Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

Efficient Modeling of Thin Wires in a Lossy Medium by Finite Elements Applied to Grounding Systems

A procedure is proposed to accurately model thin wires in lossy media by finite element analysis. It is based on the determination of a suitable element width in the vicinity of the wire, which strongly depends on the wire radius to yield accurate results. The approach is well adapted to the analysis of grounding systems. The numerical results of the application of finite element analysis with the suitably chosen element width are compared with both analytical results and those computed by a commercial package for the analysis of grounding systems, showing very good agreement.

Finite Element Analysis of 2 Immediate Loading Systems in Edentulous Mandible: Rigid and Semirigid Splinting of Implants

Purpose: The objective of this study was to evaluate the stress on the cortical bone around single body dental implants supporting mandibular complete fixed denture with rigid (Neopronto System-Neodent) or semirigid splinting system (Barra Distal System-Neodent). Methods and Materials: Stress levels on several system components were analyzed through finite element analysis. Focusing on stress concentration at cortical bone around single body dental implants supporting mandibular complete fixed dentures with rigid ( Neopronto System-Neodent) or semirigid splinting system ( Barra Distal System-Neodent), after axial and oblique occlusal loading simulation, applied in the last cantilever element. Results: The results showed that semirigid implant splinting generated lower von Mises stress in the cortical bone under axial loading. Rigid implant splinting generated higher von Mises stress in the cortical bone under oblique loading. Conclusion: It was concluded that the use of a semirigid system for rehabilitation of edentulous mandibles by means of immediate implant-supported fixed complete denture is recommended, because it reduces stress concentration in the cortical bone. As a consequence, bone level is better preserved, and implant survival is improved. Nevertheless, for both situations the cortical bone integrity was protected, because the maximum stress level findings were lower than those pointed in the literature as being harmful. The maximum stress limit for cortical bone (167 MPa) represents the threshold between plastic and elastic state for a given material. Because any force is applied to an object, and there is no deformation, we can conclude that the elastic threshold was not surpassed, keeping its structural integrity. If the force is higher than the plastic threshold, the object will suffer permanent deformation. In cortical bone, this represents the beginning of bone resorption and/or remodeling processes, which, according to our simulated loading, would not occur. ( Implant Dent 2010; 19:39-49)

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Finite-size particles, advection, and chaos: A collective phenomenon of intermittent bursting

We consider finite-size particles colliding elastically, advected by a chaotic flow. The collisionless dynamics has a quasiperiodic attractor and particles are advected towards this attractor. We show in this work that the collisions have dramatic effects in the system's dynamics, giving rise to collective phenomena not found in the one-particle dynamics. In particular, the collisions induce a kind of instability, in which particles abruptly spread out from the vicinity of the attractor, reaching the neighborhood of a coexisting chaotic saddle, in an autoexcitable regime. This saddle, not present in the dynamics of a single particle, emerges due to the collective particle interaction. We argue that this phenomenon is general for advected, interacting particles in chaotic flows.

Dynamical estimates of chaotic systems from Poincare recurrences

We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov-Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Henon map and experimentally in a Chua's circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3263943]

Decoherence-free evolution of time-dependent superposition states of two-level systems and thermal effects

In this paper we detail some results advanced in a recent letter [Prado et al., Phys. Rev. Lett. 102, 073008 (2009).] showing how to engineer reservoirs for two-level systems at absolute zero by means of a time-dependent master equation leading to a nonstationary superposition equilibrium state. We also present a general recipe showing how to build nonadiabatic coherent evolutions of a fermionic system interacting with a bosonic mode and investigate the influence of thermal reservoirs at finite temperature on the fidelity of the protected superposition state. Our analytical results are supported by numerical analysis of the full Hamiltonian model.

Conservation laws, integrability, and transport in one-dimensional quantum systems

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where a conserved spin current exists.

Protecting a quantum state from environmental noise by an incompatible finite-time measurement

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

Universal and nonuniversal contributions to block-block entanglement in many-fermion systems

We calculate the entanglement entropy of blocks of size x embedded in a larger system of size L, by means of a combination of analytical and numerical techniques. The complete entanglement entropy in this case is a sum of three terms. One is a universal x- and L-dependent term, first predicted by Calabrese and Cardy, the second is a nonuniversal term arising from the thermodynamic limit, and the third is a finite size correction. We give an explicit expression for the second, nonuniversal, term for the one-dimensional Hubbard model, and numerically assess the importance of all three contributions by comparing to the entropy obtained from fully numerical diagonalization of the many-body Hamiltonian. We find that finite-size corrections are very small. The universal Calabrese-Cardy term is equally small for small blocks, but becomes larger for x > 1. In all investigated situations, however, the by far dominating contribution is the nonuniversal term stemming from the thermodynamic limit.

An electromechanical finite element model for piezoelectric energy harvester plates

Vibration-based energy harvesting has been investigated by several researchers over the last decade. The goal in this research field is to power small electronic components by converting the waste vibration energy available in their environment into electrical energy. Recent literature shows that piezoelectric transduction has received the most attention for vibration-to-electricity conversion. In practice, cantilevered beams and plates with piezoceramic layers are employed as piezoelectric energy harvesters. The existing piezoelectric energy harvester models are beam-type lumped parameter, approximate distributed parameter and analytical distributed parameter solutions. However, aspect ratios of piezoelectric energy harvesters in several cases are plate-like and predicting the power output to general (symmetric and asymmetric) excitations requires a plate-type formulation which has not been covered in the energy harvesting literature. In this paper. an electromechanically coupled finite element (FE) plate model is presented for predicting the electrical power output of piezoelectric energy harvester plates. Generalized Hamilton`s principle for electroelastic bodies is reviewed and the FE model is derived based on the Kirchhoff plate assumptions as typical piezoelectric energy harvesters are thin structures. Presence of conductive electrodes is taken into account in the FE model. The predictions of the FE model are verified against the analytical solution for a unimorph cantilever and then against the experimental and analytical results of a bimorph cantilever with a tip mass reported in the literature. Finally, an optimization problem is solved where the aluminum wing spar of an unmanned air vehicle (UAV) is modified to obtain a generator spar by embedding piezoceramics for the maximum electrical power without exceeding a prescribed mass addition limit. (C) 2009 Elsevier Ltd. All rights reserved.

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.

Toward Optimal Design of Piezoelectric Transducers Based on Multifunctional and Smoothly Graded Hybrid Material Systems

This work explores the design of piezoelectric transducers based on functional material gradation, here named functionally graded piezoelectric transducer (FGPT). Depending on the applications, FGPTs must achieve several goals, which are essentially related to the transducer resonance frequency, vibration modes, and excitation strength at specific resonance frequencies. Several approaches can be used to achieve these goals; however, this work focuses on finding the optimal material gradation of FGPTs by means of topology optimization. Three objective functions are proposed: (i) to obtain the FGPT optimal material gradation for maximizing specified resonance frequencies; (ii) to design piezoelectric resonators, thus, the optimal material gradation is found for achieving desirable eigenvalues and eigenmodes; and (iii) to find the optimal material distribution of FGPTs, which maximizes specified excitation strength. To track the desirable vibration mode, a mode-tracking method utilizing the `modal assurance criterion` is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept. The optimization algorithm is constructed based on sequential linear programming, and the concept of continuum approximation of material distribution. To illustrate the method, 2D FGPTs are designed for each objective function. In addition, the FGPT performance is compared with the non-FGPT one.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.