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

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

Ground Heave Due to Pile Driving

The factors which influence ground heave due to pile driving outside the construction site are discussed. Elevation survey data are presented for nine case studies in the Boston area where the subsoil conditions consist of an insensitive clay deposit in the range of 60 to 110 feet thick. Curves of heave vs. normalized distance exhibit a trend of increasing heave with increased volumetric displacement ratio. Patterns of ground heave typically occur as radially shaped contours decreasing in magnitude away from pile driving. Building and ground movements observed several years after completion of pile driving indicate that the heave is temporary, and is followed by a net settlement. Eight factors which influence heave due to pile driving are briefly discussed. Pile driving can be designed to minimize or prevent heave by properly planning the methods and sequence of pile installation

Dynamics of Diblock Copolymers in Dilute Solutions

We consider the dynamics of freely translating and rotating diblock (A-B), Gaussian copolymers, in dilute solutions. Using the multiple scattering technique, we have computed the diffusion and the friction coefficients D_AB and Zeta_AB, and the change Eta_AB in the viscosity of the solution as functions of x = N_A/N and t = l_B/l_A, where N_A, N are the number of segments of the A block and of the whole copolymer, respectively, and l_A, l_B are the Kuhn lengths of the A and B blocks. Specific regimes that maximize the efficiency of separation of copolymers with distinct "t" values, have been identified.Comment: 20 pages Revtex, 7 eps figures, needs epsf.tex and amssymb.sty, submitted to Macromolecule

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

A Formalism for Scattering of Complex Composite Structures. 1 Applications to Branched Structures of Asymmetric Sub-Units

We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural scattering in terms of three equations expressing the sub-unit scattering. The structural scattering expressions allows a composite structures to be used as sub-units within the formalism itself. This allows the scattering expressions for complex hierarchical structures to be derived with great ease. The formalism is furthermore generic in the sense that the scattering due to structural connectivity is completely decoupled from internal structure of the sub-units. This allows sub-units to be replaced by more complex structures. We illustrate the physical interpretation of the formalism diagrammatically. By applying a self-consistency requirement we derive the pair distributions of an ideal flexible polymer sub-unit. We illustrate the formalism by deriving generic scattering expressions for branched structures such as stars, pom-poms, bottle-brushes, and dendrimers build out of asymmetric two-functional sub-units.Comment: Complete rewrite generalizing the formalism to arbitrary functional sub-units and including a new Feynmann like diagrammatic interpretatio

Some Relations between Twisted K-theory and E8 Gauge Theory

Recently, Diaconescu, Moore and Witten provided a nontrivial link between K-theory and M-theory, by deriving the partition function of the Ramond-Ramond fields of Type IIA string theory from an E8 gauge theory in eleven dimensions. We give some relations between twisted K-theory and M-theory by adapting the method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we construct the twisted K-theory torus which defines the partition function, and also discuss the problem from the E8 loop group picture, in which the Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this, we encounter some mathematics that is new to the physics literature. In particular, the eta differential form, which is the generalization of the eta invariant, arises naturally in this context. We conclude with several open problems in mathematics and string theory.Comment: 23 pages, latex2e, corrected minor errors and typos in published versio

Consistent coarse-graining strategy for polymer solutions in the thermal crossover from Good to Theta solvent

We extend our previously developed coarse-graining strategy for linear polymers with a tunable number n of effective atoms (blobs) per chain [D'Adamo et al., J. Chem. Phys. 137, 4901 (2012)] to polymer systems in thermal crossover between the good-solvent and the Theta regimes. We consider the thermal crossover in the region in which tricritical effects can be neglected, i.e. not too close to the Theta point, for a wide range of chain volume fractions Phi=c/c* (c* is the overlap concentration), up to Phi=30. Scaling crossover functions for global properties of the solution are obtained by Monte-Carlo simulations of the Domb-Joyce model. They provide the input data to develop a minimal coarse-grained model with four blobs per chain. As in the good-solvent case, the coarse-grained model potentials are derived at zero density, thus avoiding the inconsistencies related to the use of state-dependent potentials. We find that the coarse-grained model reproduces the properties of the underlying system up to some reduced density which increases when lowering the temperature towards the Theta state. Close to the lower-temperature crossover boundary, the tetramer model is accurate at least up to Phi<10, while near the good-solvent regime reasonably accurate results are obtained up to Phi<2. The density region in which the coarse-grained model is predictive can be enlarged by developing coarse-grained models with more blobs per chain. We extend the strategy used in the good-solvent case to the crossover regime. This requires a proper treatment of the length rescalings as before, but also a proper temperature redefinition as the number of blobs is increased. The case n=10 is investigated. Comparison with full-monomer results shows that the density region in which accurate predictions can be obtained is significantly wider than that corresponding to the n=4 case.Comment: 21 pages, 14 figure

D-Branes, Tachyons and K-Homology

We present an overview of the ways in which D-brane charges are classified in terms of K-theory, emphasizing the natural physical interpretations of a homological classification within a topological setting.Comment: 18 pages AMSTeX, 3 eps figures; Based on invited lecture given at the Workshop on Algebraic Geometry and Physics ``K-Theory, Derived Categories and Strings'', University of Genoa, Genoa, Italy, June 18-21 2002; V2: Clarifying comments and reference adde

The scaling behaviour of screened polyelectrolytes

We present a field-theoretic renormalization group (RG) analysis of a single flexible, screened polyelectrolyte chain (a Debye-H\"uckel chain) in a polar solvent. We point out that the Debye-H\"uckel chain may be mapped onto a local field theory which has the same fixed point as a generalised $n \to 1$ Potts model. Systematic analysis of the field theory shows that the system is one with two interplaying length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. To illustrate this, we solve the RG equation and explicitly calculate the exponents and the mean end-to-end length of the chain.Comment: 6 pages, 1 figure; changed title and slight modification to tex