Related papers: Dimensional analysis and Rutherford Scattering
We derive the modified diffusion equations defined on kappa-space-time and using these, investigate the change in the spectral dimension of kappa-space-time with the probe scale. These deformed diffusion equations are derived by applying…
We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…
I describe a version of so-called naive dimensional analysis, a rule for estimating the sizes of terms in an effective theory below the scale of chiral symmetry breaking induced by a strong gauge interaction. The rule is simpler and more…
The scattering phase shift encodes a good amount of physical information which can be used to study resonances from scattering data. Among others, it can be used to calculate the continuum density of states and the collision time in a…
The two parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$ is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman's Poisson-Dirichlet distribution. The two parameter Dirichlet…
Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical…
An extension of the H-theorem for dissipative particle dynamics (DPD) to the case of a multi-component fluid is made. Detailed balance and an additional H-theorem are proved for an energy-conserving version of the DPD algorithm. The…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
The variational theorem for the scattering length [Cherny and Shanenko, Phys. Rev. E 62, 1646 (2000)] is extended to one and two dimensions. It is shown that the arising singularities can be treated in terms of generalized functions. The…
A conditional diffusion model has been developed to analyze intricate conductance fluctuations called universal conductance fluctuations or quantum fingerprints appearing in quantum transport phenomena. The model reconstructs impurity…
The dynamics of a freely diffusing particle in a two-dimensional channel with cross sectional area $A(x)$, can be effectively described by a one-dimensional diffusion equation under the action of a potential of mean force $U(x)=-k_BT\ln…
The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
The phenomenon of Taylor or shear-induced dispersion of a non-passive scalar field in a pulsatile pipe flow is investigated, accounting for the scalar field's influence on fluid density and transport coefficients. By employing multiple…
The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in the…
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regular inhomogeneities. This technique is then applied to a…
Impact of single particle onto a rigid substrate leads to its deformation and fragmentation. The flow associated with the particle spreading on a solid substrate after impact is extremely complicated. In this theoretical study a simplified…
It is demonstrated by molecular dynamics simulations that liquids interacting via the Buckingham potential are strongly correlating, i.e., have regions of their phase diagram where constant-volume equilibrium fluctuations in the virial and…
From recent analysis of the $\pi\pi$ scattering amplitude, it has been claimed that there exists a broad and light $\sigma$ meson. However, if this meson really exists, it must also appear in other observables such as the pion scalar form…