6,330 research outputs found
Viscoplasticity: A thermodynamic formulation
A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity, as it applies to initially isotropic materials. Three fundamental internal state variables are admitted. They are: a tensor valued back stress for kinematic effects, and the scalar valued drag and yield strengths for isotropic effects. All three are considered to phenomenologically evolve according to competitive processes between strain hardening, strain induced dynamic recovery, and time induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is put forth. This theory allows each of the three fundamental internal variables to be composed as a sum of independently evolving constituents
A viscoplastic theory applied to copper
A phenomenologically based viscoplastic model is derived for copper. The model is thermodynamically constrained by the condition of material dissipativity. Two internal state variables are considered. The back stress accounts for strain-induced anisotropy, or kinematic hardening. The drag stress accounts for isotropic hardening. Static and dynamic recovery terms are not coupled in either evolutionary equation. The evolution of drag stress depends on static recovery, while the evolution of back stress depends on dynamic recovery. The material constants are determined from isothermal data. Model predictions are compared with experimental data for thermomechanical test conditions. They are in good agreement at the hot end of the loading cycle, but the model overpredicts the stress response at the cold end of the cycle
On the thermodynamics of stress rate in the evolution of back stress in viscoplasticity
A thermodynamic foundation using the concept of internal state variables is presented for the kinematic description of a viscoplastic material. Three different evolution equations for the back stress are considered. The first is that of classical, nonlinear, kinematic hardening. The other two include a contribution that is linear in stress rate. Choosing an appropriate change in variables can remove this stress rate dependence. As a result, one of these two models is shown to be equivalent to the classical, kinematic hardening model; while the other is a new model, one which seems to have favorable characteristics for representing ratchetting behavior. All three models are thermodynamically admissible
Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
The critical behavior of long straight rigid rods of length (-mers) on
square and triangular lattices at intermediate density has been studied. A
nematic phase, characterized by a big domain of parallel -mers, was found.
This ordered phase is separated from the isotropic state by a continuous
transition occurring at a intermediate density . Two analytical
techniques were combined with Monte Carlo simulations to predict the dependence
of on , being . The first involves
simple geometrical arguments, while the second is based on entropy
considerations. Our analysis allowed us also to determine the minimum value of
(), which allows the formation of a nematic phase on a
triangular lattice.Comment: 23 pages, 5 figures, to appear in The Journal of Chemical Physic
D3 branes in a Melvin universe: a new realm for gravitational holography
The decoupling limit of a certain configuration of D3 branes in a Melvin
universe defines a sector of string theory known as Puff Field Theory (PFT) - a
theory with non-local dynamics but without gravity. In this work, we present a
systematic analysis of the non-local states of strongly coupled PFT using
gravitational holography. And we are led to a remarkable new holographic
dictionary. We show that the theory admits states that may be viewed as brane
protrusions from the D3 brane worldvolume. The footprint of a protrusion has
finite size - the scale of non-locality in the PFT - and corresponds to an
operator insertion in the PFT. We compute correlators of these states, and we
demonstrate that only part of the holographic bulk is explored by this
computation. We then show that the remaining space holographically encodes the
dynamics of the D3 brane tentacles. The two sectors are coupled: in this
holographic description, this is realized via quantum entanglement across a
holographic screen - a throat in the geometry - that splits the bulk into the
two regions in question. We then propose a description of PFT through a direct
product of two Fock spaces - akin to other non-local settings that employ
quantum group structures.Comment: 44 pages, 13 figures; v2: minor corrections, citations added; v3:
typos corrected in section on local operators, some asymptotic expansions
improved and made more consistent with rest of paper in section on non-local
operator
T-duality and Differential K-Theory
We give a precise formulation of T-duality for Ramond-Ramond fields. This
gives a canonical isomorphism between the "geometrically invariant" subgroups
of the twisted differential K-theory of certain principal torus bundles. Our
result combines topological T-duality with the Buscher rules found in physics.Comment: 23 pages, typos corrected, submitted to Comm.Math.Phy
Twisted K-Theory of Lie Groups
I determine the twisted K-theory of all compact simply connected simple Lie
groups. The computation reduces via the Freed-Hopkins-Teleman theorem to the
CFT prescription, and thus explains why it gives the correct result. Finally I
analyze the exceptions noted by Bouwknegt et al.Comment: 16 page
The Elliptic curves in gauge theory, string theory, and cohomology
Elliptic curves play a natural and important role in elliptic cohomology. In
earlier work with I. Kriz, thes elliptic curves were interpreted physically in
two ways: as corresponding to the intersection of M2 and M5 in the context of
(the reduction of M-theory to) type IIA and as the elliptic fiber leading to
F-theory for type IIB. In this paper we elaborate on the physical setting for
various generalized cohomology theories, including elliptic cohomology, and we
note that the above two seemingly unrelated descriptions can be unified using
Sen's picture of the orientifold limit of F-theory compactification on K3,
which unifies the Seiberg-Witten curve with the F-theory curve, and through
which we naturally explain the constancy of the modulus that emerges from
elliptic cohomology. This also clarifies the orbifolding performed in the
previous work and justifies the appearance of the w_4 condition in the elliptic
refinement of the mod 2 part of the partition function. We comment on the
cohomology theory needed for the case when the modular parameter varies in the
base of the elliptic fibration.Comment: 23 pages, typos corrected, minor clarification
Global Spinors and Orientable Five-Branes
Fermion fields on an M-theory five-brane carry a representation of the double
cover of the structure group of the normal bundle. It is shown that, on an
arbitrary oriented Lorentzian six-manifold, there is always an Sp(2) twist that
allows such spinors to be defined globally. The vanishing of the arising
potential obstructions does not depend on spin structure in the bulk, nor does
the six-manifold need to be spin or spin-C. Lifting the tangent bundle to such
a generalised spin bundle requires picking a generalised spin structure in
terms of certain elements in the integral and modulo-two cohomology of the
five-brane world-volume in degrees four and five, respectively.Comment: 18 pages, LaTeX; v2: version to appear in JHE
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