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The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…
An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically…
We present a new formula to numerically construct configurations in rotational equilibrium, which consist of multiple layers. Each layer rotates uniformly or differentially according to cylindrical rotation-laws that are different from…
We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…
Bodies of density one half (of the fluid in which they are immersed) that can float in all orientations are investigated. It is shown that expansions starting from and deforming the (hyper)sphere are possible in arbitrary dimensions and…
Entangled polymers are an important class of materials for their toughness, processability, and functionalizability. However, physically detailed modeling of highly entangled polymers can prove challenging, especially as one considers…
Using the volume averaging technique of Jackson (1997), we derive a set of two-fluid equations that describe the dynamics of a mono-disperse non-Brownian colloidal suspension in the semi-dilute regime. The equations are tensorial and can be…
Systems whose potential energies consists of pieces that scale as r^-2 together with pieces that scale as r^2, show no violent relaxation to Virial equilibrium but may pulsate at considerable amplitude for ever. Despite this pulsation these…
This paper proposes a systematic and novel component level co-rotational (CR) framework, for upgrading existing 3D continuum finite elements to flexible multibody analysis. Without using any model reduction techniques, the high efficiency…
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
We consider the problem of shaping the transient step response of nonlinear systems to satisfy a class of integral constraints. Such constraints are inherent in hybrid energy systems consisting of energy sources and storage elements. While…
We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…
In this work I develop a new framework for anisotropic hydrodynamics that generalizes the leading order of the hydrodynamic expansion to the full (3+1)-dimensional anisotropic massive case. Following previous works, my considerations are…
For some non-linear field theories which allow for soliton solutions, submodels with infinitely many conservation laws can be defined. Here we investigate the symmetries of the submodels, where in some cases we find a symmetry enhancement…
We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully…
Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents…
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…
Multipole expansions depend on the coordinate system, so that coefficients of multipole moments can be set equal to zero by an appropriate choice of coordinates. Therefore, it is meaningless to say that a physical system has a nonvanishing…
In this paper, we are concerned with a model of polytropic gas flow, which consists the mass equation, the momentum equation and a varying entropy equation. First, a new technique, to set up a relation between the Riemann invariants of the…