scholarly journals SURVIVAL PROBABILITY (HEAT CONTENT) AND THE LOWEST EIGENVALUE OF DIRICHLET LAPLACIAN

2011 ◽  
Vol 25 (15) ◽  
pp. 1993-2007
Author(s):  
PAVOL KALINAY ◽  
LADISLAV ŠAMAJ ◽  
IGOR TRAVĚNEC
Keyword(s):  
Survival Probability ◽  
Heat Content ◽  
Simple Algorithm ◽  
Time Behavior ◽  
Dirichlet Laplacian ◽  
Geometric Characteristics ◽  
Long Time ◽  
Time Expansion ◽  
Short Time ◽  
Lowest Eigenvalue

We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary "star-shaped" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this expansion, we look for a Padé interpolation between the short-time and the long-time behavior of the survival probability, i.e., between geometric characteristics of the boundary and the lowest eigenvalue of the Dirichlet Laplacian.

scholarly journals Tunneling-Induced Decay of Wave Packets Localized Beyond an Asymmetric Potential Barrier

2020 ◽  
pp. 32-47
Author(s):  
Mikhail L. Strekalov
Keyword(s):  
Potential Barrier ◽  
Survival Probability ◽  
Asymptotic Series ◽  
Solvable Model ◽  
Particle Energy ◽  
Time Behavior ◽  
Initial State ◽  
Exactly Solvable ◽  
Time Domains ◽  
Long Time

The time behavior of a wave packet, transmitted through a potential barrier, is investigated for all times assuming it to be initially located outside the asymmetric barrier. The survival probability of the initial state, which characterizes the decay of the unstable quantum system in three time domains, is discussed. The presence of initial, exponential, and long-time regimes is a general feature of the decay process. We analytically found the three crucial points of time that separate these regimes. These characteristic times are set by simple formulae, including momentum distribution. It is then shown that the radius of convergence of the cumulant expansion for the survival probability is always small. A long-time behavior of survival probability is described by the asymptotic series whose coefficients decrease with increasing particle energy but at different rates. To be specific, we have examined the exactly solvable model of tunneling through a finite range triangular barrier.

Stress Distribution in Anisotropic Viscoelastic Hollow Sphere

1965 ◽  
Vol 32 (1) ◽  
pp. 31-36 ◽  
Author(s):  
S. R. Moghe ◽  
C. C. Hsiao
Keyword(s):  
Hollow Sphere ◽  
Homogeneous Medium ◽  
Small Strain ◽  
Deformation Analysis ◽  
Isotropic Case ◽  
Time Behavior ◽  
Long Time ◽  
Linear Viscoelastic ◽  
Stress And Deformation ◽  
Short Time

The stress and deformation analysis of an anisotropic linear viscoelastic hollow sphere under a symmetrical loading on the boundaries is considered. In order to reduce some of the mathematical difficulties, assumptions of small strain with quasistatic stress-strain conditions are consistently made. The solution is found for a system of non-homogeneous anisotropic viscoelastic media, and subsequently reduced to that for a homogeneous medium. Numerical results for both short-time and long-time behavior are presented for a number of simple model media in the anisotropic viscoelastic case and compared with the result for the elastic or viscoelastic medium in the isotropic case.

scholarly journals Cusp of Non-Gaussian Density of Particles for a Diffusing Diffusivity Model

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 231
Author(s):  
M. Hidalgo-Soria ◽  
E. Barkai ◽  
S. Burov
Keyword(s):  
Diffusion Coefficient ◽  
Initial Conditions ◽  
Waiting Times ◽  
Effective Diffusion ◽  
Time Behavior ◽  
Mean Values ◽  
Gaussian Density ◽  
Long Time ◽  
Non Gaussian ◽  
Short Time

We study a two state “jumping diffusivity” model for a Brownian process alternating between two different diffusion constants, D+>D−, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times, Gaussian behavior with an effective diffusion coefficient is recovered. We show that, for equilibrium initial conditions and when the limit of the diffusion coefficient D−⟶0 is taken, the short time behavior leads to a cusp, namely a non-analytical behavior, in the distribution of the displacements P(x,t) for x⟶0. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state D+ to a δ-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non-analyticity in P(x,t). We demonstrate how super-statistical framework is a zeroth order short time expansion of P(x,t), in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.

Short-Time Tests for Long-Time Endurance

1923 ◽  
Vol 128 (4) ◽  
pp. 264-264
Author(s):  
J. W. Harsch
Keyword(s):  
Long Time ◽  
Short Time

Short time behavior and universal relations in polymer cyclization

1991 ◽  
Vol 1 (4) ◽  
pp. 471-486 ◽  
Author(s):  
Barry Friedman ◽  
Ben O'Shaughnessy
Keyword(s):  
Time Behavior ◽  
Short Time

Effect of Vial shaking on Loading Time of Epirubicin into Drug-Eluting Bead

2015 ◽  
Vol 5 (3) ◽  
Author(s):  
Kenji Ikeda ◽  
Yusuke Kawamura ◽  
Masahiro Kobayashi ◽  
Taito Fukushima ◽  
Yushi Sorin ◽  
...  
Keyword(s):  
Antitumor Agent ◽  
Loading Rates ◽  
Vortex Mixer ◽  
Long Time ◽  
Group A ◽  
Drug Eluting ◽  
Large Hepatocellular Carcinoma ◽  
Group B ◽  
Time Required ◽  
Short Time

Background: Although DC Bead has been useful in treatment of multiple and large hepatocellular carcinoma, loading time of doxorubicin into the DC Bead takes a long time of 30-120 minutes. Epirubicin is also used as an antitumor agent together with DC Bead, but its loading efficiency was not sufficiently elucidated. Methods: To shorten loading time of epirubicin into DC Bead (100-300µm, 300-500µm, 500-700µm), we examined the following three methods after mixing the drug: (a) let stand in room temperature, (b) agitated for 30 seconds with Vortex mixer, and (c) sonicated for 30 seconds with ultrasonic cleaner. After loading of epirubicin by each method, supernatant concentration for epirubicin was assayed at 5, 10, 30, 60, and 120 minutes. Results: Epirubicin loading rates for small bead (100-300µm) at 5 minutes were 82.9 % in group a, 93.8% in group b, and 79.9 % in group c. Similarly, medium bead (300-500µm), 40.1% in group a, 65.7% in group b and 45.5% in group c, respectively. In large-sized bead (500-700µm), loaded rates of epirubicin were 38.8% in group a, 59.0% in group b and 48.0% in group c. Agitation of mixture of epirubicin and DC Bead with Vortex mixer significantly shortened the loading time, but sonication did not affect the time required. Microscopic examination did not lead to any morphological change of microspheres in all the methods. Conclusions: Short time of agitation with Vortex mixer reduced the necessary time for loading of epirubicin in every standard of DC Bead.

Robust Test Method of TSOP PEMs for Space Application

2019 ◽  
Author(s):  
Yasunobu Iwai ◽  
Koichi Shinozaki ◽  
Daiki Tanaka
Keyword(s):  
Evaluation Method ◽  
Low Cost ◽  
Reliability Evaluation ◽  
Test Method ◽  
Thermal Shock Test ◽  
Space Application ◽  
Space Applications ◽  
Limit Test ◽  
Long Time ◽  
Short Time

Abstract Compared with space parts, consumer parts are highly functional, low cost, compact and lightweight. Therefore, their increased usage in space applications is expected. Prior testing and evaluation on space applicability are necessary because consumer parts do not have quality guarantees for space application [1]. However, in the conventional reliability evaluation method, the test takes a long time, and the problem is that the robustness of the target sample can’t be evaluated in a short time. In this report, we apply to the latest TSOP PEM (Thin Small Outline Package Plastic Encapsulated Microcircuit) an evaluation method that combines preconditioning and HALT (Highly Accelerated Limit Test), which is a test method that causes failures in a short time under very severe environmental conditions. We show that this method can evaluate the robustness of TSOP PEMs including solder connections in a short time. In addition, the validity of this evaluation method for TSOP PEM is shown by comparing with the evaluation results of thermal shock test and life test, which are conventional reliability evaluation methods.

The Spread of Pollutants from Harbour Sludge Depots

1984 ◽  
Vol 16 (3-4) ◽  
pp. 623-633
Author(s):  
M Loxham ◽  
F Weststrate
Keyword(s):  
Time Scales ◽  
Molecular Diffusion ◽  
Near Field ◽  
Parameter Analysis ◽  
Migration Patterns ◽  
Long Time ◽  
Dilution Effects ◽  
Short Time ◽  
Harbour Sludge

It is generally agreed that both the landfill option, or the civil techniques option for the final disposal of contaminated harbour sludge involves the isolation of the sludge from the environment. For short time scales, engineered barriers such as a bentonite screen, plastic sheets, pumping strategies etc. can be used. However for long time scales the effectiveness of such measures cannot be counted upon. It is thus necessary to be able to predict the long term environmenttal spread of contaminants from a mature landfill. A model is presented that considers diffusion and adsorption in the landfill site and convection and adsorption in the underlaying aquifer. From a parameter analysis starting form practical values it is shown that the adsorption behaviour and the molecular diffusion coefficient of the sludge, are the key parameters involved in the near field. The dilution effects of the far field migration patterns are also illustrated.

Alteration of intrapancreatic serotonin, homocysteine, TNF-α, and NGF levels as predisposing factors for diabetes following exposure to 900-MHz waves

2021 ◽  
pp. 074823372110226
Author(s):  
Gholamali Jelodar ◽  
Mansour Azimzadeh ◽  
Fatemeh Radmard ◽  
Narges Darvishhoo
Keyword(s):  
Cell Damage ◽  
Pancreatic Beta Cell ◽  
Predisposing Factors ◽  
Male Rats ◽  
Control Group ◽  
Predisposing Factor ◽  
Time Exposure ◽  
Tnf Α ◽  
Long Time ◽  
Short Time

Exposure to mobile phone radiation causes deleterious health effects on biological systems. The objects of this study were to investigate the effect of 900-MHz radiofrequency waves (RFW) emitted from base transceiver station antenna on intrapancreatic homocysteine (Hcy), tumor necrosis factor-α (TNF-α), and nerve growth factor (NGF) as predisposing factors involved in pancreatic beta cell damage. Thirty male rats (Sprague-Dawley, 200 ± 10 g) were randomly divided into the control (without any exposure) and exposed groups: short time (2 h/day), long time (4 h/day), and exposed to 900-MHz RFW for 30 consecutive days. On the last days of the experiment, animals were killed and pancreas tissue was dissected out for evaluation of serotonin, Hcy, TNF-α, and NGF. There was a significant decrease in the serotonin and NGF levels in the pancreatic tissue of exposed groups compared to the control group ( p < 0.05). Also, the levels of serotonin and NGF in the long-time exposure were significantly lower than the short-time exposure ( p < 0.05). However, levels of Hcy and TNF-α were significantly increased in the pancreas of exposed groups compared to the control groups ( p < 0.05). Exposure to 900-MHz RFW decreased pancreatic NGF and serotonin levels and increased the proinflammatory markers (Hcy and TNF-α), which can be a predisposing factor for type 2 diabetes.

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

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