Search results for "Recursion"
showing 10 items of 61 documents
Pattern formation through phase bistability in oscillatory systems with space-modulated forcing.
2010
We propose a novel forcing technique of spatially extended self-oscillatory systems able to excite phase bistability and the dissipative structures associated with it. The forcing is time periodic at a frequency close to the oscillators' frequency and is spatially modulated. The effects of this type of forcing are demonstrated analytically and numerically in a directly driven complex Ginzburg-Landau equation. Both spatially periodic and spatially random drives prove to be effective.
Test of molecular mode coupling theory for general rigid molecules
2000
We report recent progress on the test of mode coupling theory for molecular liquids (MMCT) for molecules of arbitrary shape. The MMCT equations in the long time limit are solved for supercooled water including all molecular degrees of freedom. In contrast to our earlier treatment of water as a linear molecule, we find that the glass-transition temperature ${T}_{c}$ is overestimated by the theory as was found in the case of simple liquids. The nonergodicity parameters are calculated from the ``full'' set of MMCT equations truncated at ${l}_{\mathrm{co}}=2.$ These results are compared (i) with the nonergodicity parameters from MMCT with ${l}_{\mathrm{co}}=2$ in the ``dipole'' approximation ${…
Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance.
2000
We show that a self-oscillatory system, driven at two frequencies close to that of the unforced system (resonance 1:1), becomes phase locked and exhibits two equivalent stable states of opposite phases. For spatially extended systems this phase bistability results in patterns characteristic for real order parameter systems, such as phase domains, labyrinths, and phase spatial solitons. In variational cases, the phase-locking mechanism is interpreted as a result of the periodic "rocking" of the system potential. Rocking could be tested experimentally in lasers and in oscillatory chemical reactions.
Recursive method for computing matrix elements for two-body interactions
2015
A recursive method for the efficient computation of two-body matrix elements is presented. The method consists of a set of recursion relations for the computationally demanding radial integral and adds one more tool to the set of computational methods introduced by Horie and Sasaki [H. Horie and K. Sasaki, Prog. Theor. Phys. 25, 475 (1961)]. The neutrinoless double-$\ensuremath{\beta}$ decay will serve as the primary application and example, but the method is general and can be applied equally well to other kinds of nuclear structure calculations involving matrix elements of two-body interactions.
A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting
2016
The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finit…
Measure, category and learning theory
1995
Measure and category (or rather, their recursion theoretical counterparts) have been used in Theoretical Computer Science to make precise the intuitive notion “for most of the recursive sets.” We use the notions of effective measure and category to discuss the relative sizes of inferrible sets, and their complements. We find that inferrible sets become large rather quickly in the standard hierarchies of learnability. On the other hand, the complements of the learnable sets are all large.
Indefinite integrals of quotients of special functions
2018
ABSTRACTA new method is presented for deriving indefinite integrals involving quotients of special functions. The method combines an integration formula given previously with the recursion relations obeyed by the function. Some additional results are presented using an elementary method, here called reciprocation, which can also be used in combination with the new method to obtain additional quotient integrals. Sample results are given here for Bessel functions, Airy functions, associated Legendre functions and the three complete elliptic integrals. All results given have been numerically checked with Mathematica.
A reduction theorem for the Galois–McKay conjecture
2020
We introduce H {\mathcal {H}} -triples and a partial order relation on them, generalizing the theory of ordering character triples developed by Navarro and Späth. This generalization takes into account the action of Galois automorphisms on characters and, together with previous results of Ladisch and Turull, allows us to reduce the Galois–McKay conjecture to a question about simple groups.
Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity
2018
We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and $$\pm \infty $$ . Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.
On-shell recursion relations for all Born QCD amplitudes
2007
We consider on-shell recursion relations for all Born QCD amplitudes. This includes amplitudes with several pairs of quarks and massive quarks. We give a detailed description on how to shift the external particles in spinor space and clarify the allowed helicities of the shifted legs. We proof that the corresponding meromorphic functions vanish at z --> infinity. As an application we obtain compact expressions for helicity amplitudes including a pair of massive quarks, one negative helicity gluon and an arbitrary number of positive helicity gluons.