Strain Hardening of Polymer Glasses: Entanglements, Energetics, and Plasticity

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.Comment: 15 pages, 12 figures: significant revision

Hydrodynamic limit for a boundary driven stochastic lattice gas model with many conserved quantities

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics we considered consists of a weakly asymmetric simple exclusion process with collision among particles having different velocities

Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

An alternating descent method for the optimal control of the inviscid Burgers equation in the presence of shocks.

We introduce a new optimization strategy to compute numerical approximations of minimizers for optimal control problems governed by scalar conservation laws in the presence of shocks. We focus on the 1 − d inviscid Burgers equation. We first prove the existence of minimizers and, by a -convergence argument, the convergence of discrete minima obtained by means of numerical approximation schemes satisfying the so called onesided Lipschitz condition (OSLC). Then we address the problem of developing efficient descent algorithms. We first consider and compare the existing two possible approaches: the so-called discrete approach, based on a direct computation of gradients in the discrete problem and the so-called continuous one, where the discrete descent direction is obtained as a discrete copy of the continuous one. When optimal solutions have shock discontinuities, both approaches produce highly oscillating minimizing sequences and the effective descent rate is very weak. As a solution we propose a new method, that we shall call alternating descent method, that uses the recent developments of generalized tangent vectors and the linearization around discontinuous solutions. This method distinguishes and alternates the descent directions that move the shock and those that perturb the profile of the solution away of it producing very efficient and fast descent algorithms

A dynamical systems approach to the tilted Bianchi models of solvable type

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VI$_h$ and VII$_h$) with a perfect fluid and a linear barotropic $\gamma$-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi VII$_0$ models. We prove the important result that for non-inflationary Bianchi type VII$_h$ models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VII$_h$ invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exists closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VII$_h$ models there is a bifurcation in which a set of equilibrium points turn into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VII$_h$ models in this region the solution curves approach a compact surface which is topologically a torus.Comment: 29 page

Spin injection and spin accumulation in all-metal mesoscopic spin valves

We study the electrical injection and detection of spin accumulation in lateral ferromagnetic metal-nonmagnetic metal-ferromagnetic metal (F/N/F) spin valve devices with transparent interfaces. Different ferromagnetic metals, permalloy (Py), cobalt (Co) and nickel (Ni), are used as electrical spin injectors and detectors. For the nonmagnetic metal both aluminium (Al) and copper (Cu) are used. Our multi-terminal geometry allows us to experimentally separate the spin valve effect from other magneto resistance signals such as the anomalous magneto resistance (AMR) and Hall effects. We find that the AMR contribution of the ferromagnetic contacts can dominate the amplitude of the spin valve effect, making it impossible to observe the spin valve effect in a 'conventional' measurement geometry. In a 'non local' spin valve measurement we are able to completely isolate the spin valve signal and observe clear spin accumulation signals at T=4.2 K as well as at room temperature (RT). For aluminum we obtain spin relaxation lengths (lambda_{sf}) of 1.2 mu m and 600 nm at T=4.2 K and RT respectively, whereas for copper we obtain 1.0 mu m and 350 nm. The spin relaxation times tau_{sf} in Al and Cu are compared with theory and results obtained from giant magneto resistance (GMR), conduction electron spin resonance (CESR), anti-weak localization and superconducting tunneling experiments. The spin valve signals generated by the Py electrodes (alpha_F lambda_F=0.5 [1.2] nm at RT [T=4.2 K]) are larger than the Co electrodes (alpha_F lambda_F=0.3 [0.7] nm at RT [T=4.2 K]), whereas for Ni (alpha_F lambda_F<0.3 nm at RT and T=4.2 K) no spin signal is observed. These values are compared to the results obtained from GMR experiments.Comment: 16 pages, 12 figures, submitted to PR

On metric-connection compatibility and the signature change of space-time

We discuss and investigate the problem of existence of metric-compatible linear connections for a given space-time metric which is, generally, assumed to be semi-pseudo-Riemannian. We prove that under sufficiently general conditions such connections exist iff the rank and signature of the metric are constant. On this base we analyze possible changes of the space-time signature.Comment: 18 standard LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are require

Observation of narrow baryon resonance decaying into pKs0pK^0_s in pA-interactions at 70GeV/c70 GeV/c with SVD-2 setup

SVD-2 experiment data have been analyzed to search for an exotic baryon state, the $\Theta^+$-baryon, in a $pK^0_s$ decay mode at $70 GeV/c$ on IHEP accelerator. The reaction $pA \to pK^0_s+X$ with a limited multiplicity was used in the analysis. The $pK^0_s$ invariant mass spectrum shows a resonant structure with $M=1526\pm3(stat.)\pm 3(syst.) MeV/c^2$ and $\Gamma < 24 MeV/c^2$. The statistical significance of this peak was estimated to be of $5.6 \sigma$. The mass and width of the resonance is compatible with the recently reported $\Theta^+$- baryon with positive strangeness which was predicted as an exotic pentaquark ($uudd\bar{s}$) baryon state. The total cross section for $\Theta^+$ production in pN-interactions for $X_F\ge 0$ was estimated to be $(30\div120) \mu b$ and no essential deviation from A-dependence for inelastic events $(\sim A^{0.7})$ was found.Comment: 8 pages, 7 figures, To be submitted to Yadernaya Fizika. v3-v5 - Some references added, minor typos correcte

Block bond-order potential as a convergent moments-based method

The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi bonds by introducing block elements, which produces rapid convergence of the energies and forces within insulators, semiconductors, metals, and molecules. The method gives the first convergent results for vacancies in semiconductors using a moments-based method with a low number of moments. Our use of the Lanczos basis simplifies the calculations of the band energy and forces, which allows the application of the method to the molecular dynamics simulations of large systems. As an illustration of this convergent O(N) method we apply the block bond-order potential to the large scale simulation of the deformation of a carbon nanotube.Comment: revtex, 43 pages, 11 figures, submitted to Phys. Rev.