stability of foundations near slopes is one of the important and complicated problems in geotechnical engineering, which has been investigated by various methods such as limit equilibrium, limit analysis, slip-line, finite element and discrete element. the complexity of this problem is resulted from the combination of two probable failures: foundation failure and overall slope failure. the curr...

An analytical solution for a self-consistent particle equilibrium distribution in an RF field with uniform transverse focusing is applied to the problem of the high brightness beam current limit. The distribution function in phase space is determined as a stationary function of the energy integral. Particle distribution of the bright beam always tends to such a shape that the space charge beam ...

A ratio–dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E∗ at the positive octant is unstable. Here we characterize the existence of Hopf bifurcations for the systems. In particular we provide a positive answer to the above question...

A theory for noise-driven subcritical instabilities in spatially extended systems is put forward. The theory allows one to calculate the critical bifurcation parameter for a first-order phase transition in such non-equilibrium systems in the thermodynamic limit and analyse the mechanism of phase transition. Two examples with distinctive features are studied in detail to demonstrate the usefulne...

The existence of an equilibrium in an extended Walrasian economic model of exchange is confirmed constructively by an iterative scheme. In this scheme, truncated variational inequality problems are solved in which the agents’ budget constraints are relaxed by a penalty representation. Epi-convergence arguments are employed to show that, in the limit, a virtual equilibrium is obtained, if not ac...

Relaxation of the thermal Casimir or van der Waals force (the high temperature limit of the Casimir force) for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit, the usual zero frequency Matsubara mode component of the Casimir force is ...

Based on Rabinovich system, a 4D Rabinovich system is generalized to study hidden attractors, multiple limit cycles and boundedness of motion. In the sense of coexisting attractors, the remarkable finding is that the proposed system has hidden hyperchaotic attractors around a unique stable equilibrium. To understand the complex dynamics of the system, some basic properties, such as Lyapunov exp...

The IPCC suggests a “likely range” for the equilibrium climate sensitivity of atmospheric carbon dioxide. At the recommended upper limit of this likely range, the calculated temperature rise (using the quasi-steady approximation) is found to be substantially higher than the observed historical data. Theoretically, the quasi-steady response is indeed expected to be higher than the actual (time d...

We study the dynamics of a Hamiltonian system of N classical spins with infiniterange interaction. We present numerical results which confirm the existence of metaequilibrium Quasi Stationary States (QSS), characterized by non-Gaussian velocity distributions, anomalous diffusion, Lévy walks and dynamical correlation in phase-space. We show that the Termodynamic Limit (TL) and the Infinite-Time ...

We considerN single server infinite buffer queues with service rate β. Customers arrive at rate Nα, choose L queues uniformly, and join the shortest. We study the processes t ∈ R+ 7→ R t = (R t (k))k∈N for large N , where R t (k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We con...