Dynamics of fluctuations below a stationary bifurcation to electroconvection in the planar nematic liquid crystal N4

We fitted C(k,tau,epsilon) proportional to exp([-sigma(k,epsilon)tau] to time-correlation functions C(k,tau,epsilon) of structure factors S(k,t,epsilon) of shadowgraph images of fluctuations below a supercritical bifurcation at V(0)=V(c) to electroconvection of a planar nematic liquid crystal in the presence of a voltage V=sqrt[2]V(0)cos((2pift) [k=(p,q) is the wave vector and epsilon identical with V(2)(0)/V(2)(c)-1]. There were stationary oblique (normal) rolls at small (large) f. Fits of a modified Swift-Hohenberg form to sigma(k,epsilon) gave f-dependent critical behavior for the minimum decay rates sigma(0)(epsilon) and the correlation lengths xi(p,q)(epsilon).     

Statistics of the number of zero crossings: from random polynomials to the diffusion equation

We consider a class of real random polynomials, indexed by an integer d, of large degree n and focus on the number of real roots of such random polynomials. The probability that such polynomials have no real root in the interval [0, 1] decays as a power law n(-theta(d)) where theta(d)>0 is the exponent associated with the decay of the persistence probability for the diffusion equation with random initial conditions in space dimension d. For n even, the probability that such polynomials have no root on the full real axis decays as n(-2[theta(d)+theta(2)]). For d=1, this connection allows for a physical realization of real random polynomials. We further show that the probability that such polynomials have exactly k real roots in [0, 1] has an unusual scaling form given by n(-phi(k/logn)) where phi(x) is a universal large deviation function.     

Turbulence in noninteger dimensions by fractal Fourier decimation

Fractal decimation reduces the effective dimensionality D of a flow by keeping only a (randomly chosen) set of Fourier modes whose number in a ball of radius k is proportional to k(D) for large k. At the critical dimension D(c)=4/3 there is an equilibrium Gibbs state with a k(-5/3) spectrum, as in V. L'vov et al., Phys. Rev. Lett. 89, 064501 (2002). Spectral simulations of fractally decimated two-dimensional turbulence show that the inverse cascade persists below D=2 with a rapidly rising Kolmogorov constant, likely to diverge as (D-4/3)(-2/3).     

Time evolution of quantum fractals

We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.     

Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness, and global exponential stability of periodic solution for shunting inhibitory cellular neural networks with impulses, dx(ij)dt=-a(ij)x(ij)- summation operator(C(kl)inN(r)(i,j))C(ij) (kl)f(ij)[x(kl)(t)]x(ij)+L(ij)(t), t>0,t not equal t(k); Deltax(ij)(t(k))=x(ij)(t(k) (+))-x(ij)(t(k) (-))=I(k)[x(ij)(t(k))], k=1,2,...] . Furthermore, the numerical simulation shows that our system can occur in many forms of complexities, including periodic oscillation and chaotic strange attractor. To the best of our knowledge, these results have been obtained for the first time. Some researchers have introduced impulses into their models, but analogous results have never been found.     

Generalized counting rule for hard exclusive processes

We derive a generalized counting rule for hard exclusive processes involving parton orbital angular momentum and hadron helicity flip. We start with a systematic way to enumerate the Fock components of a hadronic light-cone wave function with n partons and orbital angular momentum projection l(z). We show that the wave-function amplitude psi(n)(x(i),k(i perpendicular ),l(zi)) has a leading behavior 1/(k(2)( perpendicular ))[n(+|l(z)|+min(n(')+|l(')(z)|)]/2-1) when all parton transverse momenta are uniformly large, where n(') and l(')(z) are the number of partons and orbital angular momentum projection, respectively, of an amplitude that mixes under renormalization. Besides the generalized counting rule, the result can be used as a constraint in modeling the hadronic light-cone wave functions.     

Ordered valence-bond states in symmetric two-dimensional spin-orbital systems

We consider a superexchange Hamiltonian, H = -SUM ()(2S(i) . S(j)-(1/2)) (2T(i) . T(j)-(1/2)), which describes systems with orbital degeneracy and strong electron-phonon coupling in the limit of large on-site repulsion. In an SU(4) Schwinger boson representation, a reduced spin-orbital interaction is derived exactly, and a mean field theory has been developed. In one dimension, a spin-orbital liquid state with a finite gap is obtained. On a two-dimensional square lattice a novel type of spin-orbital ferromagnetically ordered state appears, while spin and orbital are antiferromagnetic. An important relation has been found, relating the spin and orbital correlation functions to the combined spin-orbital ones.     

Theoretical study of the stereodynamics of the He＋HD^＋ reaction

This paper investigates the stereodynamics of the reaction He+HD+ by the quasi-classical trajectory(QCT) method using the most accurate AQUILANTI surface [Aquilanti et al 2000 Mol.Phys.98 1835].The distribution P(φr) of dihedral angle and the distribution P(θr) of angle between k and j have been presented at three different collision energies.Four generalized polarization-dependent differential cross-sections(2π/σ)(dσ00/dωt),(2π/σ)(dσ20/dωt),(2π/σ)(dσ22+/dωt),(2π/σ)(dσ21 /dωt) are also calculated.Some interesting results are obtained from the comparison of the stereodynamics of the title reaction at different collision energies.     

Observation of the Hadronic transitions chi(b1,2)(2P)-->omegaUpsilon(1S)

The CLEO Collaboration has made the first observations of hadronic transitions among bottomonium (bbmacr;) states other than the dipion transitions among Upsilon(nS) states. In our study of Upsilon(3S) decays, we find a significant signal for Upsilon(3S)-->gammaomegaUpsilon(1S) that is consistent with radiative decays Upsilon(3S)-->gammachi(b1,2)(2P), followed by chi(b1,2)(2P)-->omegaUpsilon(1S). The branching ratios we obtain are B[chi(b1)(2P)-->omegaUpsilon(1S)]=(1.63(+0.35+0.16)(-0.31-0.15))% and B[chi(b2)(2P)-->omegaUpsilon(1S)]=(1.10(+0.32+0.11)(-0.28-0.10))%, in which the first error is statistical and the second is systematic.     

Experimental evidence for two gaps in the high-temperature La1.83Sr0.17CuO4 superconductor

The in-plane magnetic field penetration depth (lambda(ab)) in single-crystal La1.83Sr0.17CuO4 was investigated by muon-spin rotation (muSR). The temperature dependence of lambda(ab)(-2) has an inflection point around 10-15 K, suggesting the presence of two superconducting gaps: a large gap (Delta(1)(d)) with d-wave and a small gap (Delta(2)(s)) with s-wave symmetry. The zero-temperature values of the gaps at mu(0)H=0.02 T were found to be Delta(1)(d)(0)=8.2(1) meV and Delta(2)(s)(0)=1.57(8) meV.     

Scalings of mixed-mode regimes in a simple polynomial three-variable model of nonlinear dynamical systems

We describe scaling laws for a control parameter for various sequences of bifurcations of the LSn mixed-mode regimes consisting of single large amplitude maximum followed by n small amplitude peaks. These regimes are obtained in a normalized version of a simple three-variable polynomial model that contains only one nonlinear cubic term. The period adding bifurcations for LSn patterns scales as 1/n at low n and as 1/n2 at sufficiently large values of n. Similar scaling laws 1/k at low k and 1/k2 at sufficiently high values of k describe the period adding bifurcations for complex k(LSn)(LS(n + 1)) patterns. A finite number of basic LSn patterns and infinite sequences of complex k(LSn)(LS(n + 1)) patterns exist in the model. Each periodic pattern loses its stability by the period doubling bifurcations scaled by the Feigenbaum law. Also an infinite number of the broken Farey trees exists between complex periodic orbits. A family of 1D return maps constructed from appropriate Poincaré sections is a very fruitful tool in studies of the dynamical system. Analysis of this family of maps supports the scaling laws found using the numerical integration of the model.     

First observation of the P-wave spin-singlet bottomonium states hb(1P) and hb(2P)

We report the first observations of the spin-singlet bottomonium states h(b)(1P) and h(b)(2P). The states are produced in the reaction e(+)e(-)→h(b)(nP)π(+)π(-) using a 121.4 fb(-1) data sample collected at energies near the Υ(5S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We determine M[h(b)(1P)]=(9898.2(-1.0-1.1)(+1.1+1.0)) MeV/c(2) and M[h(b)(2P)]=(10,259.8±0.6(-1.0)(+1.4)) MeV/c(2), which correspond to P-wave hyperfine splittings ΔM(HF)=(+1.7±1.5) and (+0.5(-1.2)(+1.6)) MeV/c(2), respectively. The significances of the h(b)(1P) and h(b)(2P) are 5.5σ and 11.2σ, respectively. We find that the production of the h(b)(1P) and h(b)(2P) is not suppressed relative to the production of the Υ(1S), Υ(2S), and Υ(3S).     

Joint free-energy distribution in the random directed polymer problem

We consider two configurations of a random directed polymer of length L confined to a plane and ending in two points separated by 2u. Defining the mean free-energy F[over ] and the free-energy difference F;{'} of the two configurations, we determine the joint distribution function P(L,u)(F[over ],F(')) using the replica approach. We find that for large L and large negative free energies F[over ], the joint distribution function factorizes into longitudinal [P(L,u)(F[over ])] and transverse [P(u)(F('))] components, which furthermore coincide with results obtained previously via different independent routes.     

Scale-free networks on lattices

We suggest a method for embedding scale-free networks, with degree distribution Pk approximately k(-lambda), in regular Euclidean lattices accounting for geographical properties. The embedding is driven by a natural constraint of minimization of the total length of the links in the system. We find that all networks with lambda>2 can be successfully embedded up to a (Euclidean) distance xi which can be made as large as desired upon the changing of an external parameter. Clusters of successive chemical shells are found to be compact (the fractal dimension is df=d), while the dimension of the shortest path between any two sites is smaller than 1: dmin=(lambda-2)/(lambda-1-1/d), contrary to all other known examples of fractals and disordered lattices.     

Residual symmetries for neutrino mixing with a large θ13 and nearly maximal δD

The residual Z(2)(s)(k) and Z(2)(s)(k) symmetries induce a direct and unique phenomenological relation with θx (≡ θ13) expressed in terms of the other two mixing angles θs(≡ θ12) and θa(≡ θ23) and the Dirac CP phase δD. Z(2)(s)(k) predicts a θx probability distribution centered around 3°-6° with an uncertainty of 2°-4°, while those from Z(2)(s)(k) are approximately a factor of 2 larger. Either result fits the T2K, MINOS, and Double Chooz measurements. Alternately, a prediction for the Dirac CP phase δD results in a peak at ± 74° (± 106°) for Z(2)(s)(k) or ± 123° (± 57°) for Z(2)(s)(k) which is consistent with the latest global fit. We also give a distribution for the leptonic Jarlskog invariant Jν which can provide further tests from measurements at T2K and NOνA.     

Magnetization processes in nanocrystalline gadolinium

The thermal decline in magnetization, M(T), at fixed magnetic field (H) under 'zero-field-cooled' (ZFC) and 'field-cooled' (FC) conditions, the time evolution of ZFC magnetization, M(ZFC)(t), at fixed temperature and field, M(H) hysteresis loops/isotherms, and ac susceptibility have been measured on polycrystalline Gd samples with average grain sizes of d = 12 and 18 nm. The irreversibility in magnetization, M(irr), occurring below a characteristic temperature that reduces with increasing H, is completely suppressed above a grain-size-dependent threshold field, H*. At low fields (H ≤ 100 Oe), M(irr)(T), like the coercive field, H(c)(T), exhibits a minimum at ～16 K and a broad peak at ～50 K before going to zero at T ? T(C) (Curie temperature). At fixed temperature (T < T(C)) and field (H ? H*), where M(irr) is finite, M(ZFC) has a logarithmic dependence on time. The magnetic viscosity (S) at H = 1 Oe and T ≤ 290 K is independent of the measurement time above ～2 ms but for t < 2 ms it is strongly time-dependent. S(T) peaks at T ? T(C) for H = 1 Oe. A magnetic field reduces the peak height and shifts the peak in S(T) to lower temperatures. All the above observations are put on a consistent theoretical footing within the framework of a model in which the intra-grain magnetizations overcome the energy barriers (brought about by the intra-grain and grain-boundary/interfacial magnetic anisotropies) by the thermal activation process. These field- and temperature-dependent energy barriers, that separate the high-energy metastable (ZFC) state from the stable minimum-energy (FC) state, are independent of time for t ? 2 ms and have a very broad distribution. We show that the shape anisotropy plays a decisive role in the magnetization reversal process, and that the magnetocrystalline and magnetostatic fluctuations, prevalent in the grain-boundary and interfacial regions, govern the approach-to-saturation of magnetization in nanocrystalline Gd.     

Search for CP violation in τ±→K(S)0π±ντ decays at Belle

We report on a search for CP violation in τ(±)→K(S)(0)π(±)ν(τ) decays using a data sample of 699 fb(-1) collected by the Belle experiment at the KEKB electron-positron asymmetric-energy collider. The CP asymmetry is measured in four bins of the invariant mass of the K(S)(0)π(±) system and found to be compatible with zero with a precision of O(10(-3)) in each mass bin. Limits for the CP violation parameter Im(η(S)) are given at the 90% confidence level. These limits are |Im(η(S))| < 0.026 or better, depending on the parametrization used to describe the hadronic form factors, and improve upon previous limits by 1 order of magnitude.     

Universal order statistics of random walks

We study analytically the order statistics of a time series generated by the positions of a symmetric random walk of n steps with step lengths of finite variance σ(2). We show that the statistics of the gap d(k,n) = M(k,n)-M(k+1,n) between the kth and the (k+1)th maximum of the time series becomes stationary, i.e., independent of n as n → ∞ and exhibits a rich, universal behavior. The mean stationary gap exhibits a universal algebraic decay for large k, ~d(k,∞)-/σ 1/sqrt[2πk], independent of the details of the jump distribution. Moreover, the probability density (pdf) of the stationary gap exhibits scaling, Pr(d(k,∞) = δ) ~/= (sqrt[k]/σ)P(δsqrt[k]/σ), in the regime δ~ (d(k,∞)). The scaling function P(x) is universal and has an unexpected power law tail, P(x) ~ x(-4) for large x. For δ> (d(k,∞)) the scaling breaks down and the pdf gets cut off in a nonuniversal way. Consequently, the moments of the gap exhibit an unusual multiscaling behavior.     

Complex methyl group and hydrogen-bonded proton motions in terms of the Arrhenius and Schrödinger equations

Equations for the temperature dependence of the spectral densities J(is)(m)(momega(I) +/-omega(T)), where m=1, 2, omega(I) and omega(T) are the resonance and tunnel splitting angular frequencies, in the presence of a complex motion, have been derived. The spin pairs of the protons or deuterons of the methyl group perform a complex motion consisting of three component motions. Two of them involve mass transportation over the barrier and through the barrier. They are characterized by k((H)) (Arrhenius) and k((T)) (Schr?dinger) rate constants, respectively. The third motion causes fluctuations of the frequencies (nomega(I)+/-omega(T)) and it is related to the lifetime of the methyl spin at the energy level influenced by the rotor-bath interactions. These interactions induce rapid transitions, changing the symmetry of the torsional sublevels either from A to E or from E(a) to E(b). The correlation function for this third motion (k((omega)) rate constant) has been proposed by Müller-Warmuth et al. The spectral densities of the methyl group hindered rotation (k((H)), k((T)) and k((omega)) rate constants) differ from the spectral densities of the proton transfer (k((H)) and k((T)) rate constants) because three compound motions contribute to the complex motion of the methyl group. The recently derived equation [Formula: see text] , where [Formula: see text] and [Formula: see text] are the fraction and energy of particles with energies from zero to E(H), is taken into account in the calculations of the spectral densities. This equation follows from Maxwell's distribution of thermal energy. The spectral densities derived are applied to analyse the experimental temperature dependencies of proton and deuteron spin-lattice relaxation rate in solids containing the methyl group. A wide range of temperatures from zero Kelvin up to the melting point is considered. It has been established that the motion characterized by k((omega)) influences the spin-lattice relaxation up to the temperature T(tun) only. This temperature is directly determined by the equation C(p)T=E(H) (thermal energy=activation energy), where C(p) is the molar heat capacity. Probably the cessation of the third motion is a result of the de Broglie wavelength related to this motion becoming too short. As shown recently, the potential barrier can be an obstacle for the de Broglie wave. The theoretical equations derived in this paper are compared to those known in the literature.