Approximate solutions to fractional subdiffusion equations

The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann-Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Wright function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Wright function and error estimations.     

一种直接测量W-J参数的实验方法

本文探索了一种直接测量W-J参数的方法. 实验选用NaCl作为试样, 在快速压缩过程中原位测量样品的温度和压力的变化值. 通过温度修正使测量值在原理上更符合等熵压缩过程的结果, 并采用大幅度增压结合中值定理得出中点压力处温度随压力的变化率, 进而根据R=(P/T) (∂T/∂P)_S关系式求出W-J参数, 整个过程没有引入其他参数. 此外, 作为对比, 我们还从相关的物态方程、经验公式和已知参数出发计算了NaCl的W-J参数及其随压力变化的关系. 结果表明: 实验测得的NaCl的W-J参数随压力增加而增加; 实验结果与计算值符合得很好. 这说明快速增压直接测量物质的W-J参数是一种可行且可靠的方法. 关键词： NaCl W-J参数 快速增压 高压     

How to measure the polarization of top quarks

The production of polarized top quarks will be reflected in the polarization of T¹ mesons and can be observed experimentally through their dominant weak decays. It is shown that energy and transverse momentum distributions of top-meson decay products are effected and eventually enhanced or depleted by a factor between 0.5 and 1.5. Parity-violating effects in the lepton distribution from top decay could be observed.     

Ratchet transport with subdiffusion

We introduce a model which combines the subdiffusive dynamics and the ratchet effect. Using a subordination ideology, we show that the resulting directed transport is sublinear, 〈 x(t)〉≃Jt^β, β< 1. The proposed model may be relevant to a phenomenon of saltatory microbiological motility.     

Field-induced dispersion in subdiffusion

We discuss the response of continuous-time random walks to an oscillating external field within the generalized master equation approach. We concentrate on the time dependence of the two first moments of the walker's displacement. We show that for power-law waiting-time distributions with 0相似文献   

How to measure the pomeron phasein diffractive dipion photoproduction

The study of charge asymmetry of pions in the high-energy process ep → eπ⁺π^-p (γp → π⁺π^-p) at very small dipion momenta offers a method to measure the phase of the forward hadronic (quasi-) elastic amplitude γp → ρp. We estimate the potential of such measurements at HERA. Received: 19 February 2004, Revised: 1 August 2005, Published online: 3 November 2005     

How to measure the charm density in the proton

We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio R(x, Q ²) = F _L /F _T and/or the azimuthal cos(2φ) asymmetry in DIS. Our approach is based on the following observations. First, the ratio R(x, Q ²) = F _L /F _T and azimuthal cos(2φ) asymmetry in heavy-quark leptoproduction are stable, both parametrically and perturbatively, within pQCD. Second, both these quantities are sensitive to resummation of the mass logarithms of the type α_sln(Q ²/m ²). We conclude that the heavy-quark densities in the nucleon can, in principle, be determined from high-Q ² data on the Callan-Gross ratio and/or the azimuthal asymmetry. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.     

How to measure the earth's velocity with respect to absolute space

In our absolute space-time theory the time dilation is treated as an absolute phenomenon and it appears as a result of the motion of the material systems with respect to absolute space. Hence, comparing the courses of two atomic clocks put at two antipodal points of the equator (which in the different hours of the day move with different velocities with respect to the absolute space), one can establish the velocity of the Earth as a whole.     

How to measure the internuclear vector from photoelectron angular distributions

This paper uses a nonperturbative scattering theory to study photoelectron angular distributions of homonuclear diatomic molecules irradiated by circularly polarized laser fields. This study shows that the nonisotropic feature of photoelectron angular distributions is not due to the polarization of the laser field but the internuclear vector of the molecules. It suggests a method to measure the molecular orientation and the internuclear distance of molecules through the measurement of photoelectron angular distributions.     

How to measure the magnetic moment of the tau lepton

We present a method for obtaining bounds on the magnetic moment of the lepton. In order to do this, we study the radiative decayW as a function of the anomalous magnetic moment of the ,a . One can obtain bounds as good asa < 4.05×10^–2, 2.25×10^–2, 4.5×10^–3, and 2.5×10^–3 at the present Fermilab, future Fermilab, SSC, and LHC, respectively.     

How to measure the phase diffusion dynamics in the micromaser

We propose a realistic scheme for measuring the micromaser linewidth by monitoring the phase diffusion dynamics of the cavity field. Our strategy consists of exciting an initial coherent state with the same photon number distribution as the micromaser steady-state field, singling out a purely diffusive process in the system dynamics. After the injection of a counterfield, measurements of the population statistics of a probe atom allow us to derive the micromaser linewidth in all ranges of the relevant parameters, establishing experimentally the distinctive features of the micromaser spectrum due to the discreteness of the electromagnetic field.     

How to measure chi(3) of a nanoparticle

Most of the known methods to measure the nonlinear optical properties of materials deal with the bulk properties, but there are many demanding applications that require those measurements to be done on a single particle or a single molecule. We report a novel application of nonlinear optics to measure the third-order nonlinear optical susceptibility of nanoparticles in solutions. By measuring the power of the third harmonic generated in a diluted solution of nanoparticles, both the size and chi(3) can be extracted from a simple set of measurements.     

Confined subdiffusion in three dimensions

Three-dimensional （3D） Fick＇s diffusion equation and fractional diffusion equation are solved for different reflecting boundaries. We use the continuous time random walk model （CTRW） to investigate the time-averaged mean square dis- placement （MSD） of a 3D single particle trajectory. Theoretical results show that the ensemble average of the time-averaged MSD can be expressed analytically by a Mittag-Leffler function. Our new expression is in agreement with previous formu- las in two limiting cases： （^-δ2） ~ △1 in short lag time and （^-δ2} ~ △1 -α in long lag time. We also simulate the experimental data of mRNA diffusion in living E. coli using a 3D CTRW model under confined and crowded conditions. The simulation results are well consistent with experimental results. The calculations of power spectral density （PSD） further indicate the subdiffsive behavior of an individual trajectory.     

How to measure energy dissipation in dynamic mode atomic force microscopy

When studying a mechanical system like an atomic force microscope (AFM) in dynamic mode it is intuitive and instructive to analyse the forces involved in tip–sample interaction. A different but complementary approach is based on analysing the energy that is dissipated when the tip periodically interacts with the sample surface. This method does not require solving the differential equation of motion for the oscillating cantilever, but is based entirely on the analysis of the energy flow in and out of the dynamic system. Therefore the problem of finding a realistic model to describe the tip–sample interaction in terms of non-linear force–distance dependencies and damping effects is omitted. Instead, it is possible to determine the energy dissipated by the tip–sample interaction directly by measuring such quantities as oscillation amplitude, frequency, phase shift and drive amplitude. The method proved to be important when interpreting phase data obtained in tapping mode, but is also applicable to a variety of scanning probe microscopes operating in different dynamic modes. Additional electronics were designed to allow a direct mapping of local energy dissipation while scanning a sample surface. By applying this technique to the cross-section of a polymer blend a material specific contrast was observed.     

How to measure squeezing and entanglement of Gaussian states without homodyning

We propose a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection. The suggested setup needs only beam splitters and single-photon detectors. Two-mode entanglement can be detected from coincidences between photodetectors placed on the two beams.     

如何做好"用油膜法估测分子的大小"实验

介绍了“用油膜法估测分子的大小”实验的准备工作及对学生进行正确实验指导的方法。     

How to measure the bogoliubov quasiparticle amplitudes in a trapped condensate

We propose an experiment, based on two consecutive Bragg pulses, to measure the momentum distribution of quasiparticle excitations in a trapped Bose gas at low temperature. With the first pulse one generates a bunch of excitations carrying momentum q, whose Doppler line is measured by the second pulse. We show that this experiment can provide direct access to the amplitudes u(q) and v(q) characterizing the Bogoliubov transformations from particles to quasiparticles. We simulate the behavior of the nonuniform gas by numerically solving the time dependent Gross-Pitaevskii equation.     

Boundary conditions for the subdiffusion equation

The boundary conditions for the subdiffusion equations are formulated using the continuous-time random walk model, as well as several versions of the random walk model on an irregular lattice. It is shown that the boundary conditions for the same equation in different models have different forms, and this difference considerably affects the solutions of this equation.     

Multidimensional subdiffusion model: Arbitrage-free market

To capture the subdiffusive characteristics of financial markets, the subordinated process, directed by the inverse α-stale subordinator S_α(t) for 0 < α <1, has been employed as the model of asset prices. In this article, we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks. The stock price process is a multidimensional subdiffusion process directed by the inverse α-stable subordinator. This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks. Moreover, we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process by Laplace transform technique. Finally, using martingale approach, we prove that the multidimensional subdiffusion model is arbitrage-free, and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.