3,341 research outputs found
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 (-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
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
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
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