Critical points and points of the bifurcation of the rotating magnetized newtonian polytropes with a 1 ⩽ n ⩽ 1.6 index

The presence of critical points and the bifurcation points of rotating Newtonian polytropes with an index of 1 ? n ? 1.6 has been shown for the first time in this paper. The symbolic-numerical calculation error in metric L ₂ has reached the size of the 10^?4 order. The approximate analytical solution to the problem to the abovementioned accuracy has been set forth. A critical value of the polytropes index n = n _k = 1.51025 has been calculated which is the highest among the critical points and bifurcation points. The value n _k corresponds to the infinitely slow polytropes rotation. Furthermore, in this paper the presence of the period jump at the bifurcation point T _b has been predicted and the relative value of this jump ΔT _b /T _b ～ B _0in ^4/3 has been estimated.     

Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices

We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an n×n matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian symplectic ensemble (GSE) and let x _k denote eigenvalue number k. Under the condition that both k and n?k tend to infinity as n→∞, we show that x _k is normally distributed in the limit. We also consider the joint limit distribution of eigenvalues $(x_{k_{1}},\ldots,x_{k_{m}})$ from the GOE or GSE where k ₁, n?k _m and k _i+1?k _i , 1≤i≤m?1, tend to infinity with n. The result in each case is an m-dimensional normal distribution. Using a recent universality result by Tao and Vu, we extend our results to a class of Wigner real symmetric matrices with non-Gaussian entries that have an exponentially decaying distribution and whose first four moments match the Gaussian moments.     

Lie symmetries and their local determinacy for a class of differential-difference equations

Differential-difference equations (DDEs) u_n^(k)(t) = F_n(t, u_n+a,…, u_n+b) for k ≥ 2 are studied for their differential Lie symmetries. We observe that while nonintrinsic Lie symmetries do exist in such DDEs, a great many admit only the intrinsic ones. We also propose a mechanism for automating symmetry calculations for fairly general DDEs, with a variety of features exemplified. In particular, the Fermi-Pasta-Ulam system is studied in detail and its new similarity solutions given explicitly.     

Emission secondaire de petits agregats NipCn par des carbures de nickel

The intensities of emission of Ni_pC_n⁺(p = 1–3) and NiC_n^? secondary ions given by two alloys: Ni₃C and NiC 5% at. C, show off a saw-toothed behaviour according to the parity of the number n of carbon atoms. Maxima occur when n is odd for NiC_n⁺ ions and when n is even in the other cases (p = 2, 3; negative ions). Besides, the influence of the carbon concentration in the alloy can be observed.The alternations of NiC_n⁺ and Ni₂C_n⁺ ions can be interpreted from Pitzer and Clementi model (the clusters are supposed to be linear). Thus it can be found greater stabilities for NiC_2k+1 and Ni₂C_2k chains than for NiC_2k and Ni₂C_2k+1 chains respectively, which very well agrees with the “correspondence rule” between the emissions of different species of ions and their electronic properties.     

A class of exactly solvable three-body quantum mechanical problems and the universal low energy behavior

Three-body systems with two-body point interactions are studied. These systems are the universal low energy limits of three-body problems with short-range two-body forces. Hence if there are infinitely many spherically symmetric three-body bound states with energies E_n then lim_n→∞E_n/E_n+1 = e^2λσ, where σ is explicitly computed.     

Role of metastable atoms and molecules of helium in excitation transfer to hydrogen atoms

The afterglow of a discharge in helium with a small admixture of hydrogen is studied spectroscopically (p=40 Torr, [e]≤10¹¹ cm^?3). The time-resolved measurements of intensities of the first four lines of the Balmer series are performed. The concentrations of metastable helium atoms and molecules are evaluated from the relative intensity of the absorption lines. The ratios of excitation transfer rates from atoms He(2 ³ S ₁) k ₁(n) and molecules of helium He₂(a 2sσ ³Σ _u ⁺ ) k ₂(n) to atomic hydrogen H*(n) are measured to be k ₁(n=3)/k ₂(n=3)=0.04±0.02 and k ₁(n=4)/k ₂(n=4)=0.01±0.02. The ratios of excitation rate constants k ₂(n) corresponding to different states H(n) are measured to be k ₁(n=4)/k ₂(n=3)=0.023±0.01; k ₁(n=5)/k ₂(n=3)≤0.013; and k ₁(n=6)/k ₂(n=3)≤0.007.     

A Markovian Growth Dynamics on Rooted Binary Trees Evolving According to the Gompertz Curve

Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields (Probab. Theory Relat. Fields 79(4):509?C542, 1988) model. Fix n??1 and ??>0. We start at time 0 with the tree composed of a root only. At any time, each node with no descendants, independently from the other nodes, produces two successors at rate ??(n?k)/n, where k is the distance from the node to the root. Denote by Z _n (t) the number of nodes with no descendants at time t and let T _n =?? ^?1 nln(n/ln4)+(ln2)/(2??). We prove that 2^?n Z _n (T _n +n??), ?????, converges to the Gompertz curve exp(?(ln2)?e ^??|? ). We also prove a central limit theorem for the martingale associated to Z _n (t).     

Uniform Entanglement Frames

We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of k-separable circles via geometric distance for probability vectors, which include at most (k?1)-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the k-separable states more accurately.     

Moderate Deviations for Random Field Curie-Weiss Models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization S _n , which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number m, a positive real number ??, and a positive integer k such that (S _n ?nm)/n ^?? satisfies a moderate deviations principle with speed n ^1?2k(1???) and rate function ??x ^2k /(2k)!, where 1?1/(2(2k?1))<??<1.     

A First-Passage Kinetic Monte Carlo algorithm for complex diffusion–reaction systems

We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The FPKMC algorithm presented here is based on the method introduced in Oppelstrup et al. [10] and is implemented in a robust and flexible framework. Unlike standard KMC algorithms such as the n-fold algorithm, FPKMC is most efficient at low densities where it replaces the many small hops needed for reactants to find each other with large first-passage hops sampled from exact time-dependent Green’s functions, without sacrificing accuracy. We describe in detail the key components of the algorithm, including the event-loop and the sampling of first-passage probability distributions, and demonstrate the accuracy of the new method. We apply the FPKMC algorithm to the challenging problem of simulation of long-term irradiation of metals, relevant to the performance and aging of nuclear materials in current and future nuclear power plants. The problem of radiation damage spans many decades of time-scales, from picosecond spikes caused by primary cascades, to years of slow damage annealing and microstructure evolution. Our implementation of the FPKMC algorithm has been able to simulate the irradiation of a metal sample for durations that are orders of magnitude longer than any previous simulations using the standard Object KMC or more recent asynchronous algorithms.     

Collective hamiltonians with Kac-Moody algebraic conditions

We describe the general framework for constructing collective-theory hamiltonians whose hermiticity requirements imply a Kac-Moody algebra of constraints on the associated jacobian. We give explicit examples for the algebras sl(2)_k and sl(3)_k. The reduction to W_n-constraints, relevant to n-matrix models, is described for the jacobians.     

Multiplicity distributions in the generalized Feynman gas model

Multiplicity distributions Ψ_n^(k) in the generalized Feynman gas model of order k (defined by saying that all integrated correlation functions f_n except f₁,…,f_k are zero) are derived and expressed in terms of Poisson distributions with different ”average multiplicities”, which are related to the integrated correlation functions. The relations between Ψ_n^(k) and Ψ_n^(j) for arbitrary positive integers k,j are found. An intuitive picture to gain a better feeling for these relations is developed.On the basis of our formulae we show that the experimentally observed multiplicity distributions (between 50 GeV/c and 303 GeV/c incoming momentum) can be well reproduced by those of a Feynman gas model of order two. Other applications of our formulae are suggested.     

Transverse instability of a plane front of fast impact ionization waves

The transverse instability of a plane front of fast impact ionization waves in p ⁺-n-n ⁺ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration ??_b ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum s _M at k = k _M, then decreases, and becomes negative at k > k ₀₁. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and ??smearing?? of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ? k _M have been established: at fixed ??_b values and the maximum field strength on the front E _0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k ₀₁ ?? N. The parameters s _M, k _M, and k ₀₁, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E _0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave.     

Reconstruction and selection of J/ψ → e + e − decays registered by CBM setup in 25 AGeV AuAu collisions

The problem of reconstructing and selecting J/? → e ⁺ e ^? decays registered by the CBM setup in AuAu collisions at 25 AGeV beam energy is considered. The key task in this problem is fast and reliable electron-positron identification using the energy losses of charged particles in the Transition Radiation Detector (TRD). We consider two methods for solving this problem: an artificial neuron network (ANN) and a modified non-parametric goodness-of-fit ω _n ^k criterion. Our analysis shows that both approaches give similar results for the J/? → e ⁺ e ^? yield and the signal-to-background ratio. Compared with the ω _n ^k criterion, the method based on ANN has a number of disadvantages which are discussed in detail. Taking into consideration the very simple software implementation of the ω _n ^k algorithm, it can be used for J/? → e ⁺ e ^? decays selection in a real-time experiment.     

Inclusion of transverse quark momenta in the quark-gluon string model

The dependence of distribution functions of quarks, antiquarks, diquarks and their fragmentation into hadrons on the transverse momentumk _t is discussed in the frame of the quark-gluon string model. We then discuss the division ofk _t between 2n-quark-antiquark chains, orn-pomeron showers. Hadron and hadron-nuclear processesp?p,p?A,K ⁺?p,K ⁺?A are analysed. A strong dependence of the observed values on the numbern is derived by this method, which is of special importance for the analysis of hadron-nucleus collisions. Our method is compared with the regulark _t division method.     

Spanning Forests on Random Planar Lattices

The generating function for spanning forests on a lattice is related to the q-state Potts model in a certain q→0 limit, and extends the analogous notion for spanning trees, or dense self-avoiding branched polymers. Recent works have found a combinatorial perturbative equivalence also with the (quadratic action) O(n) model in the limit n→?1, the expansion parameter t counting the number of components of the forest. We give a random-matrix formulation of this model on the ensemble of degree-k random planar lattices. For k=3, a correspondence is found with the Kostov solution of the loop-gas problem, which arise as a reformulation of the (logarithmic action) O(n) model, at n=?2. Then, we show how to perform an expansion around the t=0 theory. In the thermodynamic limit, at any order in t we have a finite sum of finite-dimensional Cauchy integrals. The leading contribution comes from a peculiar class of terms, for which a resummation can be performed exactly.     

Super-exponential inflation from a dynamical foliation of a 5D vacuum state

We introduce super-exponential inflation (ω<−1) from a 5D Riemann-flat canonical metric on which we make a dynamical foliation. The resulting metric describes a super accelerated expansion for the early universe well known as super-exponential inflation that, for very large times, tends to an asymptotic de Sitter (vacuum dominated) expansion. The scalar field fluctuations are analyzed. The important result here obtained is that the spectral index for energy density fluctuations is not scale invariant, and for cosmological scales becomes ns(k<k_?)?1. However, for astrophysical scales this spectrum changes to negative values ns(k>k_?)<0.     

Bifurcation to infinitely many sinks

This paper considers one parameter families of diffeomorphisms {F _t } in two dimensions which have a curve of dissipative saddle periodic pointsP _t , i.e.F _t ⁿ (P _t )=P _t and |detDF _t ⁿ (P _t )|<1. The family is also assumed to create new homoclinic intersections of the stable and unstable manifolds ofP _t as the parameter varies throught ₀. Gavirlov and Silnikov proved that if the new homoclinic intersections are created nondegenerately att ₀, then there is an infinite cascade of periodic sinks, i.e. there are parameter valuest _n accumulating att ₀ for which there is a sink of periodn [GS2, Sect. 4]. We show that this result is true for real analytic diffeomorphisms even if the homoclinic intersection is created degenerately. We give computer evidence to show that this latter result is probably applicable to the Hénon map forA near 1.392 andB equal ?0.3. Newhouse proved a related result which showed the existence of infinitely many periodic sinks for a single diffeomorphism which is a perturbation of a diffeomorphism with a nondegenerate homoclinic tangency. We give the main geometric ideas of the proof of this theorem. We also give a variation of a key lemma to show that the result is true for a fixed one parameter family which creates a nondegenerate tangency. Thus under the nondegeneracy assumption, not only is there a cascade of sinks proved by Gavrilov and Silnikov, but also a single parameter valuet* with infinitely many sinks.     

Index of a family of Dirac operators on loop space

We use methods of constructive field theory to generalize index theory to an infinite-dimensional setting. We study a family of Dirac operatorsQ on loop space. These operators arise in the context of supersymmetric nonlinear quantum field models with HamiltoniansH=Q ². In these modelsQ is self-adjoint and Fredholm. A natural grading operator Γ exists such that ΓQ+QΓ=0. We studyQ ₊=P _? QP ₊, whereP _±=1/2 (1±Γ) are the orthogonal projections onto the eigenspaces of Γ. We calculate the indexi(Q ₊) for Wess-Zumino models defined by a superpotentialV(ω). HereV is a polynomial of degreen≧2. We establish thati(Q ₊)=n?1=degδV. In particular, the field theory models have unbroken supersymmetry, and (forn≧3) they have degenerate vacua. We believe that this is the first index theorem for a Dirac operator that couples infinitely many degrees of freedom.     

Diffusive, super-diffusive and ballistic transport in the long-range correlated 1D Anderson model

In this paper, we study the 1D Anderson model with long-range correlated on-site energies. This diagonal-correlated disorder is considered in such a way that the random sequence of site energies ε_n has a 1/k^α power spectrum, where k is the wave-vector of the modulations on the random sequence landscape. Using the Runge-Kutta method to solve the time-dependent Schrödinger equation, we compute the participation number and the Shannon entropy for an initially localized wave packet. We observe that strong correlations can induce ballistic transport associated with the emergence of low-energy extended states, in agreement with previous works in this model. We further identify an intermediate regime with super-diffusive spreading of the wave-packet.