Recent advances in theoretical models of respiratory mechanics

As an important branch of biomedical engineering, respiratory mechanics helps to understand the physiology of the respiratory system and provides fundamental data for developing such clinical technologies as ventilators. To solve different clinical problems, researchers have developed numerous models at various scales that describe biological and mechanical properties of the respiratory system. During the past decade, benefiting from the continuous accumulation of clinical data and the dramatic progress of biomedical technologies (e.g. biomedical imaging), the theoretical modeling of respiratory mechanics has made remarkable progress regarding the macroscopic properties of the respiratory process, complexities of the respiratory system, gas exchange within the lungs, and the coupling interaction between lung and heart. The present paper reviews the advances in the above fields and proposes potential future projects.     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Supersymmetric classical mechanics

The purpose of the paper is to construct a supersymmetric Lagrangian within the framework of classical mechanics which would be regarded as a candidate for passage to supersymmetric quantum mechanics. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Axially symmetric thermal-stress distribution in an infinite elastic solid containing an annular crack under torsion

Summary In the present work the axially symmetric thermal-stress distribution in an infinite elastic solid containing an annular crack under torsion has been studied. The problem is reduced to triple integral equations which in their turn are reduced to simultaneous algebraic equations by using Hankel transform technique. The quantities of physical interest have also been computed and illustrated graphically for different values of the inner and outer radius of the crack.

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Riassunto In questo lavoro si studia la distribuzione a simmetria assiale dello stress termico in un solido elastico infinito che contiene un crack annulare sotto torsione. Il problema è ridotto alle equazioni integrali triple che per contro sono ridotte ad equazioni algebriche simul tanee usando la tecnica di trasformazione di Hankel. Sono state calcolate ed illustrate graficamente per valori differenti del raggio interno ed esterno del crack anche le quantità di interesse fisico.

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Резюме В работе исследуется аксиально симметричное распределение термических напряжений в бесконечном упрутом твердом теле, содержащем кольцевые трещины при кручении. Рассматриваемая проблема сводится к интегральным уравнениям с тройными интегралами, которые, в свою очередь, сводятся к совместным алгебраическим уравнениям, испрльзуя технику преобразований Ганкеля. Вычисляются величины, представляющие физический интерес. Полученные величины иллюстрируются графически для различных значений внутреннего и внешнего радиусов трещин.

     

Ising model in a quasiperiodic transverse field,percolation, and contact processes in quasiperiodic environments

Quantum Ising models in a transverse field are related to continuous-time percolation processes whose oriented percolation versions are contact processes. We study such models in the presence of quasiperiodic disorder and prove localization in the ground state, no percolation, and extinction, respectively, for sufficiently large disorder.     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

q-Gaussians in the porous-medium equation: stability and time evolution

The stability of q-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, , the porous-medium equation, is investigated through both numerical and analytical approaches. An analysis of the kurtosis of the distributions strongly suggests that an initial q-Gaussian, characterized by an index q_i, approaches asymptotically the final, analytic solution of the porous-medium equation, characterized by an index q, in such a way that the relaxation rule for the kurtosis evolves in time according to a q-exponential, with a relaxation index q_rel ≡q_rel(q). In some cases, particularly when one attempts to transform an infinite-variance distribution (q_i ≥ 5/3) into a finite-variance one (q < 5/3), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary states to the ultimate thermal equilibrium state.     

Consistency of isotropic modified Maxwell theory: Microcausality and unitarity

The Lorentz-violating isotropic modified Maxwell theory minimally coupled to standard Dirac theory is characterized by a single real dimensionless parameter which is taken to vanish for the case of the standard (Lorentz-invariant) theory. A finite domain of positive and negative values of this Lorentz-violating parameter is determined, in which microcausality and unitarity hold. The main focus of this article is on isotropic modified Maxwell theory, but similar results for an anisotropic nonbirefringent case are presented in Appendix A.     

Donor impurity states in zinc-blende GaN/AlGaN quantum well: Quantum confinement and laser-dressed effects

Within the framework of effective-mass approximation, the effects of a laser field on the ground-state donor binding energy in zinc-blende (ZB) GaN/AlGaN quantum well (QW) have been investigated variationally. Numerical results show that the donor binding energy is highly dependent on QW structure parameters and Al composition in ZB GaN/AlGaN QW. The laser field effects are more noticeable on the donor binding energy of an impurity localized inside the QW with small well width and low Al composition. However, for the impurity located in the vicinity of the well edge of the QW, the donor binding energy is insensible to the variation of Al composition, well width and laser field intensity in ZB GaN/AlGaN QW. In particular, the competition effects between laser field and quantum confinement on impurity states have also been investigated in this paper.