scholarly journals Static component of photothermal response in non-transparent samples

2012 ◽  
Vol 25 (3) ◽  
pp. 213-224 ◽  
Author(s):  
Zlatan Soskic ◽  
Slobodanka Galovic ◽  
Nebojsa Bogojevic ◽  
Slobodan Todosijevic
Keyword(s):  
Temperature Distribution ◽  
Mean Value ◽  
Optical Absorption Coefficient ◽  
Back Side ◽  
One Dimensional ◽  
Static Component ◽  
Special Cases ◽  
Static Part ◽  
The Mean ◽  
Analytical Expressions

The paper presents the analysis of the static component of temperature distribution in non-transparent samples during photothermal measurements. Analytical expressions for static part of temperature distribution in the irradiated sample and in its surroundings are determined using one dimensional model of heat transfer in a typical photothermal environment. It is established that the dominant factors that influence the shape and the mean value of the temperature distribution are optical absorption coefficient and thermal conductances of the sample and the surroundings. Important special cases are described and analytical expressions for temperatures of the front and the back side of the sample are derived.

Stochastic Analysis of Temperature Distribution in a Solid With Random Heat Conductivity

1988 ◽  
Vol 110 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Da Yu Tzou
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Heat Conductivity ◽  
Stochastic Analysis ◽  
Solid Medium ◽  
Mean Value ◽  
Random Response ◽  
Thermal Failure ◽  
Numerical Examples ◽  
The Mean

Stochastic temperature distribution in a solid medium with random heat conductivity is investigated by the method of perturbation. The intrinsic randomness of the thermal conductivity k(x) is considered to be a distribution function with random amplitude in the solid, and several typical stochastic processes are considered in the numerical examples. The formulation used in the present analysis describes a situation that the statistical orders of the random response of the system are the same as those of the intrinsic random excitations, which is characteristic for the problem with extrinsic randomness. The maximum standard deviation of the temperature distribution from the mean value in the solid medium reveals the amount of unexpected energy experienced by the solid continuum, which should be carefully inspected in the thermal-failure design of structures with intrinsic randomness.

On the theory of resonance integrals in the statistical region

1964 ◽  
Vol 1 (02) ◽  
pp. 335-346 ◽  
Author(s):  
A. Reichel ◽  
C. A. Wilkins
Keyword(s):  
Closed Form ◽  
Mean Value ◽  
Resonance Integral ◽  
Theoretical Terms ◽  
Special Cases ◽  
The Mean

The problem of determining infinitely dilute resonance integrals is formulated in renewal theoretical terms. The mean value of the integral for a single resonance is determined in simple closed form. On the assumption that Wigner's hypothesis holds, the resonance density is determined, and a usable approximation to it is derived. An expression for the infinitely dilute resonance integral in the statistical region is then given and its value calculated in special cases and compared with the results of a previous computation.

scholarly journals Interaction of a Screw Dislocation with Interface and Wedge-Shaped Cracks in One-Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Lian he Li ◽  
Yue Zhao
Keyword(s):  
Screw Dislocation ◽  
Electric Fields ◽  
Electric Displacement ◽  
Image Force ◽  
Coupling Constants ◽  
Geometrical Parameters ◽  
Intensity Factors ◽  
One Dimensional ◽  
Special Cases ◽  
Analytical Expressions

Interaction of a screw dislocation with wedge-shaped cracks in one-dimensional hexagonal piezoelectric quasicrystals bimaterial is considered. The general solutions of the elastic and electric fields are derived by complex variable method. Then the analytical expressions for the phonon stresses, phason stresses, and electric displacements are given. The stresses and electric displacement intensity factors of the cracks are also calculated, as well as the force on dislocation. The effects of the coupling constants, the geometrical parameters of cracks, and the dislocation location on stresses intensity factors and image force are shown graphically. The distribution characteristics with regard to the phonon stresses, phason stresses, and electric displacements are discussed in detail. The solutions of several special cases are obtained as the results of the present conclusion.

scholarly journals Research on Intelligent Compaction Technology of Subgrade Based on Regression Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ziyi Hou ◽  
Xiao Dang ◽  
Yezhen Yuan ◽  
Bo Tian ◽  
Sili Li
Keyword(s):  
Resilient Modulus ◽  
Single Point ◽  
Mean Value ◽  
Test Results ◽  
Intelligent Compaction ◽  
One Dimensional ◽  
Remote Monitoring System ◽  
The Mean ◽  
The One ◽  
Compaction Degree

A remote monitoring system with the intelligent compaction index CMV as the core is designed and developed to address the shortcomings of traditional subgrade compaction quality evaluation methods. Based on the actual project, the correlation between the CMV and conventional compaction indexes of compaction degree K and dynamic resilient modulus E is investigated by applying the one-dimensional linear regression equation for three types of subgrade fillers, clayey gravel, pulverized gravel, and soil-rock mixed fill, and the scheme of fitting CMV to the mean value of conventional indexes is adopted, which is compared with the scheme of fitting CMV to the single point of conventional indexes in the existing specification. The test results show that the correlation between the CMV and conventional indexes of clayey gravel and pulverized gravel is much stronger than that of soil-rock mixed subgrades, and the correlation coefficient can be significantly improved by fitting CMV to the mean of conventional indexes compared with single-point fitting, which can be considered as a new method for intelligent rolling correlation verification.

scholarly journals On the spectra of Schrödinger and Jacobi operators with complex-valued quasi-periodic algebro-geometric coefficients

2005 ◽  
Author(s):  
◽  
Vladimir Batchenko
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Complex Plane ◽  
Mean Value ◽  
Qualitative Behavior ◽  
Conditional Stability ◽  
One Dimensional ◽  
Jacobi Operators ◽  
The Mean ◽  
Complex Valued

In this thesis we characterize the spectrum of one-dimensional Schrödinger operators. H = -d2/dx2+V in L2(R; dx) with quasi-periodic complex-valued algebro geometric, potentials V (i.e., potentials V which satisfy one (and hence infinitely many) equation(s) of the stationary Korteweg-de Vries (KdV) hierarchy) associated with nonsingular hyperelliptic curves. The spectrum of H coincides with the conditional stability set of H and can explicitly be described in terms of the mean value of the inverse of the diagonal Green's function of H. As a result, the spectrum of H consists of finitely many simple analytic arcs and one semi-infinite simple analytic arc in the complex plane. Crossings as well as confluences of spectral arcs are possible and discussed as well. These results extend to the Lp(R; dx)-setting for p 2 [1,1). In addition, we apply these techniques to the discrete case and characterize the spectrum of one-dimensional Jacobi operators H = aS+ + a-S- b in 2(Z) assuming a, b are complex-valued quasi-periodic algebro-geometric coefficients. In analogy to the case of Schrödinger operators, we prove that the spectrum of H coincides with the conditional stability set of H and can also explicitly be described in terms of the mean value of the Green's function of H. The qualitative behavior of the spectrum of H in the complex plane is similar to the Schrödinger case: the spectrum consists of finitely many bounded simple analytic arcs in the complex plane which may exhibit crossings as well as confluences.

Random response of dielectric elastomer balloon to electrical or mechanical perturbation

2016 ◽  
Vol 28 (2) ◽  
pp. 195-203 ◽  
Author(s):  
Xiaoling Jin ◽  
Zhilong Huang
Keyword(s):  
Joint Probability ◽  
Stochastic Averaging ◽  
Stretch Ratio ◽  
Dielectric Elastomer ◽  
Mean Value ◽  
Rate Of Change ◽  
Random Response ◽  
First Case ◽  
Special Cases ◽  
The Mean

Random response of dielectric elastomer balloon disturbed by electrical or mechanical fluctuation is analytically investigated in this article. The stochastic differential equation governing the oscillating behavior around the stable equilibrium position is first derived by introducing the translation transformation. The stationary joint probability density about the disturbing stretch ratio and its rate of change is analytically established by adopting the stochastic averaging of energy envelope; the statistics quantities, such as the mean value and the standard deviation of the disturbing stretch ratio, are then subsequently calculated. Two special cases, the first case with only voltage fluctuation and the second one with only pressure variation, are discussed in detail, and the random response properties are summarized. The accuracy of the analytical solution is verified by comparing with the Monte Carlo simulation for the perturbation with weak intensity, and the valid ranges for the mean voltage and pressure are illustrated. This work provides an effective technique to evaluate the detection precision of new type of sensors based on the dielectric elastomer.

scholarly journals Classical path from quantum motion for a particle in a transparent box

2014 ◽  
Vol 36 (2) ◽  
Author(s):  
Salvatore De Vincenzo
Keyword(s):  
Undergraduate Students ◽  
Free Particle ◽  
Mean Value ◽  
Position Operator ◽  
One Dimensional ◽  
Quantum Numbers ◽  
Classical Path ◽  
The Mean ◽  
Basic Ideas ◽  
Quantum Motion

We consider the problem of a free particle inside a one-dimensional box with transparent walls (or equivalently, along a circle with a constant speed) and discuss the classical and quantum descriptions of the problem. After calculating the mean value of the position operator in a time-dependent normalized complex general state and the Fourier series of the function position, we explicitly prove that these two quantities are in accordance by (essentially) imposing the approximation of high principal quantum numbers on the mean value. The presentation is accessible to advanced undergraduate students with a knowledge of the basic ideas of quantum mechanics.

Excursions above a fixed level by n-dimensional random fields

1976 ◽  
Vol 13 (2) ◽  
pp. 276-289 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Stochastic Process ◽  
Random Field ◽  
Random Fields ◽  
Mean Value ◽  
Regularity Conditions ◽  
Gaussian Field ◽  
Differential Topology ◽  
One Dimensional ◽  
Excursion Set ◽  
The Mean

For an n-dimensional random field X(t) we define the excursion set A of X(t) by A = [t ∊ S: X(t) ≧ u] for real u and compact S ⊂ Rn. We obtain a generalisation of the number of upcrossings of a one-dimensional stochastic process to random fields via a characteristic of the set A related to the Euler characteristic of differential topology. When X(t) is a homogeneous Gaussian field satisfying certain regularity conditions we obtain an explicit formula for the mean value of this characteristic.

First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes

2009 ◽  
Vol 16 (04) ◽  
pp. 325-350 ◽  
Author(s):  
Mario Abundo
Keyword(s):  
Diffusion Process ◽  
Diffusion Processes ◽  
Exit Time ◽  
Skew Brownian Motion ◽  
One Dimensional ◽  
Mean Exit Time ◽  
The Mean ◽  
The Right ◽  
Analytical Expressions ◽  
Skew Diffusion

For a, b > 0, we consider a temporally homogeneous, one-dimensional diffusion process X(t) defined over I = (-b, a), with infinitesimal parameters depending on the sign of X(t). We suppose that, when X(t) reaches the position 0, it is reflected rightward to δ with probability p > 0 and leftward to -δ with probability 1 - p, where δ > 0. Closed analytical expressions are found for the mean exit time from the interval (-b, a), and for the probability of exit through the right end a, in the limit δ → 0+, generalizing the results of Lefebvre, holding for asymmetric Wiener process. Moreover, in alternative to the heavy analytical calculations, a numerical method is presented to estimate approximately the quantities above. Furthermore, on the analogy of skew Brownian motion, the notion of skew diffusion process is introduced. Some examples and numerical results are also reported.

Excursions above a fixed level by n-dimensional random fields

1976 ◽  
Vol 13 (02) ◽  
pp. 276-289 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Stochastic Process ◽  
Random Field ◽  
Random Fields ◽  
Mean Value ◽  
Regularity Conditions ◽  
Gaussian Field ◽  
Differential Topology ◽  
One Dimensional ◽  
Excursion Set ◽  
The Mean

For an n-dimensional random field X(t) we define the excursion set A of X(t) by A = [t ∊ S: X(t) ≧ u] for real u and compact S ⊂ Rn. We obtain a generalisation of the number of upcrossings of a one-dimensional stochastic process to random fields via a characteristic of the set A related to the Euler characteristic of differential topology. When X(t) is a homogeneous Gaussian field satisfying certain regularity conditions we obtain an explicit formula for the mean value of this characteristic.

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