such equations plays a significant role in explaining the future pattern of these problems. It is difficult sometimes to establish the exact solutions of some difference equations. Consequently, this work investigates the equilibrium points, local stability, global stability and periodicity of two difference equations. This paper also aims to find the analytic solutions of the respective equations and plots some 2D figures for some obtained results. The used method can be easily applied for other high-order difference equations. [ABSTRACT FROM AUTHOR]

Copyright of Revista Integración is the property of Universidad Industrial de Santander 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.)

TheThis research refers tofocuses on the relationships that occur from the perspective of functional time--space perspective, in correlation to the objects--subjects of reality, establishing a triadic comparison frombased on the concepts of work, proportional dynamic equilibrium, and time--space. Considering the relation time--space--speed, relationship as the matrix of the object reality, this is applicable to both of the object and of the subject, in relation to the activity that is carried out through it or with it. Finally, the technique of equivalence between the equations and several types of these is proposed, which canmay be applicable to a diversityvariety of disciplinary practices, facilitating the analysis of the useful life of the materials, generating a precise evaluation through the categories of time, space, and speed, starting from the equation E=MC², as athe guiding principle of the research process, deriving several possibilities of application through the equation of the proportional dynamic equilibrium equation. [ABSTRACT FROM AUTHOR]

The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular fields to the domain away from the singularities, in completely characterizing the equations of equilibrium and compatibility/incompatibility over the entire domain, is established and illustrated with examples. The uniqueness of the solution to the stress problem of incompatible linear elasticity, allowing for singular fields, is proved. The uniqueness fails when the problem is considered solely in terms of the restricted maps. As further applications of our framework, a general stress solution, in response to point supported body force and defect fields, is derived and a generalized notion of the force acting on a defect is developed. [ABSTRACT FROM AUTHOR]

We consider in this paper a diffusion-convection reaction equation in one space dimension. The main assumptions are about the reaction term, which is monostable, and the diffusivity, which changes sign once or even more than once; then, we deal with a forward-backward parabolic equation. Our main results concern the existence of globally defined traveling waves, which connect two equilibria and cross both regions where the diffusivity is positive and regions where it is negative. We also investigate the monotony of the profiles and show the appearance of sharp behaviors at the points where the diffusivity degenerates. In particular, if such points are interior points, then the sharp behaviors are new and unusual. [ABSTRACT FROM AUTHOR]

This work presents the effect of orientation angles and boundary conditions on the pure bending coefficient of thin rectangular laminated composite plates using Euler-Bernoulli equilibrium equation. The total potential energy function was applied assuming that the thin rectangular laminated composite plate was subjected to only pure bending effect, through this means, the Euler-Bernoulli governing equation of equilibrium was obtained. The governing Equation obtained was minimized to obtain Equation for obtaining the pure bending coefficient of thin rectangular laminated composite plate. Different orientation angles of laminas and boundary conditions were considered to know their effect on pure bending coefficient. Some of the plate boundary condition considered were SSSS, CCCC SSCC and SCSC. The orientation angles considered were 0°0°, 0°90°, 0°0°0°, 0°90° 0°, 0°0°0° 0°, and 0°90°90° 0°. The aspect ratio considered ranges from 1-2 for elastic modular ratio E1/E2 = 25; G12/E2 = 0.5; V12 = 0.25. For any laminated composite plate considered, the orthotropic plate has the same pure bending coefficients but the value increases with increase in the aspect ratio. When other orientations were considered, the change in orientation angles produces change in the pure bending coefficient which increases with increase in aspect ratio. The maximum pure bending coefficient was obtained when SSSS thin rectangular laminated composite Plate was considered for two laminas with orientation 0°90° as 0.0174 while the minimum pure bending coefficient was obtained when CCCC thin laminate composite plate was considered for orthotropic plate as 0.00153. [ABSTRACT FROM AUTHOR]

The work is aimed at the construction of an algorithm for studying the equilibrium states of a reinforced plate near critical points, using the first (cubic terms) nonlinear terms of the potential energy expansion. Using geometrically nonlinear analysis of displacement, deformation and stress fields, the Eigenforms of buckling were calculated and bifurcation solutions and solutions for equilibrium curves with limit points were constructed depending on the initial imperfections. [ABSTRACT FROM AUTHOR]