Unusual eigenvalue spectrum and relaxation in the Levy-Ornstein-Uhlenbeck process

We consider the rates of relaxation of a particle in a harmonic well, subject to Levy noise characterized by its Levy index mu. Using the propagator for this Levy-Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue spectrum of the associated Fokker-Planck operator has the form (n + m mu)nu where nu is the force constant characterizing the well, and n, m is an element of N. If mu is irrational, the eigenvalues are all nondegenerate, but rational mu can lead to degeneracy. The maximum degeneracy is shown to be 2. The left eigenfunctions of the fractional Fokker-Planck operator are very simple while the right eigenfunctions may be obtained from the lowest eigenfunction by a combination of two different step-up operators. Further, we find that the acceptable eigenfunctions should have the asymptotic behavior vertical bar x vertical bar(-n1-n2 mu) as vertical bar x vertical bar -> infinity, with n(1) and n(2) being positive integers, though this condition alone is not enough to identify them uniquely. We also assert that the rates of relaxation of LOUP are determined by the eigenvalues of the associated fractional Fokker-Planck operator and do not depend on the initial state if the moments of the initial distribution are all finite. If the initial distribution has fat tails, for which the higher moments diverge, one can have nonspectral relaxation, as pointed out by Toenjes et al. Phys. Rev. Lett. 110, 150602 (2013)].

Breathers and thermal relaxation as a temporal process: A possible way to detect breathers in experimental situations

Breather stability and longevity in thermally relaxing nonlinear arrays is investigated under the scrutiny of the analysis and tools employed for time series and state reconstruction of a dynamical system. We briefly review the methods used in the analysis and characterize a breather in terms of the results obtained with such methods. Our present work focuses on spontaneously appearing breathers in thermal Fermi-Pasta-Ulam arrays but we believe that the conclusions are general enough to describe many other related situations; the particular case described in detail is presented as another example of systems where three incommensurable frequencies dominate their chaotic dynamics (reminiscent of the Ruelle-Takens scenario for the appearance of chaotic behavior in nonlinear systems). This characterization may also be of great help for the discovery of breathers in experimental situations where the temporal evolution of a local variable (like the site energy) is the only available/measured data. © 2005 American Institute of Physics.

The development of a hot rolling process for variable cross-section I-beams

To meet targeted reductions in CO 2 emissions by 2050, demand for metal must be cut, for example through the use of lightweight technologies. However, the efficient production of weight optimized components often requires new, more flexible forming processes. In this paper, a novel hot rolling process is presented for forming I-beams with variable cross-section, which are lighter than prismatic alternatives. First, the new process concept is presented and described. A detailed computational and experimental analysis is then conducted into the capabilities of the process. Results show that the process is capable of producing defect free I-beams with variations in web depth of 30-50%. A full analysis of the process then indicates the likely failure modes, and identifies a safe operating window. Finally, the implications of these results for producing lightweight beams are discussed. © 2012 Elsevier B.V. All rights reserved.

Photoionization of 1s electron and corresponding shake-up process in ground and excited lithium atoms

The cross sections of the 18 electron photoionization and corresponding shake-up processes for Li atoms in the ground state 1s(2)2s and excited states 1s(2)2p, 1s(2)3p, 1s(2)3p and 1s(2)3d are calculated using the multi-configuration Dirac-Fock method. The latest experimental photoelectron spectrum at hv = 100 eV [Cubaynes D et al. Phys. Rev. Lett. 99 (2007) 213004] has been reproduced by the present theoretical investigation excellently. The relative intensity of the shake-up satellites shows that the effects of correlation and relaxation become more important for the higher excited states of the lithium atom, which are explained very well by the spatial overlap of the initial and final state wavefunctions. In addition, strong dependence of the cross section on the atomic orbitals of the valence electrons are found, especially near the threshold.

Slow cross-symmetry phase relaxation in complex collisions

We discuss the effect of slow phase relaxation and the spin off-diagonal S-matrix correlations on the cross-section energy oscillations and the time evolution of the highly excited intermediate systems formed in complex collisions. Such deformed intermediate complexes with strongly overlapping resonances can be formed in heavy-ion collisions, bimolecular chemical reactions, and atomic cluster collisions. The effects of quasiperiodic energy dependence of the cross sections, coherent rotation of the hyperdeformed similar or equal to(3 : 1) intermediate complex, Schrodinger cat states, and quantum-classical transition are studied for Mg-24 + Si-28 heavy-ion scattering.

A material model for multiaxial stretching and stress relaxation of polypropylene under process conditions

Polypropylene sheets have been stretched at 160 °C to a state of large biaxial strain of extension ratio 3, and the stresses then allowed to relax at constant strain. The state of strain is reached via a path consisting of two sequential planar extensions, the second perpendicular to the first, under plane stress conditions with zero stress acting normal to the sheet. This strain path is highly relevant to solid phase deformation processes such as stretch blow moulding and thermoforming, and also reveals fundamental aspects of the flow rule required in the constitutive behaviour of the material. The rate of decay of stress is rapid, and such as to be highly significant in the modelling of processes that include stages of constant strain. A constitutive equation is developed that includes Eyring processes to model both the stress relaxation and strain rate dependence of the stress. The axial and transverse stresses observed during loading show that the use of a conventional Levy-Mises flow rule is ineffective, and instead a flow rule is used that takes account of the anisotropic state of the material via a power law function of the principal extension ratios. Finally the constitutive model is demonstrated to give quantitatively useful representation of the stresses both in loading and in stress relaxation.

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor. (c) 2007 American Institute of Physics

NUCLEAR SPIN 3/2 ELECTRIC QUADRUPOLE RELAXATION AS A QUANTUM COMPUTATION PROCESS

In this work we applied a quantum circuit treatment to describe the nuclear spin relaxation. From the Redfield theory, we obtain a description of the quadrupolar relaxation as a computational process in a spin 3/2 system, through a model in which the environment is comprised by five qubits and three different quantum noise channels. The interaction between the environment and the spin 3/2 nuclei is described by a quantum circuit fully compatible with the Redfield theory of relaxation. Theoretical predictions are compared to experimental data, a short review of quantum channels and relaxation in NMR qubits is also present.

Evaluation of the Chinese version of the disability of the arm, shoulder and hand (DASH-HKPWH): cross-cultural adaptation process, internal consistency and reliability study

Abstract
The Disability of the Arm, Shoulder and Hand (DASH) was translated into Chinese by a physiotherapy team of the Prince of Wales Hospital, Hong Kong (DASH-HKPWH).

Objectives
This study evaluated the cross-cultural adaptation process, face validity, internal consistency and reliability of the DASH-HKPWH.

Method
Language officers and medical professionals from different fields were invited to translate and evaluate the face validity of the DASH-HKPWH. 88 patients were recruited to complete two DASH questionnaires on two occasions 1-2 weeks apart.

Results
Some adjustments were made to the translations based on the cultural and linguistic practice in Hong Kong. The face validity was satisfactory with a mean endorsement score of 3.2. The difference between the mean of DASH scores was not significant (t = −0.35, p = 0.73). The ICC (1,1) and Cronbach's alpha for the 30-item Disability/Symptom of the DASH-HKPWH was 0.77 and 0.94, respectively.

Conclusion
The translation was valid and reliable and acceptably equivalent to the original version. The questionnaire is suitable for measuring changes experienced by patients with any upper extremity disorders.

Cross-talk with β2-adrenoceptors enhances ligand affinity properties from endothelial alpha1D-adrenoceptors that mediates carotid relaxation

Objectives Our main objectives were to investigate the affinity properties of endothelial and muscular α1D-adrenoceptors and to characterize the cross-talk between endothelial α1D- adrenoceptors and β2-adrenoceptors in rat carotid. Methods Relaxation and contraction concentration-response curves for phenylephrine (α1-adrenergic agonist) were obtained in carotid rings in absence or presence of increasing concentrations of BMY7378 (α 1D-adrenergic antagonist), combined or not with increasing concentration of ICI-118,551 (β2-adrenergic antagonist). Schild analysis was used to estimate the affinity constant from pA2 values of BMY7378. Key Findings BMY7378 produced an unsurmountable antagonism on phenylephrine-induced relaxation but a surmountable antagonism on phenylephrine-induced contraction. BMY7378 potency was higher in inhibiting the relaxation than the contraction induced by phenylephrine because the rightward shifts induced by BMY7378 were greater in the relaxation. The apparent pA 2 value for BMY7378 in phenylephrine-induced relaxation was greater than in contraction. When combined with ICI-118,551, BMY7378 yielded a surmountable antagonism on phenylephrine-induced relaxation and presented a pA2 value similar to that obtained in phenylephrine-induced contraction. Conclusions Endothelial α1D-adrenoceptors, which mediates rat carotid relaxation, present high ligand affinity because of the cross-talk with β2-adrenoceptors, which explains the higher potency of phenylephrine in inducing relaxation than contraction and the atypical unsurmountable antagonism produced by BMY7378 on phenylephrine-induced relaxation. © 2013 Royal Pharmaceutical Society.

Cross-cultural perceptions in the leadership process: Theoretical perspective on the influence of culture on self-concepts and manager worker attributions

This article examines the influence of culture on the way managers and workers perceive causes of success and failure in organizational tasks. The author argues that selfserving and actor-observer biases, as well as other attribution errors, will be moderated by culture. Specifically, managers and workers with a sociocentric self-concept from high-context cultures may be biased toward external attributions, while managers from low-context cultures with an idiocentric self-concept have a tendency to make more internal attributions. These variations in attributions have consequences that affect both managers and workers. Theoretical propositions and implications for international management practices are discussed. © 2005 Wiley Periodicals, Inc.