In this paper, based on the homogeneous balance principle and two improved projective Riccati Equations, exact solutions to the general form of BBM equation and the generalized BBM-Burgers equation with nonlinear terms of any order are obtained, which include several kinds of solitary wave solutions and periodic wave solutions. Some of them are found for the first time.

ARTICLE OUTLINE Definition of the Subject and Importance Introduction Granular Matter and its Statistical Mechanics Nonequilibrium statistical mechanics Liouville equation Stationary homogeneous state Macroscopic Balance Equations ”Normal” States and Hydrodynamics Navier-Stokes Approximation Constitutive equations Green-Kubo expressions Hydrodynamic equations Discussion and Outlook Bibliography...

Chondrocytes are the living cells in articular cartilage (AC). They synthesize and maintain the extracellular matrix. Their activity is regulated by the interplay of genetic and environmental factors, such as soluble mediators, extracellular matrix composition, and mechanical factors. The mechanical environment of the chondrocytes has a significant influence on the health of the joint. In past ...

In the present paper, an asymptotic model is constructed for the short-time deformation of an articular cartilage layer modeled as transversely isotropic, transversely homogeneous (TITH) biphasic material. It is assumed that the layer thickness is relatively small compared with the characteristic size of the normal surface load applied to the upper surface of the cartilage layer, while the bott...

Biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability in which strong excitatory synaptic inputs are canceled by strong inhibitory inputs on average, and irregular spiking activity is driven by fluctuating synaptic currents. Most previous studies of balanced networks assume a homogeneous or distance-dependent conn...

Several models in mathematical physics are described by quasilin ear hyperbolic systems with source term which in several cases may become sti Here a suitable central numerical scheme for such problems is developed and application to shallow water equations Broadwell model and Extended Thermodynamics are mentioned The numerical methods are a generalization of the Nessyahu Tadmor scheme to the n...

In order to solve the problems of ill-balanced task allocation, long response time, low throughput rate and poor performance when the cluster system is assigning tasks, we introduce the concept of entropy in thermodynamics into load balancing algorithms. This paper proposes a new load balancing algorithm for homogeneous clusters based on the Maximum Entropy Method (MEM). By calculating the entr...

The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions, etc.), detailed mechanisms include both reversible and irreversible reactions. In this case, the principle of detailed balance cannot be ...