相关论文: Multifractal dimension spectra in polymer physics
In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
We study fluctuations of particle absorption by a three-dimensional domain with multiple absorbing patches. The domain is in contact with a gas of interacting diffusing particles. This problem is motivated by living cell sensing via…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We show that the spectral dimension on non-generic branched polymer models with susceptibility exponent $\gamma$ is given by $2/(1+\gamma)$. For those models with negative $\gamma$ we find that the spectral dimension is 2.
The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered.…
A new multiplicity distribution with multifractal properties which can be used in high-energy physics and quantum optics is proposed. It may be considered as a generalization of the negative-binomial distribution. We find the structure of…
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the…
We investigate the phase diagram of a self-avoiding walk model of a 3-star polymer in two dimensions, adsorbing at a surface and being desorbed by the action of a force. We show rigorously that there are four phases: a free phase, a…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
We show that the spectral dimension on non-generic branched polymers with positive susceptibility exponent is given by $d_s=2/(1+\gamma)$. For those models with $\gamma<0$ we find that $d_s=2$.
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
We analyze the features of the graphene mono- and multilayer reflectance in the far-infrared region as a function of frequency, temperature, and carrier density taking the intraband conductance and the interband electron absorbtion into…
The transition between ballistic and diffusive motion poses difficult problems in several fields of physics. In this work we show how to calculate the spectra of the correlation functions between fields of arbitrary spatial dependence as…
We study the Dirichlet boundary value problem for viscoelastic diffusion in polymers. We show that its weak solutions generate a dissipative semiflow. We construct the minimal trajectory attractor and the global attractor for this problem.
The formation of breakdown pattern on an insulating surface under the influence of a transverse magnetic field is theoretically investigated. We have generalized the Dielectric Breakdown Model (DBM) for the case of external magnetic field.…
Based on transfer matrix techniques and finite size scaling, we study the oriented polymer (self-avoiding walk) with nearest neighbor interaction. In the repulsive regime, various critical exponents are computed and compared with exact…
In this paper we apply the spectral theory of linear diffusions to study the one-dimensional Liouville Brownian Motion and Liouville Brownian excursions from a given point. As an application we estimate the fractal dimensions of level sets…