Hierarchy Of Couplings Research Articles

A Hierarchy of Differential-Difference Equations and TheirIntegrable Couplings

Starting from a discrete spectral problem, the correspondinghierarchy of nonlinear differential-difference equation is proposed.It is shown that the hierarchy possesses the bi-Hamiltionianstructures. Further, two integrable coupling systems for the hierarchyare constructed through enlarged Lax pair method.

Mechanics-based statistics of failure risk of quasibrittle structures and size effect on safety factors.

In mechanical design as well as protection from various natural hazards, one must ensure an extremely low failure probability such as 10(-6). How to achieve that goal is adequately understood only for the limiting cases of brittle or ductile structures. Here we present a theory to do that for the transitional class of quasibrittle structures, having brittle constituents and characterized by nonnegligible size of material inhomogeneities. We show that the probability distribution of strength of the representative volume element of material is governed by the Maxwell-Boltzmann distribution of atomic energies and the stress dependence of activation energy barriers; that it is statistically modeled by a hierarchy of series and parallel couplings; and that it consists of a broad Gaussian core having a grafted far-left power-law tail with zero threshold and amplitude depending on temperature and load duration. With increasing structure size, the Gaussian core shrinks and Weibull tail expands according to the weakest-link model for a finite chain of representative volume elements. The model captures experimentally observed deviations of the strength distribution from Weibull distribution and of the mean strength scaling law from a power law. These deviations can be exploited for verification and calibration. The proposed theory will increase the safety of concrete structures, composite parts of aircraft or ships, microelectronic components, microelectromechanical systems, prosthetic devices, etc. It also will improve protection against hazards such as landslides, avalanches, ice breaks, and rock or soil failures.

Semi-direct sums of Lie algebras and continuous integrable couplings

A relation between semi-direct sums of Lie algebras and integrable couplings of continuous soliton equations is presented, and correspondingly, a feasible way to construct integrable couplings is furnished. A direct application to the AKNS spectral problem leads to a novel hierarchy of integrable couplings of the AKNS hierarchy of soliton equations. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards complete classification of integrable systems.

A hierarchy of global coupling induced cluster patterns during the oscillatory H2-electrooxidation reaction on a Pt ring-electrode

We report experimental results on spatiotemporal pattern formation during the oscillatory hydrogen electrooxidation reaction on a Pt ring-electrode under negative (desynchronizing) global coupling (GC). Spatially one-dimensional profiles of the interfacial potential drop along the angular direction of the ring electrode are recorded by means of a potential probe. The dynamics is investigated as a function of two control parameters, the applied voltage U and the strength of the global coupling. The latter is adjusted either by varying the distance between the working electrode (WE) and the reference electrode (RE) or by inserting a negative impedance device in series with the WE. In the absence of global coupling, uniform oscillations were destabilized by migration coupling, and electrochemical turbulence developed at large values of U (H. Varela, C. Beta, A. Bonnefont and K. Krischer, Phys. Rev. Lett., 2005, 94, 174104; ). Already low global coupling strengths sufficed to suppress turbulence. Instead, regular two-phase clusters formed. At higher coupling strength, a second type of two-phase cluster was observed as well as two types of irregular cluster patterns, which were connected with an irregular motion of the cluster boundaries and the emergence and disappearance of clusters through splitting and merging of the boundaries, respectively. Upon increasing the coupling strength even further, five-phase clusters were stabilized and at the highest coupling strength applied the cluster patterns transformed into strongly modulated pulses. The two types of two-phase clusters and the five-phase clusters are analyzed employing several signal processing techniques.

UNCOVERING SHORT-TIME CORRELATIONS BETWEEN MULTICHANNEL RECORDINGS OF BRAIN ACTIVITY: A PHASE-SPACE APPROACH

Short-time correlations in multivariate time series are notoriously difficult to detect. Extending the classical concept of correlation, we present a method to tackle this problem with little computational cost. In essence, the method uncovers multidimensional phase-locking and is especially useful for revealing changes of the dynamical coupling between different brain areas. The approach also permits us to estimate the shortest time-window in which the coupling occurs. Furthermore, the coupling can be quantified by a measure that defines a metric space. Therefore it may be used to identify task-dependent coupling hierarchies between two brain areas. We illustrate the analysis technique by studying the dynamical coupling between two brain regions involved in olfactory processing in the honeybee. We show that the neural activity in both areas is coupled with each other and that the coupling increases significantly during odor processing.

Coupling methodologies for environmental models

Environmental models have been developed to address narrowly defined issues. As these issues become broader and scientific understanding grows, models become more complex. A variety of methodologies couple environmental models to address multifaceted issues, such as cross-media effects, risk analysis, and environmental justice investigations. This study analyzes, from a modeler's perspective, various coupling methodologies according to their characteristics. This analysis is presented as a five-level coupling hierarchy, and includes a representation of a modeling framework for coupled environmental models requiring dynamic feedback during a simulation (e.g., multimedia modeling). The framework addresses the special needs for this type of modeling, including spatial locking for environmental data, autogeneration of simulation metadata, simulation verification, and automated recovery from system problems.

1H NMR Imaging of Residual Dipolar Couplings in Cross-Linked Elastomers: Dipolar-Encoded Longitudinal Magnetization, Double-Quantum, and Triple-Quantum Filters

Contrastfilters for NMR imaging of residual 1H dipolar couplings of elastomers are introduced based on dipolar-encoded longitudinal magnetization, as well as double- and triple-quantum coherences. The spin response is discussed in the initial excitation time regime for methylene, methyl, and methine protons applicable to poly(isoprene) and other elastomers, taking into account the hierarchy of dipolar couplings and the associated editing features of multiple-quantum experiments. The efficiency of these filters is investigated for a series of cross-linked poly(isoprene) samples. Spatially resolved dipolar-encoded longitudinal magnetization decays and double-quantum and triple-quantum buildup curves are presented for a phantom made of poly(isoprene) with different cross-link densities. Two-dimensional images representing residual dipolar couplings are presented using dipolar-encoded longitudinal magnetization, double-quantum, and triple-quantum contrast filters. Images from dipolar-encoded longitudinal magnetization and triple-quantum coherences show the highest resolution and contrast, respectively.

Beyond the standard embedding in M-theory on [formula omitted

In this paper we discuss compactifications of M-theory to four dimensions on X × S 1/ Z 2 , in which non-standard embeddings in the E 8 × E 8 vacuum gauge bundle are considered. At the level of the effective field theory description of Horava and Witten, this provides a natural extension of well known results at weak coupling, to strongly coupled E 8 × E 8 heterotic strings. As an application of our results, we discuss models which exhibit an anomalous U(1) A symmetry in four dimensions, and show how this emerges from the reduction of the d = 11 topological term C ∧ G ∧ G, and how it is consistent with d = 4 anomaly cancellation in M-theory. As a further application of non-standard embeddings, we show how it is possible to obtain an inverse hierarchy of gauge couplings, where the observable sector is more strongly coupled than the hidden one. The basic construction and phenomenological viability of these scenarios is demonstrated.

The rovibrational dynamics of hydroxylamine

AbstractThe combination of overtone spectroscopy and detailed quantum mechanical modelling of rovibrational dynamics provides an unique tool for investigating many aspects of intramolecular dynamics such as dynamical symmetries, coupling hierarchies, and the separation of time scales, which control the intramolecular energy flow at high excitations relevant for unimolecular reactions.Hydroxylamine NH2OH, which plays an important role in N/O/H chemistry in general, provides an intriguing example for the interplay between high frequency stretch‐bend motions and low frequency torsion/inversion tunneling. This paper discusses the dynamical analysis of its high resolution infrared absorption spectrum up to the visible range on the basis of up to five‐dimensional ab initio models using vibrational DVR grids of several million points.The torsion‐inversion process is found to follow a consecutive mechanism with very slow (≥ 1 μs) inversion tunneling below the trans‐cis isomerisation barrier (2673 cm−1 at MP2/TZ2P). The metastable cis isomer shows localised zero point and fundamental level eigenfunctions. From the overtone spectrum fast energy redistribution is deduced within the OH and NH2 manifolds, respectively, on time scales below 100 fs. A direct coupling between the two moieties leads to a slow decay of OH stretching excitation within 3 ps. Further significant contributions to the effective homogeneous broadening observed in high OH stretch overtones are predicted from the 1,2‐H shift leading to ammonia oxide NH3O with a barrier around 18200 cm−1 (CASPT2) and a NH3O well depth exceeding 1 eV.The spectroscopic characterisation of the metastable isomers of hydroxyl amine, cis‐NH2OH and NH3O, by stimulated emission pumping experiments is suggested on the basis of ab initio calculations for electronically excited states.

Neutrino mass and lepton mixing hierarchies and future oscillation experiments

Future experiments searching for neutrino oscillations are discussed on the assumption of the existence of a hierarchy in the neutrino masses. Different scenarios for the hierarchy of coupling among lepton families are considered. Relations and inequalities among transition probabilities are derived. The inequalities follow the pattern in the hierarchy of coupling among lepton generations. Simpson's 17 keV neutrino is discussed. It is shown that if such a heavy neutrino exist, the probability of the transition v e→ v τ will not exceed approximately 2×10 −2 independently of the nature (Dirac or Marjorana) and the number of the neutrino mass eigenstates.

Quark mixings and mass hierarchy from radiative corrections

We discuss a scheme where both quark mass hierarchy and mixing angles arise out of radiative corrections and are therefore calculable. No horizontal symmetry or Yukawa coupling hierarchy is required. Masses obey the pattern m u :m c :m t ⋍λ 2:λ:1 (similarly for the down sector), where λ is the loop expansion parameter. The observed quark isodoublet splitting is also obtained. For the mixing angles, we find an interesting result where V ub is of O( λ 2), whereas V us and V cb are each of O(λ). We present a model implementing this scheme where a crucial role is played by a pair of isosinglet heavy quarks.

27 3 Yukawa couplings for a three-generation superstring model

We calculate the 27 3 Yukawas for a phenomenologically viable three-generation model based on a particular Calabi-Yau compactification of the heterotic superstring. We find that CP violation and an interesting hierarchy of couplings may develop as a function of the vacuum complex structure.

Simultaneous bootstrap of mesonic and baryonic trajectories in DTU

We present a mechanism for achieving a simultaneous bootstrap of both mesons and baryons within the framework of Dual Topological Unitarization (DTU). Our model conforms to the rules required for a bootstrap theory of quarks as recently proposed. Our main results are equal-splitting relations such as α ϱ − α Δ = α Δ − α B , where B designates b aryonium and a new hierarchy of couplings.