3,240,733 research outputs found

    Numerical analysis of parabolic p-Laplacian: Approximation of trajectories

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    The long time numerical approximation of the parabolic p-Laplacian problem with a time-independent forcing term and sufficiently smooth initial data is studied. Convergence and stability results which are uniform for t is an element of [0, infinity) are established in the L-2, W-1,W-p norms for the backward Euler and the Crank-Nicholson schemes with the finite element method (FEM). This result extends the existing uniform convergence results for exponentially contractive semigroups generated by some semilinear systems to nonexponentially contractive semigroups generated by some quasilinear systems

    On products of skew rotations

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    Let H1(p,q)H_1(p,q), H2(p,q)H_2(p,q) be two time-independent Hamiltonians with one degree of freedom and {S1t}\{S_1^t\}, {S2t}\{S_2^t\} be the one-parametric groups of shifts along the orbits of Hamiltonian systems generated by H1H_1, H2H_2. In some problems of population genetics there appear the transformations of the plane having the form T(h1,h2)=S2h2ā‹…S1h1T^{(h_1,h_2)}=S^{h_2}_2\cdot S_1^{h_1} under some conditions on H1H_1, H2H_2. We study in this paper asymptotical properties of trajectories of T(h1,h2)T^{(h_1,h_2)}.Comment: 13 pages, 10 figure

    Non-Markovian stochastic Liouville equation and anomalous relaxation kinetics

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    The kinetics of phase and population relaxation in quantum systems induced by noise with anomalously slowly decaying correlation function P (t) ~ (wt)^{- alpha}, where 0 < alpha < 1 is analyzed within continuous time random walk approach. The relaxation kinetics is shown to be anomalously slow. Moreover for alpha < 1 in the limit of short characteristic time of fluctuations w^{-1} the kinetics is independent of w. As alpha \to 1 the relaxation regime changes from the static limit to fluctuation narrowing. Simple analytical expressions are obtained describing the specific features of the kinetics.Comment: 7 pages, 2 figure

    Out-of-equilibrium thermodynamic relations in systems with aging and slow relaxation

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    The experimental time scale dependence of thermodynamic relations in out-of-equilibrium systems with aging phenomena is investigated theoretically by using only aging properties of the two-time correlation functions and the generalized fluctuation-dissipation theorem (FDT). We show that there are two experimental time regimes characterized by different thermal properties. In the first regime where the waiting time is much longer than the measurement time, the principle of minimum work holds even though a system is out of equilibrium. In the second regime where both the measurement time and the waiting time are long, the thermal properties are completely different from properties in equilibrium. For the single-correlation-scale systems such as pp-spin spherical spin-glasses, contrary to a fundamental assumption of thermodynamics, the work done in an infinitely slow operation depends on the path of change of the external field even when the waiting time is infinite. On the other hand, for the multi-correlation-scale systems such as Sherrington-Kirkpatrick model, the work done in an infinitely slow operation is independent of the path. Our results imply that in order to describe thermodynamic properties of systems with aging it is essential to consider the experimental time scales and history of a system as a state variable is necessary.Comment: 28 pages(REVTeX), 4 figure(EPS). To be published in Phys. Rev.

    Symmetries shape the current in ratchets induced by a bi-harmonic force

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    Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The bi-harmonic force f(t)=Ļµ1cosā”(qĻ‰t+Ļ•1)+Ļµ2cosā”(pĻ‰t+Ļ•2)f(t)=\epsilon_1\cos(q \omega t+\phi_1)+\epsilon_2\cos(p\omega t+\phi_2) does it for almost any choice of Ļ•1\phi_{1} and Ļ•2\phi_{2}, provided pp and qq are two co-prime integers such that p+qp+q is odd. It has been widely observed, in experiments in Josephson-junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape vāˆĻµ1pĻµ2qcosā”(pĻ•1āˆ’qĻ•2+Īø0)v\propto\epsilon_1^p\epsilon_2^q\cos(p \phi_{1} - q \phi_{2} + \theta_0) for small amplitudes, where Īø0\theta_0 depends on the damping (Īø0=Ļ€/2\theta_0=\pi/2 if there is no damping, and Īø0=0\theta_0=0 for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system.Comment: 4 page

    In vivo evaluation of operative torque generated by two Nickel-Titanium rotary instruments during root canal preparation

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    Objectives This in vivo study evaluated the operative torque and preparation time of ProTaper NEXT (Dentsply Maillefer; Ballaigues, Switzerland) and EdgeFile X7 (EdgeEndo; Albuquerque, New Mexico, United States) rotary systems during root canal preparation of maxillary premolars. Materials and Methods Ten double-rooted maxillary premolars with independent canals were selected. Each canal in each tooth was prepared with one of the rotary systems (n = 10), ProTaper NEXT or EdgeFile X7. The instruments were rotated at 300 rpm with maximum torque set at 2 N.cm using an electric motor (KaVo; Biberach, Germany) that automatically recorded torque values at every 1/10th of a second (ds). Statistical Analysis Operative torque (N.cm) and preparation time (s) of the first shaping instrument (size 17/.04) of both rotary systems were recorded and statistically compared using the Mann-Whiney U test with a significance level set at 5%. Results No instrument exhibited flute deformation or underwent intracanal failure. No differences were found between the instruments regarding the maximum (peak) torque values (p &gt; 0.05). EdgeFile X7 17/.04 required significantly less preparation time (3.75 seconds interquartile range [IQR]: 3.2-9.0) than ProTaper NEXT X1 (15.45 seconds IQR: 8.35-21.1) (p &lt; 0.05). The median operative torque values of ProTaper NEXT X1 (0.26 N.cm; IQR: 0.18-0.49) were significantly higher compared with EdgeFile X7 17/.04 (0.09 N.cm; IQR: 0.05-0.17) (p &lt; 0.05). Conclusions Although no difference was found between the median peak torque values of ProTaper NEXT X1 and EdgeFile X7 17/.04 instruments, the operative torque and instrumentation time results were impacted by their different designs and alloys during clinical preparation of root canals
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