Speedy Motions of a Body Immersed in an Infinitely Extended Medium

We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Ψ. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound (runaway effect). Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Ψ(r) diverges at short distances like gr ^−α , g,α>0, by showing that the runaway effect still occurs if α<2.     

Step bunching during the epitaxial growth of a generic binary-compound thin film

A discrete-continuum theory for the step-flow growth by chemical beam or metalorganic vapor-phase epitaxy of a generic binary-compound thin film is developed from basic considerations of continuum physics in accordance with the second law of thermodynamics. Our theory accounts for dissipation, chemical and otherwise; allows for departures from equilibrium; and generalizes the classical, variationally derived Gibbs-Thomson relation along the steps. In contrast to existing models, the diffusing species are coupled through a chemical reaction whereby bulk molecules are crystallized from adatoms attaching to the step edges. The linear stability analysis of the resulting free-boundary problem for a periodic train of rectilinear steps yields pairing in the presence of the normal Ehrlich-Schwoebel barrier for both species, counter to the predictions of standard Burton-Cabrera-Frank models for single-species growth. In particular, we show that the onset of step bunching occurs as long as the adatom equilibrium coverage of either species is sufficiently high, a condition met, e.g., during the epitaxy of gallium arsenide. The physical origin of this instability is to be found in the dependence of the step chemical potential on the jump in the adatom grand canonical potential, a term that couples adjacent terraces and—counter to elastic, entropic, or electrostatic interactions between steps—is attractive.     

Hypertractions and hyperstresses convey the same mechanical information

A strengthened and generalized version of the standard Virtual Work Principle is shown to imply, in addition to bulk and boundary balances, a one-to-one correspondence between surface and edge hypertractions and hyperstress fields in second-gradient continua. When edge hypertractions are constitutively taken null, the hyperstress is shown to take the form it has for a relevant example of second-gradient fluid-like material, referred to as a Navier–Stokes—α fluid.     

The adjoint representation inside the exterior algebra of a simple Lie algebra

For a simple complex Lie algebra g$\mathfrak{g}$ we study the space of invariants A=(?g^?⊗g^?)^g$A={(?{\mathfrak{g}}^{?}\otimes {\mathfrak{g}}^{?})}^{\mathfrak{g}}$, which describes the isotypic component of type g$\mathfrak{g}$ in ?g^?$?{\mathfrak{g}}^{?}$, as a module over the algebra of invariants (?g^?)^g${(?{\mathfrak{g}}^{?})}^{\mathfrak{g}}$. As main result we prove that A   is a free module, of rank twice the rank of g$\mathfrak{g}$, over the exterior algebra generated by all primitive invariants in (?g^?)^g${(?{\mathfrak{g}}^{?})}^{\mathfrak{g}}$, with the exception of the one of highest degree.     

A mathematical model of anorexia and bulimia

In this paper, we propose a mathematical model to study the dynamics of anorexic and bulimic populations. The model proposed takes into account, among other things, the effects of peers' influence, media influence, and education. We prove the existence of three possible equilibria that without media influences are disease‐free, bulimic‐endemic, and endemic. Neglecting media and education effects, we investigate the stability of such equilibria, and we prove that under the influence of media, only one of such equilibria persists and becomes a global attractor. Which of the three equilibria becomes global attractor depends on the other parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure

We develop a loosely coupled fluid‐structure interaction finite element solver based on the Lie operator splitting scheme. The scheme is applied to the interaction between an incompressible, viscous, Newtonian fluid, and a multilayered structure, which consists of a thin elastic layer and a thick poroelastic material. The thin layer is modeled using the linearly elastic Koiter membrane model, while the thick poroelastic layer is modeled as a Biot system. We prove a conditional stability of the scheme and derive error estimates. Theoretical results are supported with numerical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1054–1100, 2015     

Tolerances as images of congruences in varieties defined by linear identities

An identity s = t is linear if each variable occurs at most once in each of the terms s and t. Let T be a tolerance relation of an algebra ${\mathcal{A}}$ in a variety defined by a set of linear identities. We prove that there exist an algebra ${\mathcal{B}}$ in the same variety and a congruence θ of ${\mathcal{B}}$ such that a homomorphism from ${\mathcal{B}}$ onto ${\mathcal{A}}$ maps θ onto T.