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.     

Diffusion-type operators,Liouville theorems and gradient estimates on complete manifolds

We study Liouville theorems and gradient estimates for solutions of Eq. (1.1) with the help of a diffusion operator and the related geometry.     

Path-integral solution of the one-dimensional Dirac quantum cellular automaton

Quantum cellular automata, which describe the discrete and exactly causal unitary evolution of a lattice of quantum systems, have been recently considered as a fundamental approach to quantum field theory and a linear automaton for the Dirac equation in one dimension has been derived. In the linear case a quantum cellular automaton is isomorphic to a quantum walk and its evolution is conveniently formulated in terms of transition matrices. The semigroup structure of the matrices leads to a new kind of discrete path-integral, different from the well known Feynman checkerboard one, that is solved analytically in terms of Jacobi polynomials of the arbitrary mass parameter.     

On the number of minimal models of a log smooth threefold

We give a topological bound on the number of minimal models of a class of three-dimensional log smooth pairs of log general type.     

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.     

Experimental behaviour of the free surface in a uniform laminar stream

Summary It has been experimentally shown that in a uniform laminar free surface flow, the boundary conditions at the free surface cannot be represented by a simple non-shear condition.This statement is in particular supported by some experiments performed by the author on a high viscosity oil flow in a rectangular pipe. A surface shear viscosity may be introduced in order to characterize the behaviour of the free surface (Boussinesq).The velocity profile was measured along the axis of simmetry of the cross section. The results were in agreement with these of some numerical computations based on the above model. Similar agreement was not achieved on comparing the experimental and theoretical values obtained for the shape factor, a global parameter depending on the shape of the cross section.Such a disagreement cannot be due to experimental error and suggests that the above model is unable.

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Sommario E' fatto sperimentalmente accertato che in un moto laminare uniforme le condizioni al contorno sulla superficie libera non possono essere rappresentate dalla semplice assenza di tensioni tangenziali superficiali. Una chiara conferma viene dalla attuale serie di misure eseguite su una condotta rettangolare percorsa da olio.Per caratterizzare il comportamento della superficie libera si introduce un coefficiente di viscosità tangenziale superficiale, nell'ipotesi di comportamento newtoniano della superficie stessa (Boussinesq).I confronti fra i nostri risultati sperimentali ed i risultati numerici derivanti da tale ipotesi mostrano una possibile concordanza nella distribuzione di velocità sull'asse di simmetria della condotta ma mettono in evidenza andamenti decisamente discordanti per quanto riguarda il comportamento di un coefficiente globale, variabile con la forma della sezione.Tale discordanza non è attribuibile ad errori di misura ed indica l'inadeguatezza di un modello basato sull'ipotesi di comportamento newtoniano della superficie libera.