Using “quasiphotons” to compute wave fields in an elastic medium

Quasiphoton solutions are constructed for longitudinal and transversal waves in an elastic medium. The quasiphotons are then applied to determine the fields of nonstationary high-frequency point sources in a medium with parameters dependent on two Euclidean coordinates.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 89–103, 1985.     

“Quasiphoton” in an active medium. II. An example: The one-dimensional wave equation with a small deviating argument

In the present work we use the example of the one-dimensional wave equation with a small deviating argument to illustrate the constructions of the author's previous paper Quasiphoton in an active medium. The significance of the concept of propagation velocity introduced there, as well as the relation between the change in the propagation frequency along a ray and the parameters characterizing the concentrated solution, are discussed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 136–142, 1986.In conclusion, the author wants to express his sincrere gratitude to I. A. Molotkov for suggesting this problem, and to the participants of the diffraction seminar of LGU-LOMI for stimulating discussions.     

Simulation of mass transport in series arrays of membranes with “active” solute flow

The behaviour of the volume and solute flows across a series array of several membranes is investigated by simulation, using a model based on the linear thermodynamics of irreversible processes. Locally linear phenomenological equations are integrated along the direction of the flows, giving non-linear flow-force relationships whose shape is in good agreement with the observations. The simulation also shows that an asymmetry of the array is required, in order to obtain both the non-linearity of the flows and the coupling between the water and solute transport, when the former is coupled to a chemical reaction (metabolism coupled ‘active transport).     

Interacting Fisher–Wright diffusions in a catalytic medium

We study the longtime behaviour of interacting systems in a randomly fluctuating (space–time) medium and focus on models from population genetics. There are two prototypes of spatial models in population genetics: spatial branching processes and interacting Fisher–Wright diffusions. Quite a bit is known on spatial branching processes where the local branching rate is proportional to a random environment (catalytic medium). Here we introduce a model of interacting Fisher–Wright diffusions where the local resampling rate (or genetic drift) is proportional to a catalytic medium. For a particular choice of the medium, we investigate the longtime behaviour in the case of nearest neighbour migration on the d-dimensional lattice. While in classical homogeneous systems the longtime behaviour exhibits a dichotomy along the transience/recurrence properties of the migration, now a more complicated behaviour arises. It turns out that resampling models in catalytic media show phenomena that are new even compared with branching in catalytic medium. Received: 15 November 1999 / Revised version: 16 June 2000 / Published online: 6 April 2001     

Deductive physiologic analysis in the presence of “will” as an undefined variable

In physiological research, inductive reasoning has traditionally been the rule, rather than the exception. This is because mathematical formulations of human body function inevitably lead to indeterminate situations where there are more unknown quantities than there are equations to describe them. This paper discusses a deductive approach to the study of human body dynamics, where the indeterminateness is usually associated with the presence of “will” as an undefined variable. The point is made that “will” may be quantified by viewing musculoskeletal mechanics in terms of a minimum energy principle. Thus, variational and optimization methods may be employed to generate additional equations of motion which render the problem determinate in a deductive sense. Several examples illustrate the succesful use of variational methods in biodynamic modelling.     

Lamé system of elasticity theory in a plane orthotropic medium

The authors develop a functional-theoretic approach to solving boundary-value problems for the Lamé system of elasticity theory. Special attention is paid to the case of a plane orthotropic medium. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 53, Suzdal Conference-2006, Part 1, 2008.     

Lifetime levels and fracture of polyethylene terephthalate exposed to γ radiation and an aqueous medium

Conclusion 1. An analysis of the lifetime distribution curves obtained by varying the test conditions has revealed discrete lifetime levels in PETP due to the presence in the material of structural defects with different degrees of dangerousness. These defects are found at the edges, at the surface and in the interior of the specimens.2. Water affects irradiated and unirradiated PETP by reducing the probability of failure, rendering the structural defects less dangerous and, as a result, increasing the lifetime and impeding the fracture process.3. On the dose range investigated, rays affect PETP specimens by causing defects that reduce the lifetime and facilitate the fracture process, the defects produced becoming more dangerous as the dose increases.V. I. Lenin Tadzhik State University, Dushanbe. Translated from Mekhanika Polimerov, No. 6, pp. 1060–1064, November–December, 1978.     

Electro-mechanical coupling properties of band gaps in an with periodically attached “spring-mass” resonators

The model of a locally resonant (LR) epoxy/PZT-4 phononic crystal (PC)nanobeam with “spring-mass” resonators periodically attached to epoxy is proposed. The corresponding band structures are calculated by coupling Euler beam theory, nonlocal piezoelectricity theory and plane wave expansion (PWE) method. Three complete band gaps with the widest total width less than 10GHz can be formed in the proposed nanobeam by comprehensively comparing the band structures of three kinds of LR PC nanobeams with...     

Numerical modeling of seismic and acoustic-gravity waves propagation in an “Earth-Atmosphere” model in the presence of wind in the air

In this paper, an effective numerical algorithm for 2.5D seismic and acoustic-gravitational wave propagation is applied to a combined “Earth-Atmosphere” model in the presence of wind in the air. Seismic wave propagation in an elastic half-space is described by a system of first-order dynamic equations of elasticity theory. The propagation of acoustic-gravitational waves in the atmosphere in the presence of wind is described by the linearized Navier-Stokes equations. The algorithm is based on the integral Laguerre transform with respect to time, the finite integral Fourier transform with respect to a spatial coordinate combined with a finite difference method for the reduced problem.     

“What Counts as an Insult?”

In virtue of what does a linguistic act count as an insult? I discuss five main approaches to this question, according to which an insult is determined by (i) the semantic properties of the expression used; (ii) the insulter, her intention, or attitudes; (iii) the addressee and her personal standard; (iv) the features of the speech act performed; and (v) the standard of the relevant social group. I endorse the last, objectivist account, according to which an act x counts as an insult if and only if x is assessed as demeaning when addressed at A by the standard of the relevant social group at t.     

Methodology for selecting packaging alternatives: an “action research” application in the industrial sector

Packaging could and should be considered one of the key elements that promote supply chain performance in terms of efficiency and sustainability. Although, packaging should be considered as a system comprising three different levels (primary, secondary and tertiary), in the industrial sphere design problems are usually centered exclusively on two levels: the primary packaging (the “box”) and the tertiary packaging (the “unit load”). Thus, the main object of this paper is to propose a methodology that facilitates, in a comprehensive way, decision making in packaging system design in order to reduce total costs. To do so, the methodology makes a qualitative and quantitative exploration (including a proposal of a heuristic method) to establish strategies that enable the definition, comparison and selection of an efficient range of package designs (with their associated dimensions) that is efficient and sustainable in an overall way in terms of purchasing costs, logistics costs and environmental costs. Likewise, the authors develop the successful case of a Spanish company implementing successfully the proposed methodology. To develop this case, the authors have adopted an “Action Research” approach. The empirical validation process was developed over almost 10 years.

     

Transient nonlinear optically-thick radiative–convective double-diffusive boundary layers in a Darcian porous medium adjacent to an impulsively started surface: Network simulation solutions

A boundary-layer model is described for the two-dimensional nonlinear transient thermal convection heat and mass transfer in an optically-thick fluid in a Darcian porous medium adjacent to an impulsively started vertical surface, in the presence of significant thermal radiation and buoyancy forces in an (X¹,Y¹,t¹) coordinate system. An algebraic approximation is employed to simplify the integro-differential equation of radiative transfer for unidirectional flux normal to the plate into the boundary-layer regime, by incorporating this flux term in the energy conservation equation. The conservation equations are non-dimensionalized into an (X,Y,T) coordinate system and solved using the Network Simulation Method (NSM), a robust numerical technique which demonstrates high efficiency and accuracy. The transient variation of non-dimensional streamwise velocity component (u) and temperature (T) and concentration (C) functions is computed for various selected values of Stark number (radiation–conduction interaction parameter) and Darcy number. Transient velocity (u) and steady-state local skin friction (τ_X) are also studied for various thermal Grashof number (Gr), species Grashof number (Gm), Schmidt number (Sc) and Stark number (N) values. These computations for the infinite permeability case (Da → ∞) are compared with previous finite difference solutions [Prasad et al. Int J Therm Sci 2007;46(12):1251–8] and shown to be in excellent agreement. An increase in Darcy number is seen to accelerate the flow and boost velocity. A decrease in Stark number (corresponding to an increase in thermal radiation heat transfer contribution) is shown to increase the velocity values. Temperature function is observed to fall in value with a rise in Da and increase with decrease in N (corresponding to an increase in thermal radiation heat transfer contribution). Applications of the study include rocket combustion chambers, astrophysical flows, spacecraft thermal fluid dynamics in debris-laden environments (cosmic dust), heat transfer in forest fire spread, geochemical contamination and ceramic materials processing.     

Stability analysis of Rayleigh�CB��nard convection in a porous medium

In this paper we study the problem of Rayleigh?CBénard convection in a porous medium. Assuming that the viscosity depends on both the temperature and pressure and that it is analytic in these variables we show that the Rayleigh?CBénard equations for flow in a porous media satisfy the idea of exchange of stabilities. We also show that the static conduction solution is linearly stable if and only if the Rayleigh number is less than or equal to a critical Rayleigh number. Finally, we show that a measure of the thermal energy of the fluid decays exponentially which in turn implies that the L² norm of the perturbed temperature and velocity also decay exponentially.     

Corrigendum to “New algebraic properties of an amalgamated algebra along an ideal”

At some point, after publication, we realized that Proposition 4.1(2) and Theorem 4.4 in [2 D’Anna, M., Finocchiaro, C. A., Fontana, M. (2016). New algebraic properties of an amalgamated algebra along an ideal. Commun. Algebra 44(5):1836–1851.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] hold under the assumption (not explicitly declared) that B = f(A)+J. Furthermore, we provide here the exact value for the embedding dimension of A?^fJ, also when B≠f(A)+J, under the hypothesis that J is finitely generated as an ideal of the ring f(A)+J.     

The canonical embedding of an unramified morphism in an ��tale morphism

We show that every unramified morphism ${X\to Y}$ has a canonical and universal factorization ${X\hookrightarrow E_{X/Y}\to Y}$ where the first morphism is a closed embedding and the second is étale (but not separated).     

A systematic approximation for the equations governing convection–diffusion in a porous medium

In order to take into account thermal effects in flows through porous media, one makes ad hoc modifications to Darcy’s equation by appending a term that is similar to the one that is obtained in the Oberbeck–Boussinesq approximation for a fluid. In this short paper we outline a systematic procedure for obtaining an Oberbeck–Boussinesq type of approximation for the flow of a fluid through a porous medium. In addition to establishing the appropriate equation for a flow governed by Darcy’s equation, we proceed to obtain the approximations for flows governed by equations due to Forchheimer and Brinkman.     

Solvability “in the small” of a nonstationary flow problem for an ideal incompressible fluid,I

For the system of Euler equations and the incompressibility equation one considers the following initial-boundary value problem: the field of velocities is prescribed at the initial moment and for all to one gives the following boundary conditions: on the entire boundary of the normal component of the velocity is prescribed and on that part S₁ of the boundary of where inflow occurs one prescribes the value of the velocity =rot |S₂, whose components satisfy a certain necessary equality, derived in the paper. For such a problem one proves its unique solvability on a small interval of time.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 96, pp. 39–56, 1980.