Partial Traces in Decoherence and in Interpretation: What Do Reduced States Refer to?

The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearly stating the problem, our argument is developed in three stages. First, we consider the phenomenon of environment-induced decoherence as an example of the case in which the subsystems interact with each other; we show that decoherence does not solve the measurement problem precisely because the reduced state of the measuring apparatus is not its quantum state. Second, the non-interacting case is illustrated in the context of no-collapse interpretations, in which we show that certain well-known experimental results cannot be accounted for due to the fact that the reduced states of the measured system and the measuring apparatus are conceived as their quantum states. Finally, we prove that reduced states are a kind of coarse-grained states, and for this reason they cancel the correlations of the subsystem with other subsystems with which it interacts or is entangled.     

Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity

This research presents a new technique for nonlinear Rayleigh surface wave measurements that uses a non-contact, air-coupled ultrasonic transducer; this receiver is less dependent on surface conditions than laser-based detection, and is much more accurate and efficient than detection with a contact wedge transducer. A viable experimental setup is presented that enables the robust, non-contact measurement of nonlinear Rayleigh surface waves over a range of propagation distances. The relative nonlinearity parameter is obtained as the slope of the normalized second harmonic amplitudes plotted versus propagation distance. This experimental setup is then used to assess the relative nonlinearity parameters of two aluminum alloy specimens (Al 2024-T351 and Al 7075-T651). These results demonstrate the effectiveness of the proposed technique – the average standard deviation of the normalized second harmonic amplitudes, measured at locations along the propagation path, is below 2%. Experimental validation is provided by a comparison of the ratio of the measured nonlinearity parameters of these specimens with ratios from the absolute nonlinearity parameters for the same materials measured by capacitive detection of nonlinear longitudinal waves.     

Molecular dynamics and finite elements: an approach to couple different worlds

The procedure proposed here couples a continuum with a particle region by introducing an overlapping bridging domain where both regions exchange information. Beyond existing methods, the particle region is computed by Molecular Dynamics (MD) at finite temperature, using a code that has been developed by our co-workers of the Theoretical Physical Chemistry Group at TU Darmstadt. It is also used in the wide field of physical chemistry for various approaches. In contrast to MD procedures employing periodic boundary conditions (PBC), stochastic boundary conditions (SBC) allow for the definition of static anchor points. These additional artificial particles are coupled to the continuum part and serve as information transmitter. The continuum is treated classically by the Finite Element Method (FEM) which has been adapted based on the Arlequin and the bridging domain method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cardiovascular fluid-structure interaction: A partitioned approach utilizing the p-FEM

In this paper, we propose a technique for simulating the fluid-structure interaction in blood vessels. A partitioned approach is used, which allows for an independent discretization of the fluid domain and the structural domain. We choose the finite volume method to solve the Navier-Stokes equations and the p-version of the finite element method (p-FEM) to solve the equations of geometrically nonlinear structural dynamics. The solution strategy can be seen as a first approach towards a comprehensive study of the hemodynamics in vascular substitutes with the goal of improving their long term functionality. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New Poincaré-type inequalities

We present some Poincaré-type inequalities for quadratic matrix fields with applications e.g. in gradient plasticity or fluid dynamics. In particular, applications to the pseudostress–velocity formulation of the stationary Stokes problem and to infinitesimal gradient plasticity are discussed.     

Usage of systematic multi-body equations of motion for the design of a nonlinear vehicle dynamics controller

In this article the authors outline how systematic multi-body equations can efficiently be used to derive a model for the design of a nonlinear vehicle dynamics controller for truck-semitrailer combinations, steering the last trailer axle. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plasmon‐enhanced Raman scattering by suspended carbon nanotubes

We report plasmon‐enhanced Raman scattering of the order of 10³ by a metallic carbon nanotube partially suspended inside a near‐field cavity. The tube is part of a small bundle, and is interfaced with an Au nanodisc dimer using a recently developed assembly scheme based on dielectrophoretic deposition. Spatially resolved Raman measurements with two excitation wavelengths and two orthogonal polarizations confirm that the enhancement arises from a 65 nm long suspended tube segment. We show that the orientation of the tube inside the cavity can be as effective for generating enhancement as placing the nanotube precisely in a plasmonic hotspot. Position and shape of the G‐peak show that the suspended part of the tube is free of strain and doped with a Fermi energy shift ≤40 meV. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Optimal single machine scheduling of products with components and changeover cost

We consider the problem of scheduling products with components on a single machine, where changeovers incur fixed costs. The objective is to minimize the weighted sum of total flow time and changeover cost. We provide properties of optimal solutions and develop an explicit characterization of optimal sequences, while showing that this characterization has recurrent properties. Our structural results have interesting implications for practitioners, primarily that the structure of optimal sequences is robust to changes in demand.     

A feasible theory of truth over combinatory algebra

We define an applicative theory of truth _TPT${\mathsf{T}}_{\mathsf{PT}}$ which proves totality exactly for the polynomial time computable functions. _TPT${\mathsf{T}}_{\mathsf{PT}}$ has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system _TPT${\mathsf{T}}_{\mathsf{PT}}$ has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic.