Fluctuation-driven directed transport in the presence of Lévy flights

The role of Lévy flights on fluctuation-driven transport in time independent periodic potentials with broken spatial symmetry is studied. Two complementary approaches are followed. The first one is based on a generalized Langevin model describing overdamped dynamics in a ratchet type external potential driven by Lévy white noise with stability index α in the range 1<α<2. The second approach is based on the space fractional Fokker-Planck equation describing the corresponding probability density function (PDF) of particle displacements. It is observed that, even in the absence of an external tilting force or a bias in the noise, the Lévy flights drive the system out of the thermodynamic equilibrium and generate an up-hill current (i.e., a current in the direction of the steeper side of the asymmetric potential). For small values of the noise intensity there is an optimal value of α yielding the maximum current. The direction and magnitude of the current can be manipulated by changing the Lévy noise asymmetry and the potential asymmetry. For a sharply localized initial condition, the PDF of staying at the minimum of the potential exhibits scaling behavior in time with an exponent bigger than the −1/α exponent corresponding to the force free case.     

Subordination scenario of the Cole-Davidson relaxation

The non-exponential relaxation is shown to result from the temporal subordination of an initial, exponentially decaying state by inverse tempered α-stable processes. In contrast to the ordinary α-stable processes the tempered α-stable ones are characterized by the finiteness of their moments. This approach establishes a direct link between the Cole-Cole and the Cole-Davidson relaxation laws.     

Time and scale Hurst exponent analysis for financial markets

We use a new method of studying the Hurst exponent with time and scale dependency. This new approach allows us to recover the major events affecting worldwide markets (such as the September 11th terrorist attack) and analyze the way those effects propagate through the different scales. The time-scale dependence of the referred measures demonstrates the relevance of entropy measures in distinguishing the several characteristics of market indices: “effects” include early awareness, patterns of evolution as well as comparative behaviour distinctions in emergent/established markets.     

On the existence of ion-acoustic solitary waves in a gravitating dusty plasma having charge fluctuation

Theoretical investigation on the propagation of ion-acoustic waves in an unmagnetized self-gravitating plasma has been made for the existence of solitary waves using the reductive perturbation method. It is observed that nonlinear excitations follow a coupled third-order partial differential equation which is slightly different from the usual case of coupled Korteweg-de Vries (K-dV) system. It appears that the system so deduced is a two-component generalization of the previous one derived by Paul et al. (1999) in which it was shown that ion-acoustic solitary waves can not exist in such system.     

Cluster growth poised on the edge of break-up: Size distributions with small exponent power-laws

In many naturally occurring growth processes, cluster size distributions of power-law form n(s)∝s^−τ with small exponents 0<τ<1 are observed. We suggest here that such distributions emerge naturally from cluster growth, where size dependent aggregation is counterbalanced by size dependent break-up. The model used in the study is a simple reaction kinetic model including only monomer-cluster processes. It is shown that under such conditions power-law size distributions with small exponents are obtained. Therefore, the results suggest that the ubiquity of small exponent power-law distributions is related to the growth process, where aggregation driven cluster growth is poised on the edge of cluster break-up.     

Entropy-driven phase transitions with influence of the field-dependent diffusion coefficient

We present a comprehensive study of phase transitions in a single-field reaction-diffusion stochastic systems with a field-dependent mobility of a power-law form and internal fluctuations. Using variational principles and mean-field theory we have shown that the noise can sustain spatial patterns and leads to phase transitions type of “order-disorder”. These phase transitions can be critical and non-critical in character. Our theoretical results are verified by computer simulations.     

Oscillation modes in Coulomb clusters with variable charges

The mode spectra of small N=3 and N=7 clusters of dust particles with fluctuating charges are analyzed. It is demonstrated that the main effect related to the charge fluctuations is a splitting of the spectrum modes. The splitting depends the value of the charge variance. It is found that the most affected mode is the fundamental pure rotational mode. The least affected modes are pure translational ones while other modes demonstrate mixed response to the variance of the charge fluctuations.     

Anomalous dynamic scaling of the non-local growth equations

The anomalous dynamic scaling behavior of the d+1 dimensional non-local growth equations is investigated based on the scaling approach. The growth equations studied include the non-local Kardar-Parisi-Zhang (NKPZ), non-local Sun-Guo-Grant (NSGG), and non-local Lai-Das Sarma-Villain (NLDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. Our results show that non-local interactions can affect anomalous scaling properties of surface fluctuations.     

Experimental study of transport of macroparticles in plasma RF-discharge

Experimental study of the kinematic viscosity and the diffusion is performed for macroparticles of different sizes in plasma of a capacitive radio-frequency (RF-) discharge. Experimental examination of the Einstein-Stokes relation between the viscosity and diffusion constants is carried out. A comparison of the measured transport constants with the existing numerical data is presented.     

Numerical Simulation of Dust Void Evolution in Complex Plasmas with Ionization Effect

We develop the nonlinear theory of dust voids [Phys. Rev. Lett. 90 （2003） 075001], focusing particularly on effects of the ionization, to investigate numerically the void evolution under cylindrical coordinates [Phys. Plasmas 13 （2006） 064502]. The ion velocity profile is solved by a more accurate ion motion equation with the ion convection and ionization terms. It is shown that the differences between the previous result and the one obtained with ionizations are significant for the distributions of the ion and dust velocities, the dust density, and etc., in the void formation process. Furthermore, the ionization can slow down the void formation process effectively.     

Thermodynamic properties of two-dimensional Yukawa systems

The simple analytical approximation for the energy densities in two-dimensional Yukawa systems is proposed for the wide range of parameters of non-ideal fluids. The use of this approach allows determining all thermodynamic functions and characteristics on the base of general thermodynamic relationships. The comparisons of obtained results with the numerical study of thermodynamic properties are presented. Simulations were performed for parameters typical for the laboratory dusty plasma experiments.     

Anomalous mobility and current reversals in inertial deterministic ratchets

We analyze the transport properties of inertial deterministic rocking ratchets in the presence of an external constant force. For small values of this load, we can obtain a positive current for a negative load, and vice versa. This phenomenon, in which the direction of the current is opposed to the sign of the external force, is a signature of anomalous negative mobility. We show that this anomalous mobility is possible in the deterministic case, and explain this phenomenon as current reversals associated to bifurcations in an inertial deterministic rocking ratchet in the presence of an external load.     

Results for a fractional diffusion equation with a nonlocal term in spherical symmetry

We obtain time dependent solutions for a fractional diffusion equation containing a nonlocal term by considering the spherical symmetry and using the Green function approach. The nonlocal term incorporated in the diffusion equation may also be related to the spatial and time fractional derivative and introduces different regimes of spreading of the solution with the time evolution. In addition, a rich class of anomalous diffusion processes may be described from the results obtained here.     

Diffusion in a surface: the atomic slide puzzle

We review measurements performed using scanning tunneling microscopy of the motion of impurity atoms in the Cu (001) surface. Like several other elements, the impurity that we have introduced, In, tends to embed itself in the first atomic layer of this surface. Via the motion of the embedded In atoms, we obtain direct information on the motion of the Cu atoms in the surface. In other words, we employ the In atoms as tracer particles to investigate the intrinsic motion in the first Cu layer. The peculiar statistics of the two-dimensional In diffusion allows us to conclude that the motion is assisted by a rapidly diffusing entity, which we identify as a surface vacancy, i.e. a single missing Cu atom in the outermost Cu layer. A comparison with model calculations of the statistics of the vacancy-assisted motion of terrace atoms shows that there must be an attractive interaction between an embedded In atom and a vacancy, which makes the In atom somewhat more mobile than a Cu surface atom. Such an attraction is indeed found in embedded-atom-method calculations. Nevertheless, the temperature dependence of the indium motion provides an accurate estimation of the sum E_form+E_act, representing the sum of the formation energy of a vacancy and the activation energy for the motion of vacancies through a clean Cu (001) surface. Received: 30 April 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media

The Lévy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable diffusion coefficient, is solved in the diffusion limit. That solution resolves itself to the stretched Gaussian when the order parameter μ→2. The truncation of the Lévy flights, in the exponential and power-law form, is introduced and the corresponding random walk process is simulated by the Monte Carlo method. The stretched Gaussian tails are found in both cases. The time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter. When the cutoff function falls slowly, the tail of the distribution appears to be algebraic.     

Drift velocity in the necklace model for reptation in a two-dimensional square lattice

We report the chain dynamics in the necklace model that mimics the reptation of a chain of N particles in a two-dimensional square lattice. We focus on the drift velocity under an applied static field. The characteristics of the model allow us to determine the effects of the forces on the chains and the resulting mechanisms that affect the drift velocity. Results obtained through Monte Carlo simulations were analyzed and discussed and distinct regimes as a function of the force strength and N were identified. We found that for small total applied forces, the drift velocity scales as 1/N. When the applied force to every particle is small but the total applied force is not, the tube deforms in such a way that the drift velocity does not depend on N. Large forces, applied to every particle, can straight chains such that the distance between the chain ends increases faster than the number of particles. Also, large forces can deform the chain within the tube what is directly related to a decrease of the drift velocity.     

Cylindrical and spherical dust ion-acoustic solitary waves in quantum plasmas

Dust ion-acoustic solitary waves in unmagnetized quantum plasmas are studied in spherical and cylindrical geometries. Using quantum hydrodynamic model, the electrostatic waves are investigated in the weakly nonlinear limit. A deformed Korteweg-de Vries (dKdV) equation is derived by using the reductive perturbation method and its numerical solutions are also presented. The quantum diffraction and quantum statistical effects incorporated in the system modifies the characteristics of dust ion-acoustic waves in cylindrical and spherical geometries. The role of stationary dust particles in quantum plasmas are also discussed. It is shown that the cylindrical and spherical dust ion-acoustic solitary waves behave quite differently from one-dimensional planar solitary waves in quantum plasmas.     

Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field

We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the stationary limit. If magnetic field is smaller compared to the critical value, determined by frictional anisotropy, the relaxation of the correlation is non-oscillating in time. However, in a larger magnetic field this relaxation becomes oscillating. The phenomenon is related to the statistical dependence of the components of transformed random force caused by the simultaneous influence of magnetic field and anisotropic dissipation.