Instability of potential jet streams

A Hamiltonian version has been formulated for the model of a potential jet stream of a homogeneous incompressible fluid with a free boundary. In the framework of this model, instability regimes have been analyzed. It has been shown that self-similar solutions with a compact support can be dominant structures. Analysis of the instability mechanism shows that two collapse scenarios are possible. The first scenario occurs without the deformation of the shape and leads to an intensification of the vortex sheet according to the law (t ₀ ? t)^?1, where t ₀ is the collapse time. The second scenario leads to the formation of a singularity for the surface shape and to a decrease in the intensity of the vortex sheet according to the laws (t ₀ ? t)^?1/5 and (t ₀ ? t)^1/5, respectively. The integral collapse criterion has been found.     

Nonself-similar regimes of isothermal collapse of protostellar clouds

We consider the development of inhomogeneity in the isothermal collapse of protostellar clouds. The initial and boundary conditions correspond to the classical statement of the problem on the contraction of a homogeneous cloud from a given volume. A centered rarefaction wave is shown to propagate from the outer boundary of the cloud toward its center at the first collapse stage. Analysis reveals two possible regimes of isothermal collapse, depending on the relationship between the rarefaction wave focusing time t^* and the cloud free-fall collapse time t_ff. For cold clouds, t^*=t _ff and the rarefaction wave is not reflected. In this case, as time elapses, the cloud collapse becomes self-similar with the characteristic density profile ρ～r^?2. In hot clouds, t*<t _ff and the focusing can take place before the formation of an opaque core. Since the velocities of the rarefaction wave along and across magnetic field lines in a magnetized cloud are different, its front assumes a shape elongated along magnetic field lines. Depending on the initial conditions, based on analytical estimates, we investigate various possible scenarios for the collapse of magnetic protostellar clouds.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

1<Emphasis Type="Italic">∕</Emphasis><Emphasis Type="Italic">f</Emphasis><Superscript><Emphasis Type="Italic">β</Emphasis></Superscript> noise for scale-invariant processes: how long you wait matters

We study the power spectrum which is estimated from a nonstationary signal. In particular we examine the case when the signal is observed in a measurement time window [t _w , t _w + t _m ], namely the observation started after a waiting time t _w , and t _m is the measurement duration. We introduce a generalized aging Wiener–Khinchin theorem which relates between the spectrum and the time- and ensemble-averaged correlation functions for arbitrary t _m and t _w . Furthermore we provide a general relation between the non-analytical behavior of the scale-invariant correlation function and the aging 1∕f ^β noise. We illustrate our general results with two-state renewal models with sojourn times’ distributions having a broad tail.     

Gamow Vectors and Borel Summability in a Class of Quantum Systems

We analyze the detailed time dependence of the wave function ψ(x,t) for one dimensional Hamiltonians \(H=-\partial_{x}^{2}+V(x)\) where V (for example modeling barriers or wells) and ψ(x,0) are compactly supported.We show that the dispersive part of ψ(x,t) is the Borel sum of its asymptotic series in powers of t ^?1/2, t→∞. The remainder, the difference between ψ and the Borel sum, i.e., the exponential part of the transseries of ψ, is a convergent expansion of the form \(\sum_{k=0}^{\infty}g_{k}\Gamma_{k}(x)e^{-\gamma_{k} t}\), where Γ _k are the Gamow vectors of H, and iγ _k are the associated resonances; generically, all g _k are nonzero. For large k, γ _k ～const?klog?k+k ² π ² i/4. The effect of the Gamow vectors is visible when time is not very large, and the decomposition defines rigorously resonances and Gamow vectors in a nonperturbative regime, in a physically relevant way.The decomposition allows for calculating ψ for moderate and large t, to any prescribed exponential accuracy, using optimal truncation of power series plus finitely many Gamow vectors contributions.The analytic structure of ψ is perhaps surprising: in general (even in simple examples such as square wells), ψ(x,t) turns out to be C ^∞ in t but nowhere analytic on ?⁺. In fact, ψ is t-analytic in a sector in the lower half plane and has the whole of ?⁺ a natural boundary. In the dual space, we analyze the resurgent structure of ψ.     

Correlation between the properties of the deuteron and the low-energy triplet parameters of neutron-proton scattering

The correlation between the asymptotic normalization constant for the deuteron, A_S, and the neutron-proton scattering length for the triplet case, a_t, is investigated. It is found that 99.7% of the asymptotic constant A_S is determined by the scattering length a_t. It is shown that the linear correlation between the quantities A _S ^?2 and 1/a_t provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant A_S and for the root-mean-square deuteron radius r_d, the results obtained with the experimental value recommended at present for the triplet scattering length a_t are exaggerated with respect to their experimental counterparts. By using the latest experimental data obtained for phase shifts by the group headed by Arndt, it proved to be possible to derive, for the low-energy parameters of scattering (a_t, r_t, P_t) and for the properties of the deuteron (A_S, r_d) results that comply well with experimental data.     

Extremal points for fractional boundary value problems

This article is concerned with characterizing the first extremal point, b₀, for a Riemann–Liouville fractional boundary value problem, D^α₀₊y + p(t)y = 0, 0 < t < b, y(0) = y′(0) = y″(b) = 0, 2 < α ≤ 3, by applying the theory of u₀-positive operators with respect to a suitable cone in a Banach space. The key argument is that a mapping, which maps a linear, compact operator, depending on b to its spectral radius, is continuous and strictly increasing as a function of b. Furthermore, an application to a nonlinear case is given.     

Effect of spin structures and nesting on the shape of the fermi surface and pseudogap anisotropy in the <Emphasis Type="Italic">t</Emphasis>-<Emphasis Type="Italic">t</Emphasis>′-<Emphasis Type="Italic">U</Emphasis> Hubbard models

The effect of two types of spin structures on the shape of the Fermi surface and on the map of photoemission intensities for the t-t′-U Hubbard model is investigated. The stripe phase with a period of 8α and the spiral spin structure are calculated in the mean field approximation. It is shown that, in contrast to electron-type doping, hole-doped models are unstable to the formation of such structures. Pseudogap anisotropy is different for h-and e-doping and is determined by the spin structure. In accordance with ARPES data for La_2?xSr_xCuO₄, the stripe phase is characterized by quasi-one-dimensional FS segments in the vicinity of points M(±π, 0) and by suppression of the spectral density for k _x =k _y . It is shown that spiral structures exhibit polarization anisotropy: different segments of the FS correspond to electrons with different spin polarizations.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Impurity transport in fractal media in the presence of a degrading diffusion barrier

We have analyzed the transport regimes and the asymptotic forms of the impurity concentration in a randomly inhomogeneous fractal medium in the case when an impurity source is surrounded by a weakly permeable degrading barrier. The systematization of transport regimes depends on the relation between the time t ₀ of emergence of impurity from the barrier and time t _* corresponding to the beginning of degradation. For t ₀ < t _*, degradation processes are immaterial. In the opposite situation, when t ₀ > t _*, the results on time intervals t < t _* can be formally reduced to the problem with a stationary barrier. The characteristics of regimes with t _* < t < t ₀ depend on the scenario of barrier degradation. For an exponentially fast scenario, the interval t _* < t < t ₀ is very narrow, and the transport regime occurring over time intervals t < t _* passes almost jumpwise to the regime of the problem without a barrier. In the slow power-law scenario, the transport over long time interval t _* < t < t ₀ occurs in a new regime, which is faster as compared to the problem with a stationary barrier, but slower than in the problem without a barrier. The asymptotic form of the concentration at large distances from the source over time intervals t < t ₀ has two steps, while for t > t ₀, it has only one step. The more remote step for t < t ₀ and the single step for t > t ₀ coincide with the asymptotic form in the problem without a barrier.     

Ferromagnetism of metallic compounds with the perovskite structure

On the basis of the concept of strong interaction in one unit cell, it is stated that ferromagnetic instability can occur in a system with hops between oxygen anions and transition metal (Me) cations in A_1?xB_xMeO₃ compounds. A phase diagram is constructed to describe the occurrence of ferromagnetic ordering as a function of the average number of holes (h_{t, d}) and (h_p) in the low-spin or high-spin t _2g ⁶ or high-spin 3d¹⁰ shell of the transition metal and in the 2p⁶ shells of O^2?.     

Thermally activated flux flow,vortex-glass phase transition and the mixed-state Hall effect in 112-type iron pnictide superconductors

The transport properties in the mixed state of high-quality Ca_(0.8)La_(0.2)Fe_(0.98)Co_(0.02)As_2single crystal,a newly discovered 112-type iron pnictide superconductor,are comprehensively studied by magneto-resistivity measurement.The field-dependent activation energy,U_0,is derived in the framework of thermally activated flux flow(TAFF)theory,yielding a power law dependence U_0～H~αwith a crossover at a magnetic field around 2 T in both H⊥ab and H//ab,which is ascribed to the different pinning mechanisms.Moreover,we have clearly observed the vortex phase transition from vortex-glass to vortex-liquid according to the vortex-glass model,and vortex phase diagrams are constructed for both H⊥ab and H//ab.Finally,the results of mixed-state Hall effect show that no sign reversal of transverse resistivityρ_(xy)(H)is detected,indicating that the Hall component arising from the vortex flow is in theories or experiments previously reported on some high-T_ccuprates.     

Self-gravitating Brownian particles in two dimensions: the case of N = 2 particles

We study the motion of N = 2 overdamped Brownianparticles in gravitational interaction in a space of dimensiond = 2. This is equivalent to the simplified motion of twobiological entities interacting via chemotaxis when time delay anddegradation of the chemical are ignored. This problem also bearssimilarities with the stochastic motion of two point vorticesin viscous hydrodynamics [O. Agullo, A. Verga, Phys. Rev. E 63,056304 (2001)]. We analytically obtain the probability density offinding the particles at a distance r from each other at timet. We also determine the probability that the particles havecoalesced and formed a Dirac peak at time t(i.e. the probability that the reduced particle has reached r = 0at time t). Finally, we investigate the meansquare separation \(\langle\) r ² \(\rangle\) and discuss the proper formof the virial theorem for this system. The reduced particle has anormal diffusion behavior for small times with a gravity-modifieddiffusion coefficient \(\langle\) r ² \(\rangle\) = r ₀ ² + (4k _B /ξ μ)(T–\(T_{*}\))t, wherek _B \(T_{*}\) = Gm ₁ m ₂/2 is a critical temperature, and an anomalousdiffusion for large times \(\langle\) r ² \(\rangle\) \(\propto\) \(t^{1-T_*/T}\). As a by-product, our solution also describes thegrowth of the Dirac peak (condensate) that forms at large time inthe post collapse regime of the Smoluchowski-Poisson system (orKeller-Segel model in biology) for T < T _c = GMm/(4k _B ). We find thatthe saturation of the mass of the condensate to the total mass isalgebraic in an infinite domain and exponential in a boundeddomain. Finally, we provide the general form of the virial theoremfor Brownian particles with power law interactions.     

Nucleation of vortices in superfluid<Superscript>3</Superscript>He-B

In a smooth-walled rotating container vortices nucleate spontaneously in³He-B at a critical velocityv _c (T, P) which is related to the bulk superflow instability velocityv _cb (T, P). This process takes place at the wall of the container. Vortices are also observed to nucleate at lower velocities in the bulk liquid in ionizing radiation. For this thermal neutrons are most practical since for them the absorption cross section is large in³He. An absorption event creates local overheating, a hot bubble in the cold superflow. An increasing number of vortex rings is observed to emerge from the bubble as a function of the superflow velocity.     

The reactions N14(n, α)B11 and N14(n,t)C12 observed with a gridded ionization chamber

The cross sections for the reactions N¹⁴(n, α)B¹¹ and N¹⁴(n, t)C¹² have been measured in the neutron energy range 4.0 to 6.4 MeV and at 2.5 MeV. Mono-energetic neutrons were produced in the D(d, n) He³ reaction using a gas target. The (n, α) and (n, t) disintegrations were detected in a gridded ionization chamber filled with an argonnitrogen mixture. The response of the chamber under different operation conditions is described. The excitation functions, measured with a neutron energy resolution of 40 to 50 keV, are given for theα ₀ group from the N¹⁴(n,α)B¹¹ reaction over the entire neutron energy range and for theα ₁ group and the t₀ group from N¹⁴(n, t) C¹² for neutron energies above 4.3 and 5.6 MeV, respectively.     

Phasenumwandlung zweiter Art als kritische Erscheinung eines inneren Phasengleichgewichtes

It is demonstrated that the transition in a state with two internal phases is a second order phase transition. The term internal phases means phase-like regions inside the system which are not separated by boundaries in the sense of ordinary phase boundaries, and the dimensions and shape of which as well as their properties as such are object of an equilibrium. In a generalization (quasi phases) a long ranged correlation of alternating or periodical character is considered as a typical element of the low temperature state. Such states can be described thermodynamically with the help of a new pair of variablesQ-η. The transition intoQ-η-T is generally analogous to the critical point of ordinary phase transitions inP-V-T, andη ～(?t)^1/3 andC _p～(?t)^?2/3 with a small constant of proportionality are obtained (t=T-T _u). Using the Pippard-relations in the formV-V _γ=(dT _γ/dP) (S-S _γ) the low temperature behaviour of the entropy and density surface as a function ofP andT near the transition line can be completely described. E.g. the saturation magnetization of a ferromagnetic model is derived proportional to (?t)^1/3. Under the action of a magnetic field the transition will be of first order when the saturation magnetization is achieved, without the outer field being analogous toP orQ. Should only one internal phase differ from the high temperature state we obtain an edge point (x=0 analogous to theμ ₁?x-diagram of solutions) with finite jump inC _p andη～({t). A possible relationship to the BCS- model of the supraconductors is indicated.     

Relaxation Kinetics of the Microhardness of KDP Crystals after Their Exposure to a Magnetic Field

It has been shown that potassium dihydrogen phosphate crystals change their microhardness reversibly after their exposure to a magnetic field of B = 0.8 or 1.2 T for t_m = 7–90 min. It has been found that the magnetic effect can be conveniently characterized by the quantity B²t_m, because the variation of the parameters conserving B²t_m=const does not change the result. At B²t_m < 10 T² min, the effect is almost absent. Above this threshold, the amplitude of changes in the microhardness increases and approaches a constant value of ~10% at B²t_m ≈ 19 T² min. The responses of samples of the same crystal from the faces of the prismatic and pyramidal growth sectors to exposure are different. In the former case, they soften; in the latter case, the hardening stage follows the softening stage. However, in both cases, the microhardness returns to the initial value. At B²t_m values from 19 to 37 T² min, the amplitudes and durations of the effect do not change, but in the narrow range of 37–43 T² min, the lifetime of the modified state increases sharply with transition to a new level: “sharp” peaks with a half-width of ~2 days are transformed to trapezoids with the width of the horizontal side of ~1–2 weeks. A physical scheme of the observed effects has been proposed.