Thermodynamics of high-elastic deformation of polyurethanes

The thermoelastic behavior of polyurethanes based on diethylene glycol adipate and tolylene diisocyanate with different network densities has been investigated in connection with their tensile deformation. The change in entropy and internal energy is calculated at strains up to 100%. It is shown that during extension both the entropy and the internal energy decrease. The reduction in internal energy depends on the relative importance of the physical and chemical bonds in the network and is attributable to the redistribution of intermolecular bonds.Mekhanika Polimerov, Vol. 4, No. 3, pp. 450–453, 1968     

Large Data Existence Result for Unsteady Flows of Inhomogeneous Shear-Thickening Heat-Conducting Incompressible Fluids

We consider unsteady flows of inhomogeneous, incompressible, shear-thickening and heat-conducting fluids where the viscosity depends on the density, the temperature and the shear rate, and the heat conductivity depends on the temperature and the density. For any values of initial total mass and initial total energy we establish the long-time existence of weak solution to internal flows inside an arbitrary bounded domain with Lipschitz boundary.     

Energy balance invariance for interacting particle systems

This paper studies the principle of invariance of balance of energy and its consequences for a system of interacting particles under groups of transformations. Balance of energy and its invariance is first examined in Euclidean space. Unlike the case of continuous media, it is shown that conservation and balance laws do not follow from the assumption of invariance of balance of energy under time-dependent isometries of the ambient space. However, the postulate of invariance of balance of energy under arbitrary diffeomorphisms of the ambient (Euclidean) space, does yield the correct conservation and balance laws. These ideas are then extended to the case when the ambient space is a Riemannian manifold. Pairwise interactions in the case of geodesically complete Riemannian ambient manifolds are defined by assuming that the interaction potential explicitly depends on the pairwise distances of particles. Postulating balance of energy and its invariance under arbitrary time-dependent spatial diffeomorphisms yields balance of linear momentum. It is seen that pairwise forces are directed along tangents to geodesics at their end points. One also obtains a discrete version of the Doyle–Ericksen formula, which relates the magnitude of internal forces to the rate of change of the interatomic energy with respect to a discrete metric that is related to the background metric.     

Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping

We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation.     

Maximum entropy principle closure for 14-moment system for a non-polytropic gas

In this paper, we consider a rarefied polyatomic gas with a non-polytropic equation of state. We use the variational procedure of maximum entropy principle (MEP) to obtain the closure of the binary hierarchy of 14 moments associated with the Boltzmann equation in which the distribution function depends also on the energy of internal modes. The closed partial differential system is symmetric hyperbolic and the Cauchy problem is well-posed. In the limiting case of polytropic gas in which the internal energy is a linear function of the temperature, we find, as a special case, the previous results of Pavić et al. (Physica A 392:1302–1317, 2013). This paper, therefore, completes the equivalence between the closure obtained in the phenomenological rational extended thermodynamics theory and the one obtained by the MEP for general non-polytropic gas.

     

Theoretical study and numerical simulation of textiles

We propose a new approach for developing continuum models fit to describe the mechanical behavior of textiles. We develop a physically motivated model, based on the properties of the yarns, which can predict and simulate the textile behavior. The approach relies on the selection of a suitable topological model for the patch of the textile, coupled with constitutive models for the yarn behavior. The textile structural configuration is related to the deformation through an energy functional, which depends on both the macroscopic deformation and the distribution of internal nodes. We determine the equilibrium positions of these latter, constrained to an assigned macroscopic deformation. As a result, we derive a macroscopic strain energy function, which reflects the possibly nonlinear character of the yarns as well as the anisotropy induced by the microscopic topological pattern. By means of both analytical estimates and numerical experiments, we show that our model is well suited for both academic test cases and real industrial textiles, with particular emphasis on the tricot textile.     

Energy balance invariance for interacting particle systems

This paper studies the principle of invariance of balance of energy and its consequences for a system of interacting particles under groups of transformations. Balance of energy and its invariance is first examined in Euclidean space. Unlike the case of continuous media, it is shown that conservation and balance laws do not follow from the assumption of invariance of balance of energy under time-dependent isometries of the ambient space. However, the postulate of invariance of balance of energy under arbitrary diffeomorphisms of the ambient (Euclidean) space, does yield the correct conservation and balance laws. These ideas are then extended to the case when the ambient space is a Riemannian manifold. Pairwise interactions in the case of geodesically complete Riemannian ambient manifolds are defined by assuming that the interaction potential explicitly depends on the pairwise distances of particles. Postulating balance of energy and its invariance under arbitrary time-dependent spatial diffeomorphisms yields balance of linear momentum. It is seen that pairwise forces are directed along tangents to geodesics at their end points. One also obtains a discrete version of the Doyle–Ericksen formula, which relates the magnitude of internal forces to the rate of change of the interatomic energy with respect to a discrete metric that is related to the background metric. Dedicated to the memory of Shahram Kavianpour (1975-2007). Jerrold E. Marsden: Research partially supported by the California Institute of Technology and NSF-ITR Grant ACI-0204932. Arash Yavari: Research supported by the Georgia Institute of Technology.     

Using intelligent agents for pro-active,real-time urban intersection control

The usability and effectiveness of traffic control systems greatly depends on its ability of reacting upon traffic patterns and permutations. In this research we investigate the applicability of autonomous intelligent agents in Urban Traffic Control (UTC), and why these artificial intelligent strategies are useful in UTC. We propose a system that autonomously can adapt itself, based upon internal rules and its environment, at changing environments. Both long term changes as well as short term changes are accounted for in different manner. The UTC model is primarily based on several Intelligent Traffic Signalling Agents (ITSA) and some authority agents. This approach enables us to use a UTC system, based on agent technology, capable of responding to traffic conditions in real-time. The system can maintain its integrity and stability within the overall transportation system. Due to its pro-active behaviour we are able to make better use of the capacity of intersections.     

Unit commitment in electricity pool markets

We consider an electricity generator making offers of energy into an electricity pool market over a horizon of several trading periods (typically a single trading day). The generator runs a set of generating units with given start-up costs, shut-down costs and operating ranges. At the start of each trading period the generator must submit to the pool system operator a new supply curve defining quantities of offered energy and the prices at which it wants these dispatched. The amount of dispatch depends on the supply curve offered along with the offers of the other generators and market demand, both of which are random, but do not change in response to the actions of the generator we consider. After dispatch the generator determines which units to run in the current trading period to meet the dispatch. The generator seeks a supply function that maximizes its expected profit. We describe an optimization procedure based on dynamic programming that can be used to construct optimal offers in successive time periods over a fixed planning horizon.     

Energy and coherence loss rates in a one-dimensional vibrational system interacting with a bath

We consider the problem of the dynamics of a Gaussian wave packet in a one-dimensional harmonic ocsillator interacting with a bath. This problem arises in many chemical and biochemical applications related to the dynamics of chemical reactions. We take the bath-oscillator interaction into account in the framework of the Redfield theory. We obtain closed expressions for Redfield-tensor elements, which allows finding the explicit time dependence of the average vibrational energy. We show that the energy loss rate is temperature-independent, is the same for all wave packets, and depends only on the spectral function of the bath. We determine the degree of coherence of the vibrational motion as the trace of the density-matrix projection on a coherently moving wave packet. We find an explicit expression for the initial coherence loss rate, which depends on the wave packet width and is directly proportional to the intensity of the interaction with the bath. The minimum coherence loss rate is observed for a “coherent” Gaussian wave packet whose width corresponds to the oscillator frequency. We calculate the limiting value of the degree of coherence for large times and show that it is independent of the structural characteristics of the bath and depends only on the parameters of the wave packet and on the temperature. It is possible that residual coherence can be preserved at low temperatures. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 130–144, October, 2007.     

Reformulation in mathematical programming: An application to quantum chemistry

This paper concerns the application of reformulation techniques in mathematical programming to a specific problem arising in quantum chemistry, namely the solution of Hartree-Fock systems of equations, which describe atomic and molecular electronic wave functions based on the minimization of a functional of the energy. Their traditional solution method does not provide a guarantee of global optimality and its output depends on a provided initial starting point. We formulate this problem as a multi-extremal nonconvex polynomial programming problem, and solve it with a spatial Branch-and-Bound algorithm for global optimization. The lower bounds at each node are provided by reformulating the problem in such a way that its convex relaxation is tight. The validity of the proposed approach was established by successfully computing the ground-state of the helium and beryllium atoms.     

Computation of localization degree in the sense of the Anderson criterion for a one-dimensional diagonally disordered system

For a one-dimensional diagonally disordered half-infinite chain, we consider the problem of finding the limit value as t → ∞ of the average excitation density D at the edge site of the chain under the condition that the excitation is localized at this site at t = 0. For a binary disordered chain, we obtain an expression for D that is exact in the small defect concentration limit for an arbitrary defect energy. In this case, the density D depends nonanalytically on the energy. We obtain an expression for D in the case of an arbitrary small diagonal disorder. We also calculate the relative contribution to D from states with a given energy. All the obtained results agree well with the computer simulation data.     

Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate minimum of the potential

We study the semi-classical trace formula at a critical energy level for a Schrödinger operator on Rn. We assume here that the potential has a totally degenerate critical point associated to a local minimum. The main result, which computes the contribution of this equilibrium, is valid for all time in a compact and establishes the existence of a total asymptotic expansion whose top order coefficient depends only on the germ of the potential at the critical point.     

Nonlinear mobility continuity equations and generalized displacement convexity

We consider the geometry of the space of Borel measures endowed with a distance that is defined by generalizing the dynamical formulation of the Wasserstein distance to concave, nonlinear mobilities. We investigate the energy landscape of internal, potential, and interaction energies. For the internal energy, we give an explicit sufficient condition for geodesic convexity which generalizes the condition of McCann. We take an eulerian approach that does not require global information on the geodesics. As by-product, we obtain existence, stability, and contraction results for the semigroup obtained by solving the homogeneous Neumann boundary value problem for a nonlinear diffusion equation in a convex bounded domain. For the potential energy and the interaction energy, we present a nonrigorous argument indicating that they are not displacement semiconvex.     

Initial boundary value problem for the 3D quasilinear hyperbolic equations with nonlinear damping

We investigate global existence and asymptotic behavior of the 3D quasilinear hyperbolic equations with nonlinear damping on a bounded domain with slip boundary condition, which describes the propagation of heat waves for rigid solids at very low temperature, below about 20 K. The global existence and uniqueness of classical solutions are obtained when the initial data are near its equilibrium. Time asymptotically, the internal energy is conjectured to satisfy the porous medium equation and the heat flux obeys the classical Darcy’s-type law. Based on energy estimates, we show that the classical solution converges to steady state exponentially fast in time. Moreover, we also verify that the same is true for the corresponding initial boundary value problem of porous medium equation and thus justifies the validity of Darcy’s-type law in large time.     

Optimization of the motion in a resistant medium of a body with a movable internal mass

The motion, in a resistant medium, of a system consisting of a rigid body and movable internal mass is considered. The external medium acts on the body by a force that piecewise linearly depends on its speed. The class of periodic motions of the internal mass for which the speed of this mass relative to the body is piecewise constant is studied. It is shown that, under certain conditions, the forward movement of the whole system in the medium is possible. The average speed of this movement over a period is determined. Optimal parameters of the motion of the internal mass for which the average speed of the system movement is maximal are found.     

A classification of DEA models when the internal structure of the Decision Making Units is considered

We classify the contributions of DEA literature assessing Decision Making Units (DMUs) whose internal structure is known. Starting from an elementary framework, we define the main research areas as shared flow, multilevel and network models, depending on the assumptions they are subject to. For each model category, the principal mathematical formulations are introduced along with their main variants, extensions and applications. We also discuss the results of aggregating efficiency measures and of considering DMUs as submitted to a central authority that imposes constraints or targets on them. A common feature among the several models is that the efficiency evaluation of the DMU depends on the efficiency values of its subunits thereby increasing the discrimination power of DEA methodology with respect to the black box approach.     

Financial scenario generation for stochastic multi-stage decision processes as facility location problems

The quality of multi-stage stochastic optimization models as they appear in asset liability management, energy planning, transportation, supply chain management, and other applications depends heavily on the quality of the underlying scenario model, describing the uncertain processes influencing the profit/cost function, such as asset prices and liabilities, the energy demand process, demand for transportation, and the like. A common approach to generate scenarios is based on estimating an unknown distribution and matching its moments with moments of a discrete scenario model. This paper demonstrates that the problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function. We show that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance. The resulting optimization problem can be viewed as a multi-dimensional facility location problem, for which at least good heuristic algorithms exist. For multi-stage problems, a scenario tree is constructed as a nested facility location problem. Numerical convergence results for financial mean-risk portfolio selection conclude the paper.     

Energy Spectrum Width and Nonequilibrium Energy of Rayleigh Waves Scattered on a Two-Dimensional Near-Surface Electron Layer

We obtain expressions for the energy spectrum widths of Rayleigh waves corresponding to their deformational coupling to Fermi and Boltzmann electrons in a two-dimensional layer near the surface of a semibounded solid. We evaluate the nonequilibrium energy of Rayleigh waves that depends on these widths and is caused by the same coupling to the corresponding hot electrons. We show that this energy is independent of the degeneracy degree of the electrons and is given by the mean energy of free Rayleigh waves heated up to temperature of the electrons. We find conditions under which the thermodynamics is determined by this nonequilibrium energy of Rayleigh waves in films of a certain thickness with Fermi electrons near the surface and by the equilibrium energy of bulk phonons in thicker samples. All the results are obtained using the Keldysh diagram technique applied to the case of semibounded media.