Search results for "universality"
showing 10 items of 107 documents
Proposal for Testing Lepton Universality in Upsilon Decays at a B Factory Running at Υ(3S)
2006
We present a proposal for detecting new physics at a B-factory running at the $\Upsilon(3S)$ resonance by testing lepton universality to the few percent level in the leptonic decays of the $\Upsilon(1S)$ and $\Upsilon(2S)$ resonances tagged by the dipion in the chain decay: $\Upsilon(3S) \to pi^+\pi^-\Upsilon(1S,2S)$; $\Upsilon(1S,2S) \to \ell^+\ell^-$, $\ell=e,\mu,\tau$.
Universality in Fragmentation
1999
Fragmentation of a two-dimensional brittle solid by impact and ``explosion,'' and a fluid by ``explosion'' are all shown to become critical. The critical points appear at a nonzero impact velocity, and at infinite explosion duration, respectively. Within the critical regimes, the fragment-size distributions satisfy a scaling form qualitatively similar to that of the cluster-size distribution of percolation, but they belong to another universality class. Energy balance arguments give a correlation length exponent that is exactly one-half of its percolation value. A single crack dominates fragmentation in the slow-fracture limit, as expected.
Kolmogorov-Arnold-Moser–Renormalization-Group Analysis of Stability in Hamiltonian Flows
1997
We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.
Finite size effects at phase transitions
2008
For many models of statistical thermodynamics and of lattice gauge theory computer simulation methods have become a valuable tool for the study of critical phenomena, to locate phase transitions, distinguish whether they are of first or second order, and so on. Since simulations always deal with finite systems, analysis of finite size effects by suitable finite size scaling concepts is a key ingredient of such applications. The phenomenological theory of finite size scaling is reviewed with emphasis on the concept of probability distributions of order parameter and/or energy. Attention is also drawn to recent developments concerning anisotropic geometries and anisotropic critical behavior, …
Cellular automaton for chimera states
2016
A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority (voting) rule. This suggests the universality of chimera-like behavior from a new point of view: Already simple CA rules based on the majority rule exhibit this behavior. After a short transient, we find chimera states for arbitrary initial conditions, the system spontaneously splitting into stable domains separated by static boundaries, ones synchronously oscillating and the others incoherent. When the coupling range is local, nontrivial coherent struct…
Indicators of Errors for Approximate Solutions of Differential Equations
2014
Error indicators play an important role in mesh-adaptive numerical algorithms, which currently dominate in mathematical and numerical modeling of various models in physics, chemistry, biology, economics, and other sciences. Their goal is to present a comparative measure of errors related to different parts of the computational domain, which could suggest a reasonable way of improving the finite dimensional space used to compute the approximate solution. An “ideal” error indicator must possess several properties: efficiency, computability, and universality. In other words, it must correctly reproduce the distribution of errors, be indeed computable, and be applicable to a wide set of approxi…
Universality of level spacing distributions in classical chaos
2007
Abstract We suggest that random matrix theory applied to a matrix of lengths of classical trajectories can be used in classical billiards to distinguish chaotic from non-chaotic behavior. We consider in 2D the integrable circular and rectangular billiard, the chaotic cardioid, Sinai and stadium billiard as well as mixed billiards from the Limacon/Robnik family. From the spectrum of the length matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe non-generic (Dirac comb) behavior in the integrable case and Wignerian behavior in the chaotic case. For the Robnik billiard close to the circle the distribution approaches a Poissonian dis…
Localization-delocalization transition for disordered cubic harmonic lattices.
2012
We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of $\nu = 1.550^{+0.020}_{-0.017}$ confirms the agreement with the universality class of the standard electronic Anderson model of localization. We further support our investigation with studies of the density of states…
Anomalies in b→s Transitions and Dark Matter
2018
Since 2013, the LHCb collaboration has reported on the measurement of several observables associated to $b \to s$ transitions, finding various deviations from their predicted values in the Standard Model. These include a set of deviations in branching ratios and angular observables, as well as in the observables $R_K$ and $R_{K^\ast}$, specially built to test the possible violation of Lepton Flavor Universality. Even though these tantalizing hints are not conclusive yet, the $b \to s$ anomalies have gained considerable attention in the flavor community. Here we review New Physics models that address these anomalies and explore their possible connection to the dark matter of the Universe. Af…
Ising model universality for two-dimensional lattices
1993
We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices of Delaunay type with up to 80\,000 sites. By applying reweighting techniques and finite-size scaling analyses to time-series data near criticality, we obtain unambiguous support that the critical exponents for the random lattice agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.