Vacuum polarization by a magnetic flux of special rectangular form

We consider the ground state energy of a spinor field in the background of a square well shaped magnetic flux tube. We use the zeta- function regularization and express the ground state energy as an integral involving the Jost function of a two dimensional scattering problem. We perform the renormalization by subtracting the contributions from first several heat kernel coefficients. The ground state energy is presented as a convergent expression suited for numerical evaluation. We discuss corresponding numerical calculations. Using the uniform asymptotic expansion of the special functions entering the Jost function we are able to calculate higher order heat kernel coefficients.Comment: 28 pages, 6 figure

Enthalpy recovery in semicrystalline polymers

Constitutive equations are derived for enthalpy recovery in polymeric glasses after thermal jumps. The model is based on the theory of cooperative relaxation in a version of the trapping concept. It is demonstrated that some critical temperature and some critical degree of crystallinity exist above which the energy landscape becomes homogeneous and structural relaxation ceases.Comment: 13 pages, 5 figures, LATE

Kinetics of Final Degassing of Hydrogen Desorption by Metal Hydrides

The proposed model concerns the 'confluent shrinking core' scenario and reproduces the desorption kinetic after the complete decay of the stoichiometric hydride ($\beta$-phase). The exact analytical solution is obtained, the numerical values are demonstrated by the example of magnesium hydride

Modelling structural relaxation in polymeric glasses using the aggregation-fragmentation concept

Governing equations are derived for the kinetics of physical aging in polymeric glasses. An amorphous polymer is treated as an ensemble of cooperatively rearranged regions (CRR). Any CRR is thought of as a string of elementary clusters (EC). Fragmentation of the string may occur at random time at any border between ECs. Two string can aggregate at random time to produce a new string. The processes of aggregation and fragmentation are treated as thermally activated, and the rate of fragmentation is assumed to grow with temperature more rapidly than that for coalescence. This implies that only elementary clusters are stable at the glass transition temperature, whereas below this temperature, CRRs containing several ECs remain stable as well. A nonlinear differential equation is developed for the distribution of CRRs with various numbers of ECs. Adjustable parameters of the model are found by fitting experimental data in calorimetric tests for polycarbonate, poly(methyl methacrylate), polystyrene and poly(vinyl acetate). For all materials, fair agreement is established between observations and results of numerical simulation. For PVAc, the relaxation spectrum found by matching data in a calorimetric test is successfully employed to predict experimental data in a shear relaxation test.Comment: 25 pages, 15 figure

Influence of Specific Surface Area of Powder on Hydrogen Desorption Kinetics for Metal Hydrides

The observable results for desorption kinetics by powder of metal hydride on the example of mangesium hydride are reproduced with the model formulated in terms of specific surface of powder. A volumetric measurement of hydrogen desorption process is evaluated on an example of wet ball milled magnesium hydride, and can be applied generally for any metal hydride. The exact solution of the model reproduces the shape of experimental curves for desorption process providing a satisfying agreement with experimental data

Modeling the viscoelastoplastic response of amorphous glassy polymers

Constitutive equations are derived for the viscoelastoplastic response of amorphous glassy polymers at isothermal loading with small strains. A polymer is treated as an ensemble of cooperatively relaxing regions (CRR) which rearrange at random times as they are thermally agitated. Rearrangement of CRRs reflects the viscoelastic response of the bulk medium. At low stresses, CRRs are connected with each other, which implies that the macro-strain in a specimen coincides with micro-strains in individual relaxing regions. When the average stress exceeds some threshold level, links between CRRs break and relaxing domains begin to slide one with respect to another. Sliding of micro-domains is associated with the viscoplastic behavior of polymers. Kinetic equations are proposed for viscoplastic strains and for the evolution of the threshold stress. These equations are validated by comparison with experimental data in tensile relaxation tests and in tests with constant strain rates. Fair agreement is demonstrated between results of numerical simulation and observations for a polyurethane resin and poly(methyl methacrylate).Comment: 19 pages, 12 figure

Non-entropic theory of rubber elasticity: flexible chains grafted on a rigid surface

The elastic response is studied of a single flexible chain grafted on a rigid plane and an ensemble of non-interacting tethered chains. It is demonstrated that the entropic theory of rubber elasticity leads to conclusions that disagree with experimental data. A modification of the conventional approach is proposed, where the end-to-end distribution function (treated as the governing parameter) is replaced by the average energy of a chain. It is revealed that this refinement ensures an adequate description of the mechanical behavior of flexible chains. Results of numerical simulation are compared with observations on uniaxial compression of a layer of grafted chains, and an acceptable agreement is shown between the model predictions and the experimental data. Based on the analysis of combined compression and shear, a novel micro-mechanism is proposed for the reduction of friction of polymer melts at rigid walls.Comment: 16 pages, 2 figure

Non-entropic theory of rubber elasticity: flexible chains with weak excluded-volume interactions

Strain energy density is calculated for a network of flexible chains with weak excluded-volume interactions (whose energy is small compared with thermal energy). Constitutive equations are developed for an incompressible network of chains with segment interactions at finite deformations. These relations are applied to the study of uniaxial and equi-biaxial tension (compression), where the stress--strain diagrams are analyzed numerically. It is demonstrated that intra-chain interactions (i) cause an increase in the Young's modulus of the network and (ii) induce the growth of stresses (compared to an appropriate network of Gaussian chains), which becomes substantial at relatively large elongation ratios. The effect of excluded-volume interactions on the elastic response strongly depends on the deformation mode, in particular, it is more pronounced at equi-biaxial tension than at uniaxial elongation.Comment: 21 pages, 3 figure

Stiffness of polymer chains

A formula is derived for stiffness of a polymer chain in terms of the distribution function of end-to-end vectors. This relationship is applied to calculate the stiffness of Gaussian chains (neutral and carrying electric charges at the ends), chains modeled as self-avoiding random walks, as well as semi-flexible (worm-like and Dirac) chains. The effects of persistence length and Bjerrum's length on the chain stiffness are analyzed numerically. An explicit expression is developed for the radial distribution function of a chain with the maximum stiffness.Comment: 21 pages, 6 figure

On a local formalism for time evolution of dynamical systems

The formalism of local maximization for entropy gradient producing the evolution and dynamical equations for closed systems. It eliminates the inconsistency between the reversibilty of time in dynamical equations and the strict direction of irreversible evolution for complex systems, causality contradictions and ambiguity of time flow in different systems. Independently it leads to basic principles of special relativity