6,001 research outputs found
Fractional Generalization of Gradient Systems
We consider a fractional generalization of gradient systems. We use
differential forms and exterior derivatives of fractional orders. Examples of
fractional gradient systems are considered. We describe the stationary states
of these systems.Comment: 11 pages, LaTe
Nonholonomic Constraints with Fractional Derivatives
We consider the fractional generalization of nonholonomic constraints defined
by equations with fractional derivatives and provide some examples. The
corresponding equations of motion are derived using variational principle.Comment: 18 page
Dynamic stretching is effective as static stretching at increasing flexibility
This study examined the effect of dynamic and static (standard) stretching on hamstring flexibility. Twenty-five female volleyball players were randomly assigned to dynamic (n = 12) and standard (n = 13) stretching groups. The experimental group trained with repetitive dynamic stretching exercises, while the standard modality group trained with static stretching exercises. The stretching interventions were equivalent in the time at stretch and were performed three days a week for four weeks. Both stretching groups showed significant improvements (P < .001) in range of motion (ROM) during the intervention. However, no difference in gains in the range of motion between stretching groups was observed. It was concluded that both dynamic stretching and standard stretching are effective at increasing ROM
Fractional dynamics of coupled oscillators with long-range interaction
We consider one-dimensional chain of coupled linear and nonlinear oscillators
with long-range power-wise interaction. The corresponding term in dynamical
equations is proportional to . It is shown that the
equation of motion in the infrared limit can be transformed into the medium
equation with the Riesz fractional derivative of order , when
. We consider few models of coupled oscillators and show how their
synchronization can appear as a result of bifurcation, and how the
corresponding solutions depend on . The presence of fractional
derivative leads also to the occurrence of localized structures. Particular
solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear
Schrodinger) equation are derived. These solutions are interpreted as
synchronized states and localized structures of the oscillatory medium.Comment: 34 pages, 18 figure
Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations
We propose diffusion-like equations with time and space fractional
derivatives of the distributed order for the kinetic description of anomalous
diffusion and relaxation phenomena, whose diffusion exponent varies with time
and which, correspondingly, can not be viewed as self-affine random processes
possessing a unique Hurst exponent. We prove the positivity of the solutions of
the proposed equations and establish the relation to the Continuous Time Random
Walk theory. We show that the distributed order time fractional diffusion
equation describes the sub-diffusion random process which is subordinated to
the Wiener process and whose diffusion exponent diminishes in time (retarding
sub-diffusion) leading to superslow diffusion, for which the square
displacement grows logarithmically in time. We also demonstrate that the
distributed order space fractional diffusion equation describes super-diffusion
phenomena when the diffusion exponent grows in time (accelerating
super-diffusion).Comment: 11 pages, LaTe
Broken symmetry of row switching in 2D Josephson junction arrays
We present an experimental and theoretical study of row switching in
two-dimensional Josephson junction arrays. We have observed novel dynamic
states with peculiar percolative patterns of the voltage drop inside the
arrays. These states were directly visualized using laser scanning microscopy
and manifested by fine branching in the current-voltage characteristics of the
arrays. Numerical simulations show that such percolative patterns have an
intrinsic origin and occur independently of positional disorder. We argue that
the appearance of these dynamic states is due to the presence of various
metastable superconducting states in arrays.Comment: 4 Pages, 6 Figure
Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
Fractional generalization of an exterior derivative for calculus of
variations is defined. The Hamilton and Lagrange approaches are considered.
Fractional Hamilton and Euler-Lagrange equations are derived. Fractional
equations of motion are obtained by fractional variation of Lagrangian and
Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe
Breathers in Josephson junction ladders: resonances and electromagnetic waves spectroscopy
We present a theoretical study of the resonant interaction between dynamical
localized states (discrete breathers) and linear electromagnetic excitations
(EEs) in Josephson junction ladders. By making use of direct numerical
simulations we find that such an interaction manifests itself by resonant steps
and various sharp switchings (voltage jumps) in the current-voltage
characteristics. Moreover, the power of ac oscillations away from the breather
center (the breather tail) displays singularities as the externally applied dc
bias decreases. All these features can be mapped to the spectrum of EEs that
has been derived analytically and numerically. Using an improved analysis of
the breather tail, a spectroscopy of the EEs is developed. The nature of
breather instability driven by localized EEs is established.Comment: 15 pages, 13 figure
Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
The classical fields with fractional derivatives are investigated by using
the fractional Lagrangian formulation.The fractional Euler-Lagrange equations
were obtained and two examples were studied.Comment: 9 page
Fractional Derivative as Fractional Power of Derivative
Definitions of fractional derivatives as fractional powers of derivative
operators are suggested. The Taylor series and Fourier series are used to
define fractional power of self-adjoint derivative operator. The Fourier
integrals and Weyl quantization procedure are applied to derive the definition
of fractional derivative operator. Fractional generalization of concept of
stability is considered.Comment: 20 pages, LaTe
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