Search results for "Exponent"
showing 10 items of 896 documents
Finite size effects at phase transitions
2008
For many models of statistical thermodynamics and of lattice gauge theory computer simulation methods have become a valuable tool for the study of critical phenomena, to locate phase transitions, distinguish whether they are of first or second order, and so on. Since simulations always deal with finite systems, analysis of finite size effects by suitable finite size scaling concepts is a key ingredient of such applications. The phenomenological theory of finite size scaling is reviewed with emphasis on the concept of probability distributions of order parameter and/or energy. Attention is also drawn to recent developments concerning anisotropic geometries and anisotropic critical behavior, …
Modulation transfer function of a toric intraocular lens: evaluation of the changes produced by rotation and tilt.
2011
PURPOSE: To evaluate the changes in optical quality when toric intraocular lenses (IOL) are rotated or tilted and to demonstrate that IOL rotation produces an increasing effect of aberrations. METHODS: Modulation transfer function (MTF) and average modulation were used to analyze the image quality of a toric IOL. The axis of the toric IOL was rotated 5°, 10°, 15°, 20°, 25°, and 30° in successive MTF measurements. The tilt values were 0° to 5°, in increments of 1°, plus a tilt of 15°. Pupil diameters of 3 and 5 mm were used. RESULTS: The MTF decay due to aberrations was more sensitive to rotation than tilt. The main decrement in the average modulation, of approximately 50% in both pupils, o…
LiquidHe4andHe3at negative pressure
1992
The critical pressures {ital P}{sub {ital c}} at which liquid {sup 4}He and {sup 3}He each become macroscopically unstable are determined from two kinds of microscopic calculations that reproduce the equation of state. The behavior of the sound velocity {ital c} around this critical pressure is analyzed, and the critical exponent in {ital c}{proportional to}({ital P}{minus}{ital P}{sub {ital c}}){sup {nu}} is found to be {nu}=1/4. A comparison with empirical analysis is also done.
Phase transitions in nanosystems caused by interface motion: the Ising bipyramid with competing surface fields.
2005
The phase behavior of a large but finite Ising ferromagnet in the presence of competing surface magnetic fields +/- H_s is studied by Monte Carlo simulations and by phenomenological theory. Specifically, the geometry of a double pyramid of height 2L is considered, such that the surface field is positive on the four upper triangular surfaces of the bi-pyramid and negative on the lower ones. It is shown that the total spontaneous magnetization vanishes (for L -> infinity) at the temperature T_f(H), related to the "filling transition" of a semi-infinite pyramid, which can be well below the critical temperature of the bulk. The discontinuous vanishing of the magnetization is accompanied by a…
On the critical behavior for inhomogeneous wave inequalities with Hardy potential in an exterior domain
2021
Abstract We study the wave inequality with a Hardy potential ∂ t t u − Δ u + λ | x | 2 u ≥ | u | p in ( 0 , ∞ ) × Ω , $$\begin{array}{} \displaystyle \partial_{tt}u-{\it\Delta} u+\frac{\lambda}{|x|^2}u\geq |u|^p\quad \mbox{in } (0,\infty)\times {\it\Omega}, \end{array}$$ where Ω is the exterior of the unit ball in ℝ N , N ≥ 2, p > 1, and λ ≥ − N − 2 2 2 $\begin{array}{} \displaystyle \left(\frac{N-2}{2}\right)^2 \end{array}$ , under the inhomogeneous boundary condition α ∂ u ∂ ν ( t , x ) + β u ( t , x ) ≥ w ( x ) on ( 0 , ∞ ) × ∂ Ω , $$\begin{array}{} \displaystyle \alpha \frac{\partial u}{\partial \nu}(t,x)+\beta u(t,x)\geq w(x)\quad\mbox{on } (0,\infty)\times \partial{\it\Omega}, \e…
Effect of reactant spatial distribution in theA+B→0reaction kinetics in one dimension with Coulomb interaction
1996
The effect of nonequilibrium charge screening in the kinetics of the one-dimensional, diffusion-controlled $A+B\ensuremath{\rightarrow}0$ reaction between charged reactants in solids and liquids is studied. The incorrectness of the static, Debye-H\"uckel theory is shown. Our microscopic formalism is based on the Kirkwood superposition approximation for three-particle densities and the self-consistent treatment of the electrostatic interactions defined by the nonuniform spatial distribution of similar and dissimilar reactants treated in terms of the relevant joint correlation functions. Special attention is paid to the pattern formation due to a reaction-induced non-Poissonian fluctuation sp…
Lifetime of the 4D 3/2 and 4D 5/2 metastable states in Sr II
1987
Sr+ ions were confined in a r.f. quadrupole trap for times of the order of 30 min. The metastable 4D states were populated via laser excitation of the 5P states. The weak quadrupole transition rate into the 5S 1/2 ground state at 674 and 687 nm was deduced from observation of the exponential decay. At background pressures above 10−7 mbar the radiative decay is dominated by collisional quenching. Extrapolation of the observed decay rate to zero background pressure yields the radiative lifetimes. At pressures around 10−6 mbar fine structure mixing collisions between the 4D states have been observed, which lead to corrections of the extrapolated lifetimes. As the final result we obtain 395±38 …
Localization-delocalization transition for disordered cubic harmonic lattices.
2012
We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of $\nu = 1.550^{+0.020}_{-0.017}$ confirms the agreement with the universality class of the standard electronic Anderson model of localization. We further support our investigation with studies of the density of states…
More on Transmission-Line Solitons
1996
The study of solitons on discrete lattices dates back to the early days of soliton theory (Frenkel and Kontorova 1939, Fermi et al. 1955) and is of great physical importance. Generally, the discrete nonlinear equations which model these lattices cannot be solved analytically. Consequently, one looks for possible pulse-soliton solutions in the continuum or long wavelength approximation, that is, solitons with a width much larger than the electrical length of a unit section of the electrical network, as described in Chap.3. When this approach is not workable, one has to use numerical approaches (Zabusky 1973, Eilbeck 1991) or simulations. Nevertheless, there exist some lattice models for whic…
Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
1994
We report the results of a molecular dynamics simulation of a supercooled binary Lennard-Jones mixture. By plotting the self intermediate scattering functions vs. rescaled time, we find a master curve in the $\beta$-relaxation regime. This master curve can be fitted well by a power-law for almost three decades in rescaled time and the scaling time, or relaxation time, has a power-law dependence on temperature. Thus the predictions of mode-coupling-theory on the existence of a von Schweidler law are found to hold for this system; moreover, the exponents in these two power-laws are very close to satisfying the exponent relationship predicted by the mode-coupling-theory. At low temperatures, t…