Map of discrete system into continuous

Tarasov, Vasily E.
September 2006
Journal of Mathematical Physics;Sep2006, Vol. 47 Issue 9, p092901
Academic Journal
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the continuous limit is discussed. The one-dimensional systems of coupled oscillators for this type of long-range interactions are considered. The discrete equations of motion are mapped into the continuum equation with the Riesz fractional derivative.


Related Articles

  • Discrete Dynamical Systems Associated with the Configuration Space of 8 Points in â„™3(â„‚). Takenawa, Tomoyuki // Communications in Mathematical Physics;Mar2004, Vol. 246 Issue 1, p19 

    A 3 dimensional analogue of Sakai’s theory concerning the relation between rational surfaces and discrete Painlevé equations is studied. For a family of rational varieties obtained by blow-ups at 8 points in general position in ℙ3, we define its symmetry group using the inner...

  • Discrete Space-Time Geometry and Skeleton Conception of Particle Dynamics. Rylov, Yuri // International Journal of Theoretical Physics;Jun2012, Vol. 51 Issue 6, p1847 

    It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete geometry is nonaxiomatizable and multivariant. The...

  • Fractional Pais-Uhlenbeck Oscillator. Baleanu, Dumitru; Petras, Ivo; Asad, Jihad; Velasco, Maria // International Journal of Theoretical Physics;Apr2012, Vol. 51 Issue 4, p1253 

    In this paper we study the fractional Lagrangian of Pais-Uhlenbeck oscillator. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation numerically. The numerical study is based on the so-called Grünwald-Letnikov approach,...

  • Quantum mechanics in fractional and other anomalous spacetimes. Calcagni, Gianluca; Nardelli, Giuseppe; Scalisi, Marco // Journal of Mathematical Physics;Oct2012, Vol. 53 Issue 10, p102110 

    We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of...

  • MINIMUM ENERGY CONTROL OF FRACTIONAL DESCRIPTOR POSITIVE DISCRETE–TIME LINEAR SYSTEMS. KACZOREK, TADEUSZ // International Journal of Applied Mathematics & Computer Science;Dec2014, Vol. 24 Issue 4, p735 

    Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for descriptor positive systems is formulated and solved. Sufficient conditions for the existence of a...

  • ON THE STABILITY OF LINEAR FRACTIONAL DIFFERENCE SYSTEMS. Vettori, Paolo; Pereira, Ricardo // Proceedings of the 10th Portuguese Conference on Automatic Contr;Jul2012, p173 

    A fractional linear system is defined by differential or difference equations of non-integer order. A well-known result about the stability of fractional differential systems will be extended to discrete-time systems defined by fractional difference equations. This will be accomplished using...

  • Correlation Properties of (Discrete) Fractional Gaussian Noise and Fractional Brownian Motion. Delignières, Didier // Mathematical Problems in Engineering;8/11/2015, Vol. 2015, p1 

    The fractional Gaussian noise/fractional Brownian motion framework (fGn/fBm) has been widely used for modeling and interpreting physiological and behavioral data. The concept of 1/f noise, reflecting a kind of optimal complexity in the underlying systems, is of central interest in this approach....

  • Drazin inverse matrix method for fractional descriptor discrete-time linear systems. Kaczorek, T. // Bulletin of the Polish Academy of Sciences: Technical Sciences;Jun2016, Vol. 64 Issue 2, p395 

    The Drazin inverse of matrices is applied in order to find the solutions of the state equations of fractional descriptor discrete-time linear systems. The solution of the state equation is derived and the set of consistent initial conditions for a given set of admissible inputs is established....

  • A new algorithm for a CFE-approximated solution of a discrete-time noninteger-order state equation. OPRZĘDKIEWICZ, K.; STANISŁAWSKI, R.; GAWIN, E.; MITKOWSKI, W. // Bulletin of the Polish Academy of Sciences: Technical Sciences;Sep2017, Vol. 65 Issue 4, p429 

    In the paper, a new method for solution of linear discrete-time fractional-order state equation is presented. The proposed method is simpler than other methods using directly discrete-time version of the Grünwald-Letnikov operator. The method is dedicated to use with any approximator to the...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics