Nuclear Spin-Lattice Relaxation of 82BrFe

The field dependence of the nuclear spin-lattice relaxation (SLR) of cold implanted ⁸²Br (T ≤ 25 mK) in α-Fe single crystals was investigated with nuclear magnetic resonance of oriented nuclei (NMR/ON) at low temperatures as experimental technique. The SLR at the lattice sites with the hyperfine fields found by earlier NMR/ON experiments was measured as a function of the applied external magnetic field B _ext parallel to the three principle axes [100], [110] and [111] of the iron single crystal. The data were evaluated with the full relaxation formalism in the single impurity limit and for comparison also with the often employed model of a single exponential function with an effective relaxation time T ₁′. With a phenomenological model the high field values of the relaxation rates r _{∞, [100]′} = 6.6(2) · 10⁻¹⁵ T²sK⁻¹, r _{∞, [110]} = 5.4(2) · 10⁻¹⁵ T²sK⁻¹ and r _{∞, [111]} = 5.2(1) · 10⁻¹⁵ T²sK⁻¹ were obtained.     

Numerical and experimental investigations on the mach 2 pseudo-shock wave in a square duct

This paper describes numerical and experimental investigations for the multiple shock wave/turbulent boundary layer interaction in a Mach 2 supersonic square duct. The numerical simulation is carried out with the Harten-Yee second-order accuracy TVD scheme and the Baldwin-Lomax turbulence model. The flow conditions are a free-stream Mach number ofM _∞≈=2.0 and a Reynolds number ofRe _∞;=2.5×10⁷ and the flow confinements are δ_∞/h=0.15 (case A) and δ_∞/h=0.25 (case B), respectively. The computational results for both cases show good agreement with the experimental results. Based on these agreements, the flow quantities, which are very difficult to obtain experimentally, are analyzed by numerical simulation. Moreover, the effect of flow confinement on the pseudo-shock wave characteristics is also presented.     

The Effect of the Number of Simulations on the Exponents Obtained by Finite-Size Scaling Relations of the Order Parameter and the Magnetic Susceptibility for the Four-Dimensional Ising Model on the Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4≤L≤8. The exponents in the finite-size scaling relations for the order parameter and the magnetic susceptibility at the finite-lattice critical temperature are computed to be β=0.49(7), β=0.49(5), β=0.50(1) and γ=1.04(4), γ=1.03(4), γ=1.02(4) for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are consistent with the renormalization group predictions of β=0.5 and γ=1. The values for the critical temperature of the infinite lattice T _c (∞)=6.6788(65), T _c (∞)=6.6798(69), T _c (∞)=6.6802(70) are obtained from the straight-line fit of the magnetic susceptibility maxima using 4≤L≤8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are in very good agreement with the series expansion results of T _c (∞)=6.6817(15), T _c (∞)=6.6802(2), the dynamic Monte Carlo result of T _c (∞)=6.6803(1), the cluster Monte Carlo result of T _c (∞)=6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm result of T _c (∞)=6.6802632±5×10⁻⁵.     

Development of three-dimensional turbulent separation in the neighborhood of incident crossing shock waves

The results are presented for experimental investigation of the peculiarities of the development of three-dimensional turbulent separated flows on a flat surface for the Mach number M_∞ = 4 and the Reynolds number Re₁ ∼ 55·10⁶ m⁻¹ under the conditions of the flow around two identical cylindrical bodies of revolution of diameter D = 50 mm and the body aspect ratio L _b/D = 5 with conical forebodies with semi-apex angles β_c = 30, 20, 15, and 10° located above plate in parallel to one another and to the flow. The typical stages of the three-dimensional separation development are considered under the reducing distance between the axes of the bodies within the range of Z = Δz/D = 1.06–3.0 at their fixed distance from the surface (Y = Δy/D = 0.96). The topology of limiting streamlines and the peculiarities of pressure fields on the surface as well as the gasdynamic structure of separated flows arising at the interaction of crossing bow shocks propagating from the bodies and at the interaction of secondary disturbances with the boundary layer are analysed.     

Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents

According to recent progresses in the finite size scaling theory of disordered systems, thermodynamic observables are not self-averaging at critical points when the disorder is relevant in the Harris criterion sense. This lack of self-averageness at criticality is directly related to the distribution of pseudo-critical temperatures T_c(i,L) over the ensemble of samples (i) of size L. In this paper, we apply this analysis to disordered Poland-Scheraga models with different loop exponents c, corresponding to marginal and relevant disorder. In all cases, we numerically obtain a Gaussian histogram of pseudo-critical temperatures T_c(i,L) with mean T_c^av(L) and width ΔT_c(L). For the marginal case c=1.5 corresponding to two-dimensional wetting, both the width ΔT_c(L) and the shift [T_c(∞)-T_c^av(L)] decay as L^-1/2, so the exponent is unchanged (ν_random=2=ν_pure) but disorder is relevant and leads to non self-averaging at criticality. For relevant disorder c=1.75, the width ΔT_c(L) and the shift [T_c(∞)-T_c^av(L)] decay with the same new exponent L^-1/νrandom (where ν_random ∼2.7 > 2 > ν_pure) and there is again no self-averaging at criticality. Finally for the value c=2.15, of interest in the context of DNA denaturation, the transition is first-order in the pure case. In the presence of disorder, the width ΔT_c(L) ∼L^-1/2 dominates over the shift [T_c(∞)-T_c^av(L)] ∼L^-1, i.e. there are two correlation length exponents ν=2 and that govern respectively the averaged/typical loop distribution.     

Thermodiffusion of interstitials in a film

A general expression is obtained for the thermodiffusion coefficientD _T of a film, also for its dependence on temperature, film thickness and type of concentration distribution of the interstitials, according to its profile. In neglecting interaction of interstitials with each other in a model of a film with single-plane boundaries with the vacuum and the substrate, it is shown thatD _T>D _T ^(∞) is possible, whereD _T ^(∞) is the thermodiffusion coefficient of a bulk specimen. Ural State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–46, September, 1996.     

An experimental study of the forerunners of boundary-layer localized disturbances at an enhanced turbulence level

Turbulence production processes in boundary layer at a high level of free-stream turbulence have been studied. The tests were carried out in the MT-324 subsonic wind tunnel of ITAM, SB RAS, on models of straight and 45° swept wings at Reynolds numbers Re_c1 = 97000 and Re_c2 = 137000, and also at low (Tu = 0.18 % U _∞) and high (Tu = 0.79 and 2.31 % U _∞) levels of free-stream turbulence. The longitudinal localized disturbances developing in the boundary layer under the action of free-stream turbulence were artificially modeled using local air suction through a slot on the model surface. Wave packets, or forerunners, produced in the boundary layer, in the region preceding the abrupt local change of flow velocity near the localized-disturbance fronts, were examined. The high level of free-stream turbulence was found to accelerate the downstream evolution of the wave packets and their transformation into turbulent spots.     

Formation of a plane layer of plasma under irradiation by a soft X-ray source

We investigate theoretically the formation of a plasma in a plane layer of polymer foam (density ρ = 0.002 g/cm³ and thickness 800 μm) under the action of an external source of soft X-ray radiation under the conditions of PHELIX experiments. The incident flux is assumed to have a Planck’s distribution over the spectrum with T _rad = 20–40 eV. In numerical calculations, the flux of incident X-ray radiation and the spectral constants of the target substance are varied. The action of an external X-ray radiation source on a low-density foam substance with a density of 2 mg/cm³ causes a plasma to be formed with relatively homogeneous profiles of density and temperature T = 15–35 eV. Absorption of externalradiation energy is distributed in the volume. The plasma temperature increases with increase in the external energy, and the energy passed through the plasma also increases. The results prove to be sensitive to the values of optical constants used in numeral simulation. The spectral flux of external radiation passed through the plasma is chosen as a criterion of correctness of the optical constants used in the calculations. In future experiments using the PHELIX facility, we plan to investigate the slowing-down of an ion beam in a plasma formed as a result of indirect heating of low-density polymer triacetate cellulose (TAC) foam with densities ρ = 0.001–0.01 g/cm³ under the action of a pulse of X-ray radiation, into which the laser radiation is preliminarily transformed.     

Maximum of a Fractional Brownian Motion: Probabilities of Small Values

Let b _γ (t), b _γ(0)= 0 be a fractional Brownian motion, i.e., a Gaussian process with the structure function , 0 < γ < 2. We study the logarithmic asymptotics of P _T = P{b _γ (t) < 1,□t∈TΔ} as T→∞, where Δ is either the interval (0,1) or a bounded region that contains a vicinity of 0 for the case of multidimensional time. It is shown that ln P _T = - D ln T(1 + o(1)), where D is the dimension of zeroes of b _γ (t) in the former case and the dimension of time in the latter. Received: 28 September 1998 / Accepted: 19 February 1999     

Structure and parameters of the shock layer formed when a supersonic underexpanded jet interacts with a counterpropagating hypersonic flow in the transition regime

The method of molecular dynamics (the Bird system) has been used to mathematically model a planar, strongly underexpanded supersonic jet that encounters a hypersonic flow of rarefied gas. Particular attention is paid to the structure and parameters of the shock layer close to the plane of symmetry. The results of calculations are presented for currents of a monatomic gas, simulating argon, with a Mach number of the external flow of M_∞=5.48, a Mach number at the nozzle edge of M_a=1, a ratio of the density at the nozzle edge to the density of the unperturbed flow equal to 130, and various stagnation temperatures of the external flow and of the jet. The evolution of the structure and the parameters of the shock layer as the Knudsen number Kn_∞ varies from 0.02 to 0.35 is considered. The results are compared with the data calculated for the shock layer when argon flows around thermally insulated cylinders. The main features and regularities of the relaxation of the translational degrees of freedom of the gas for external and jet flows are considered. Data are presented on the form of the distribution function over velocities and its evolution as gas moves through the shock layers. Zh. Tekh. Fiz. 68, 13–18 (July 1998)     

Convergence to equilibrium distribution. The Klein-Gordon equation coupled to a particle

The Hamiltonian system formed by a Klein-Gordon vector field and a particle in ℝ³ is considered. The initial data of the system are given by a random function, with finite mean energy density, which also satisfies a Rosenblatt- or Ibragimov-type mixing condition. Moreover, initial correlation functions are assumed to be translation invariant. The distribution μ _t of the solution at time t ∈ ℝ is studied. The main result is the convergence of μ _t to a Gaussian measure as t → ∞, where μ_∞ is translation invariant.     

Dark Matter Candidate Particles, CP Violation and Higgs Bosons

In a previous paper, we proposed the infinite sub-layer quark model, in which the proton and the neutron are made up of an infinite number of point-like (structure-less) quarks u _∞ and anti-quarks u _∞ ^CP at an infinite sub-layer level. In this paper, we propose that the dark matter is also made of an infinite number of quarks u _∞ and anti-quarks u _∞ ^CP . A pair of the ultimate quarks u _∞ and anti-quarks u _∞ ^CP would be produced in the first moments after the Big Bang and then remain as the dark matter for all time, stable against decay and subject only to the weak interaction and gravity. It is then shown that CP is violated in the doublet of u _∞ and u _∞ ^CP quarks to account for the asymmetry of the number of particles and anti-particles in the present universe. Furthermore, it is shown that the Higgs bosons are composed of u _∞ and u _∞ ^CP dark matter particles and give the masses to gauge bosons, quarks and leptons.     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Random Matrix Theory and ζ(1/2+it)

We study the characteristic polynomials Z(U, θ) of matrices U in the Circular Unitary Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are derived for the moments of |Z| and Z/Z ^*, and from these we obtain the asymptotics of the value distributions and cumulants of the real and imaginary parts of log Z as N→∞. In the limit, we show that these two distributions are independent and Gaussian. Costin and Lebowitz [15] previously found the Gaussian limit distribution for Im log Z using a different approach, and our result for the cumulants proves a conjecture made by them in this case. We also calculate the leading order N→∞ asymptotics of the moments of |Z| and Z/Z ^*. These CUE results are then compared with what is known about the Riemann zeta function ζ (s) on its critical line Re s= 1/2, assuming the Riemann hypothesis. Equating the mean density of the non-trivial zeros of the zeta function at a height T up the critical line with the mean density of the matrix eigenvalues gives a connection between N and T. Invoking this connection, our CUE results coincide with a theorem of Selberg for the value distribution of log ζ(1/2+iT) in the limit T→∞. They are also in close agreement with numerical data computed by Odlyzko [29] for large but finite T. This leads us to a conjecture for the moments of |ζ(1/2+it) |. Finally, we generalize our random matrix results to the Circular Orthogonal (COE) and Circular Symplectic (CSE) Ensembles. Received: 20 December 1999 / Accepted: 24 March 2000     

Mean flow scaling along smooth and rough wall boundary layers

Effects of the upstream conditions and the degree of the wall roughness on the mean velocity profiles and some integral flow parameters in two dimensional zero-pressure-gradient boundary layer were characterized experimentally. The results were analyzed utilizing conventional and recent scaling flow parameters for 245< Re _θ ≤ 11·10³, where Re _θ is the Reynolds number based on the free stream velocity (Ū _∞) and the momentum thickness (θ). Good correlation of the quantity ΔŪ ⁺ as a function of the roughness parameter k ⁺ was obtained for sand roughness of 1.7 < k ⁺ ≤ 172, revealing a universality of the roughness effect, where ΔŪ ⁺ = = (Ū _∞ − Ū)/u _τ and K ⁺ = ku _τ /v.The mean flow structure of the outer flow was observed not to be influenced by the degree of the wall roughness, i. e., the outer flow of either the smooth or the rough surfaces scales similarly with the various scaling parameters regardless the degree of the wall roughness. However, it made flow confined to the wall region away from the classical universality, allowing similarity hypothesis not to be identical in the wall region at least for the current range of the Reynolds number.     

A Small-Scale Density of States Formula

 Let (M,g) be a C ^∞ compact Riemann manifold with classical Hamiltonian, HC ^∞ (T ^* M). Assume that the corresponding -quantization P ₁ :=Op _ (H) is quantum completely integrable. We establish an -microlocal Weyl law on short spectral intervals of size ^2−ε;∀ε>0 for various families of operators P ₁ ^u ;uI containing P ₁ , both in the mean and pointwise a.e. for uI. The -microlocalization refers to a small tubular neighbourhood of a non-degenerate, stable periodic bicharacteristic γ⊂T ^* M−0. Received: 10 December 2001 / Accepted: 23 January 2003 Published online: 2 April 2003 RID="⋆" ID="⋆" Supported in part by an Alfred P. Sloan Research Fellowship and NSERC grant OGP01720280 Communicated by P. Sarnak     

Electronic states of boron in superconducting MgB2 studied by11B NMR

Nuclear magnetic resonance (NMR) spectra and nuclear spin-lattice relaxation rateT ₁⁻¹ of¹¹B have been measured in superconducting polycrystalline MgB₂ with 7_c^ons = 39.5 K. It is shown that (T ₁T⁻¹ and the Knight shiftK _s are independent of temperature and nearly isotropic aboveT _c. Both of these quantities are decreased gradually in going to the superconducting state. According to NMR data the density of states near the Fermi level is flat at the scale of about 500 K. Some conclusions on the orbital content of the density of states at the Fermi level were drawn and compared with the results of the band structure calculations.     

Evaluation of the rate constants of dissociative and ternary recombination reactions of argon ions on the basis of the results of ballistic experiments

AbstractExperimental data on the change in the electron density in the wake of a ballistic object traveling at velocities V _∞=3.4–4.9 km/s in argon at pressures p _∞=30–100 Torr are processed and analyzed. A reaction scheme is proposed which takes into account the recombination of charged particles, processes of ionic conversion, and the excited states of the atom. The solution of the equations of a nonequilibrium boundary layer for flow in the wake is used to formulate the inverse problem of determining the rate constants for dissociative recombination Ar ₂ ⁺ +e→Ar+Ar and ternary recombination Ar⁺+e+Ar→Ar+Ar. The “nearest-neighbor” approximation is used to obtain theoretically an expression for the ternary recombination coefficient as a function of temperature and pressure. Numerous solutions of inverse problems and a comparison with experiments demonstrates the validity of the expression obtained for the ternary recombination coefficient. It is shown that this expression is valid for moderate pressures and complements the Pitaevskii result for low pressures and the Langevin result for high pressures. Zh. Tekh. Fiz. 67, 12–18 (May 1997)