Non-zero Off Research Articles

Coherence-orbital angular momentum matrix of Schell-model sources.

The coherence-orbital angular momentum (COAM) matrix characterizes the second-order field correlations in stationary sources or fields, at a pair of spiral modes with the same or different topological charges, say l and m, and at a pair of radial positions. In this Letter, we reveal the general properties of the COAM matrix for the broad class of the Schell-model sources with circularly symmetric spectral densities. Our results imply that the structure of the COAM matrix is intimately related to the symmetries of the degree of coherence (DOC). In particular, the COAM matrix is diagonal if the DOC is real-valued and rotationally symmetric; otherwise, it may acquire non-zero off diagonal elements. In particular, if the real part of the DOC has Cartesian symmetry, the COAM matrix's elements with the even/odd index difference |l - m| contain information about the real/imaginary part of the DOC. A potential application of our results is envisioned for extracting the rotation angle of the DOC of light (or an object transparency) through measuring of the off-axis COAM matrix elements.

Perils of embedding for quantum sampling

Given quantum hardware that enables sampling from a family of natively implemented Hamiltonians, how well can one use that hardware to sample from a Hamiltonian outside that family? A common approach is to minor embed the desired Hamiltonian in a native Hamiltonian. In Phys. Rev. Research 2, 023020 (2020) it was shown that minor embedding can be detrimental for classical thermal sampling. Here, we generalize these results by considering quantum thermal sampling in the transverse-field Ising model, i.e. sampling a Hamiltonian with non-zero off diagonal terms. To study these systems numerically we introduce a modification to standard cluster update quantum Monte-Carlo (QMC) techniques, which allows us to much more efficiently obtain thermal samples of an embedded Hamiltonian, enabling us to simulate systems of much larger sizes and larger transverse-field strengths than would otherwise be possible. Our numerics focus on models that can be implemented on current quantum devices using planar two-dimensional lattices, which exhibit finite-temperature quantum phase transitions. Our results include: i) An estimate on the probability to sample the logical subspace directly as a function of transverse-field, temperature, and total system size, which agrees with QMC simulations. ii) We show that typically measured observables (diagonal energy and magnetization) are biased by the embedding process, in the regime of intermediate transverse field strength, meaning that the extracted values are not the same as in the native model. iii) By considering individual embedding realizations akin to 'realizations of disorder', we provide numerical evidence suggesting that as the embedding size is increased, the critical point shifts to increasingly large values of the transverse-field.

Robust adaptive control of underactuated ships with input saturation

This paper addresses the problem of practical stabilisation of arbitrary reference trajectories, including time-varying trajectories and fixed points for underactuated ships subjected to input saturation and parametric modelling uncertainties. Two novel coordinate transformations are introduced to deal with the problems caused by the non-zero off diagonal terms in the inertia matrix and the underactuation, respectively. Based on the backstepping technique, the dynamic surface control method and the Lyapunov's direct method, a saturated robust adaptive controller is designed to achieve practical convergence of tracking errors to a bounded area centred at zero. Some comparative simulations are performed to illustrate the effectiveness of the proposed control scheme.

One dimensional nonlocal integro-differential model & gradient elasticity model : Approximate solutions and size effects

ABSTRACTIn the present work, the close similarity that exists between Mindlin’s strain gradient elasticity and Eringens nonlocal integro-differential model is explored. A relation between length scales of nonlocal-differential model and gradient elasticity model has been arrived. Further, a relation has also been arrived between the standard and nonstandard boundary conditions in both the cases. C0-based finite element methods (FEMs) are extensively used for the implementation of integro-differential equations. This results in standard diagonally dominant global stiffness matrix with off diagonal elements occupied largely by the kernel values evaluated at various locations. The global stiffness matrix is enriched in this process by nonzero off diagonal terms and helps in incorporation of the nonlocal effect, there by accounting the long-range interactions. In this case, the diagonally dominant stiffness matrix has a band width equal to influence domain of basis function. In such cases, a very fine discretization with larger number of degrees of freedom is required to predict nonlocal effect, thereby making it computationally expensive. In the numerical examples, both nonlocal-differential and gradient elasticity model are considered to predict the size effect of tensile bar example. The solutions to integro-differential equations obtained by using various higher-order approximations are compared. Lagrangian, Bèzier and B-Spline approximations are considered for the analysis. It has been shown that such higher-order approximations have higher inter-element continuity there by increasing the band width and the nonlocal character of the stiffness matrix. The effect of considering the higher-order and higher-continuous approximation on computational effort is made. In conclusion, both the models predict size effect for one-dimensional example. Further, the higher-continuous approximation results in less computational effort for nonlocal-differential model.

실내 이동로봇의 UKF 위치 추정 및 성능 평가

Abstract This paper reports an unscented Kalman filter approach for localization of a mobile robot in an indoor environment. The method proposes a new model of measurement uncertainty which adjusts the error co-variance according to the measured distance. The method also uses non-zero off diagonal values in error co-variance matrices of motion uncertainty and measurement uncertainty. The method is tested through experi-ments in an indoor environment of 100*40 m working space using a differential drive robot which uses Laser range finder as an exteroceptive sensor. The results compare the localization performance of the pro-posed method with the conventional method which doesn’t use adaptive measurement uncertainty model. Also, the experiment verifies the improvement due to non-zero off diagonal elements in covariance matrices. This paper contributes to implementing and evaluating a practical UKF approach for mobile robot localization.Key Words : Mobile robot localization, Unscented Kalman Filter, Measurement uncertainty, Covariance matrix, exteroceptive measurement이 논문은 2013년도 정부(교육부)의 재원으로 한국연구재단의 지원을 받아 수행된 기초연구사업임(NO. NRF-2013R1A1A4A01012469)This is an Open-Access article distributed un-der the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/li-censes/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and re-production in any medium, provided the orig-inal work is properly cited.Received: Jan. 28, 2015Revised : May. 24, 2015Accepted: May. 24, 2015

Curl flux, coherence, and population landscape of molecular systems: nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics.

We established a theoretical framework in terms of the curl flux, population landscape, and coherence for non-equilibrium quantum systems at steady state, through exploring the energy and charge transport in molecular processes. The curl quantum flux plays the key role in determining transport properties and the system reaches equilibrium when flux vanishes. The novel curl quantum flux reflects the degree of non-equilibriumness and the time-irreversibility. We found an analytical expression for the quantum flux and its relationship to the environmental pumping (non-equilibriumness quantified by the voltage away from the equilibrium) and the quantum tunneling. Furthermore, we investigated another quantum signature, the coherence, quantitatively measured by the non-zero off diagonal element of the density matrix. Populations of states give the probabilities of individual states and therefore quantify the population landscape. Both curl flux and coherence depend on steady state population landscape. Besides the environment-assistance which can give dramatic enhancement of coherence and quantum flux with high voltage at a fixed tunneling strength, the quantum flux is promoted by the coherence in the regime of small tunneling while reduced by the coherence in the regime of large tunneling, due to the non-monotonic relationship between the coherence and tunneling. This is in contrast to the previously found linear relationship. For the systems coupled to bosonic (photonic and phononic) reservoirs the flux is significantly promoted at large voltage while for fermionic (electronic) reservoirs the flux reaches a saturation after a significant enhancement at large voltage due to the Pauli exclusion principle. In view of the system as a quantum heat engine, we studied the non-equilibrium thermodynamics and established the analytical connections of curl quantum flux to the transport quantities such as energy (charge) transfer efficiency, chemical reaction efficiency, energy dissipation, heat and electric currents observed in the experiments. We observed a perfect transfer efficiency in chemical reactions at high voltage (chemical potential difference). Our theoretical predicted behavior of the electric current with respect to the voltage is in good agreements with the recent experiments on electron transfer in single molecules.

Giant laser-induced voltages at room temperature in Pr doped Y—Ba—Cu—O thin films

Recent reports on high transient transverse voltages at room temperature in Y1Ba2Cu3O7 (YBCO) thin films exposed to laser irradiation show that the thermoelectric fields transverse to a laser-induced temperature gradient are caused by the nonzero off diagonal elements of the Seebeck tensor. To further enhance these signals of a size approximately 0.1 V/K we used the dependence of the Seebeck coefficient on the in plane thermoelectric properties of YBCO. Thin films with a partial substitution of Y by Pr epitaxially grown on Strontiumtitanate single crystals cut with a tilt angle of 10° between substrate surface and the cubic axis are exposed to UV photon pulses (λ = 248nm, pulse length 28 ns, fluences 5–200 mJ/cm2) at room temperature. Compared to the undoped films the an enhancement of the signal by a factor of 20 is found for Y0.8Pr0.2Ba2Cu3O7 films. Further increase of the doping level, however, caused a decrease of this peak values. This result is ascribed to the anisotropic changes of the Seebeck tensor matrix components upon doping.

Experimental Damage Investigation of a SiC-Ti Aluminide Metal Matrix Composite

Experimental investigations and procedures for the determination of damage are presented for the macro- and micro-analysis of SiC-Titanium Aluminide metal matrix composite (MMC). Uniaxial tension tests are performed on laminate specimens of two different layups. The layups are balanced symmetrically and given as (0/90)s and (±45)s, each containing four plies. Dogbone shaped flat plate specimens are fabricated from each of the layups. Specimens for the different layups are loaded to various load levels ranging from rupture load down to 70% of the rupture load at room temperature. By loading specimens to various load levels damage evolution is experimentally evaluated through a quantitative micro-analysis technique. Micro-analysis is performed using scanning electron microscopy (SEM) on three mutually perpendicular representative cross sections of all specimens for the qualitative and quantitative determination of damage. Together these representative cross sections form a representative volume element (RVE) defined for the theoretical development of damage evolution. Results from the micro-analysis are used in evaluating the damage parameters defined in a previously developed damage theory [1]. This theory uses a second order damage tensor of which it is proposed will have non-zero off diagonal terms only if the load applied to the laminate is in a direction other than parallel to the fibers. Damage parameters are evaluated for each of the load levels below the rupture load, since damage features present at this load level are beyond the range of valid damage mechanics. Two types of damage evaluations are performed for the RVE, one for the overall quantification of damage and the other quantifying damage in the matrix and fibers separately. Damage as a result of delamination is excluded in this investigation for both types of damage evaluation, but may be included if needed. The damage curves presented show graphically a consistent evolution of damage, which validates the methods used in evaluating the damage parameter. Curves for the different laminate layups show that damage profile curves are similar for different laminate layups and orientations. The off diagonal terms of the damage tensors as evaluated by the proposed scheme are found to be significant and should be included in any constitutive damage relation. Numerical verification of these observations are to be presented in a subsequent paper.

Laser-Induced Voltages at Room Temperature in YBa2Cu3O7 and PrxY1-xBa2Cu3O7 Thin Films

ABSTRACTRecent reports on high transient transverse voltages at room temperature in YBa2Cu3O7 and PrxYl-xBa2Cu3O7 thin films grown on SrTiO3 single crystal substrates, with a tilt angle between the [ 001 ] cubic axis and the substrate surface plane, have been interpreted by thermoelectric fields transverse to a laser-induced temperature gradient which are caused by the non-zero off diagonal elements of the Seebeck tensor. We have studied this effect in epitaxially grown Pr- doped, as well as undoped YBa2Cu3O7, thin films and observed for a 2 mm long YBa2Cu3O7 strip exposed to a UV photon fluence of 100 mJ/cm2 signals as large as 30 V. The unexpected high values for the signals and their doping dependence are discussed within the frame of a model based on a thermopile arrangement, the growth induced defect structure and the doping induced modifications of the material properties.

Products of basic doubly stochastic matrices over a field

It is shown that if n⩾3, then every doubly stochastic matrix of order n over a field F is a product of doubly stochastic matrices with exactly two nonzero off- diagonal entries if and only if the characteristic of F is not 2 and F has more than three elements. A number of related results are also obtained.