Observation of self-similar behavior of the 3D, nonlinear Rayleigh-Taylor instability

The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation sigma(rms) grows as alpha(sigma)gt(2), where g is the foil acceleration, t is the time, and alpha(sigma) is constant. The number of bubbles evolves as N(t) alpha(omegat sq.rt(9) + C)(-4) and the average size evolves as (t) alpha omega(2)gt(2), where C is a constant and omega = 0.83 +/- 0.1 is the measured scaled bubble-merging rate.     

Magnitudes and orientations of the 15N chemical shift tensor of [1-15N]-2'-deoxyguanosine determined on a polycrystalline sample by two-dimensional solid-state NMR spectroscopy.

The magnitudes and orientations of the 15N chemical shift tensor of [1-15N]-2'-deoxyguanosine were determined from a polycrystalline sample using the two-dimensional PISEMA experiment. The magnitudes of the principal values of the 15N chemical shift tensor of the N1 nitrogen of [1-15N]-2'-deoxyguanosine were found to be sigma11 = 54 ppm, sigma22 = 148 ppm, and sigma33 = 201 ppm with respect to (15NH4)2SO4 in aqueous solution. Comparisons of experimental and simulated two-dimensional powder pattern spectra show that sigma33N is approximately collinear with the N-H bond. The tensor orientation of sigma33N for N1 of [1-15N]-2'-deoxyguanosine is similar to the values obtained for the side chain residues of 15Nepsilon1-tryptophan and 15Npi-histidine even though the magnitudes differ significantly.     

Random-field spin models beyond 1 loop: a mechanism for decreasing the lower critical dimension

The functional renormalization group for the random-field and random-anisotropy O(N) sigma models is studied to 2 loop. The ferromagnetic-disordered (F-D) transition fixed point is found to next order in d = 4 + epsilon for N > N(c) (N(c) = 2.834 740 8 for random field, N(c) = 9.441 21 for random anisotropy). For N < N(c) the lower critical dimension d = d(lc) plunges below d(lc) = 4: we find two fixed points, one describing the quasiordered phase, the other is novel and describes the F-D transition. d(lc) can be obtained in an (N(c)-N) expansion. The theory is also analyzed at large N and a glassy regime is found.     

Local theory of solutions for the complex grassmannian andCP N−1 sigma models

We study the classical solutions of the complex Grassmannian nonlinear sigma models and of theCP ^N?1 model in two euclidean dimensions. Exact solutions of various types, which seem to be complete, are constructed explicitly in an elementary way, namely in terms of holomorphic functions and the Gramm-Schmidt orthonormalization procedure. A new type of discrete symmetry transformations which map one solution into another is presented.     

A global identity for nonlinear σ-models

An identity is presented for nonlinear sigma models (harmonic maps) which is a generalization of Green's identity. This identity provides us with a useful tool for analysing questions of the bifurcations and uniqueness of solutions of nonlinear sigma models on noncompact symmetric spaces. As an example of an application, a short proof of the no-hair theorem for charged black holes is given. The uniqueness problem of axisymmetric monopoles is discussed also.     

Massive nonlinear sigma models and BPS domain walls in harmonic superspace

Four-dimensional massive nonlinear sigma models and BPS wall solutions are studied in the off-shell harmonic superspace approach in which supersymmetry is manifest. The general nonlinear sigma model can be described by an analytic harmonic potential which is the hyper-Kähler analog of the Kähler potential in theory. We examine the massive nonlinear sigma model with multi-center four-dimensional target hyper-Kähler metrics and derive the corresponding BPS equation. We study in some detail two particular cases with the Taub-NUT and double Taub-NUT metrics. The latter embodies, as its two separate limits, both Taub-NUT and Eguchi–Hanson metrics. We find that domain wall solutions exist only in the double Taub-NUT case including its Eguchi–Hanson limit.     

The aetiology of sigma model anomalies

Certain nonlinear sigma models with fermions are ill-defined due to an anomaly which exhibits characteristics of both the nonabelian gauge theory anomaly and the SU(2) anomaly. The simplest way to diagnose the anomaly involves consideration of the global topology of the theory. We review the mathematical methods needed for this analysis and apply them to several supersymmetric sigma models. Some of these are found to be anomalous.     

Alternative formulation in the constrained Hamiltonian system of a rigid rotator

An alternative form of the constraint characterizing the motion of a rigid rotator is introduced and is shown to lead to the same constrained Hamiltonian system as the one constructed with the conventional constraintx ²=constant. In this new formulation, the canonical pairs of phase-space variables can easily be found, and the relationx ²=constant appears through an equation of motion rather than through a constraint. Application toO(N) nonlinear sigma model is also discussed.     

Quenched master field equations for unitary matrix models

We derive the quenched master field equations for constrained systems such as the O(N) non-linear sigma model, U(N)×U(N) chiral models, and U(N) lattice gauge theory. The master equations are algebraic, and involve quenching in both the space and “fifth” (Langevin) time directions. The quenched master field for the O(N) nonlinear sigma model is found exactly. The 0-dimensional unitary matrix model is solved perturbatively, and we recover the Gross-Witten result. The master equation for the U(N)×U(N) chiral model is set up for non-perturbative approximation methods, and some qualitative results are obtained.     

Prandtl-number dependence of heat transport in turbulent Rayleigh-Bénard convection

We present measurements of the Nusselt number N as a function of the Rayleigh number R and the Prandtl number sigma in cylindrical cells with aspect ratios gamma = 0.5 and 1.0. We used acetone, methanol, ethanol, and 2-propanol with Prandtl numbers sigma = 4.0, 6.5, 14.2, and 34.1, respectively, in the range 3x10(7) less, similarR less, similar10(11). At constant R, N(R,sigma) varies with sigma by only about 2%. This result disagrees with the extrapolation of the Grossmann and Lohse theory beyond its range of validity, which implies a decrease by 20% over our sigma range, but agrees with their recent extension of the theory to small Reynolds numbers.     

Nonlinear Sigma Models in (1+2) Dimensions and an Infinite Number of Conserved Currents

In this Letter, we treat nonlinear sigma models such as the C P¹-model, Q P¹-model, etc. in 1+2 dimensions. For submodels of such models, we definitely construct an infinite number of nontrivial conserved currents. Our result is a generalization of Alvarez, Ferreira and Guillen.     

Heuristic Relative Entropy Principles with Complex Measures: Large-Degree Asymptotics of a Family of Multi-variate Normal Random Polynomials

Let \(z\in \mathbb {C}\), let \(\sigma ^2>0\) be a variance, and for \(N\in \mathbb {N}\) define the integrals

$$\begin{aligned} E_N^{}(z;\sigma ) := \left\{ \begin{array}{ll} {\frac{1}{\sigma }} \!\!\!\displaystyle \int _{\mathbb {R}}\! (x^2+z^2) \frac{e^{-\frac{1}{2\sigma ^2} x^2}}{\sqrt{2\pi }}dx&{}\quad \text{ if }\, N=1,\\ {\frac{1}{\sigma }} \!\!\!\displaystyle \int _{\mathbb {R}^N}\! \prod \prod \limits _{1\le k<l\le N}\!\! e^{-\frac{1}{2N}(1-\sigma ^{-2}) (x_k-x_l)^2} \prod _{1\le n\le N}\!\!\!\!(x_n^2+z^2) \frac{e^{-\frac{1}{2\sigma ^2} x_n^2}}{\sqrt{2\pi }}dx_n &{}\quad \text{ if }\, N>1. \end{array}\right. \!\!\! \end{aligned}$$

These are expected values of the polynomials \(P_N^{}(z)=\prod _{1\le n\le N}(X_n^2+z^2)\) whose 2N zeros \(\{\pm i X_k\}^{}_{k=1,\ldots ,N}\) are generated by N identically distributed multi-variate mean-zero normal random variables \(\{X_k\}^{N}_{k=1}\) with co-variance \(\mathrm{{Cov}}_N^{}(X_k,X_l)=(1+\frac{\sigma ^2-1}{N})\delta _{k,l}+\frac{\sigma ^2-1}{N}(1-\delta _{k,l})\). The \(E_N^{}(z;\sigma )\) are polynomials in \(z^2\), explicitly computable for arbitrary N, yet a list of the first three \(E_N^{}(z;\sigma )\) shows that the expressions become unwieldy already for moderate N—unless \(\sigma = 1\), in which case \(E_N^{}(z;1) = (1+z^2)^N\) for all \(z\in \mathbb {C}\) and \(N\in \mathbb {N}\). (Incidentally, commonly available computer algebra evaluates the integrals \(E_N^{}(z;\sigma )\) only for N up to a dozen, due to memory constraints). Asymptotic evaluations are needed for the large-N regime. For general complex z these have traditionally been limited to analytic expansion techniques; several rigorous results are proved for complex z near 0. Yet if \(z\in \mathbb {R}\) one can also compute this “infinite-degree” limit with the help of the familiar relative entropy principle for probability measures; a rigorous proof of this fact is supplied. Computer algebra-generated evidence is presented in support of a conjecture that a generalization of the relative entropy principle to signed or complex measures governs the \(N\rightarrow \infty \) asymptotics of the regime \(iz\in \mathbb {R}\). Potential generalizations, in particular to point vortex ensembles and the prescribed Gauss curvature problem, and to random matrix ensembles, are emphasized.

     

A new finite N = 2 supersymmetric sigma model with higher derivatives in four dimensions

A new finite N = 2 supersymmetric sigma model with higher derivatives in four dimensions is formulated. The action of the model is determined in N = 2, d = 4 superspace in terms of N = 2 chiral real superfields. The Lagrangian of the theory under consideration is evaluated in N = 1 super-space and in components. By the methods of N = 2 superfield perturbation theory, it is shown that the constructed N = 2 model is ultraviolet-finite in all orders of quantum perturbation theory in 4-dimensional space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 85–92, April, 1990.     

Explicit Construction of Supercharges of Supersymmetric Nonlinear Sigma Models in 1 + 1 Spacetime Dimensions

Considering the N = 1 supersymmetry transformations of supersymmetric nonlinear sigma models in 1 + 1 dimensions we construct explicitly conserved Noether currents associated with supersymmetry transformations and derive the associated conserved charges in terms of the basic fields. We compare this result with superspace calculations. Finally we review the connection between extended supersymmetry and the geometry of the target space and derive an explicit form of the supercharges for extended supersymmetry.     

A study of the critical behavior of the O(N) linear and nonlinear σ models

A study of the large N behavior of both the O(N) linear and nonlinear σ models is presented. The purpose is to investigate the relationship between the disordered (ordered) phase of the linear and nonlinear sigma models. Utilizing operator product expansions and stability analyses, it is shown that for 2 ≤ d < 4, it is the dimensionless renormalized quartic coupling and $\text{λ}{}^1$ is the IR fixed point) limit of the linear σ model which yields the nonlinear σ model. It is also shown that stable large N linear σ models with λ < 0 (σ is the bare quartic coupling) can exist (at least in the context of no tachyonic states being present). A criteria valid for all dimensionalities d, less than four, is derived which determines when λ < 0 models are tachyonic free. Arguments are given showing that the d = 4 large N linear (for λ > 0) and nonlinear models are trivial. This result (i.e., triviality) is well known but only for one and two component models. Interestingly enough, the λ < 0, d = 4 linear σ model remains nontrivial and tachyonic free.     

Heat transport in turbulent rayleigh-Benard convection

We present measurements of the Nusselt number N as a function of the Rayleigh number R in cylindrical cells with aspect ratios 0. 510(7) they are consistent with N = asigma-1/12R1/4+bsigma-1/7R3/7 as proposed by Grossmann and Lohse for sigma greater, similar2.     

高激发振动态RbH（Х1Σ+,ν″=15～22）与H2,N2的振动-振动碰撞能量转移

脉冲激光激发Rb原子至6 D态,Rb(6 D)与H2反应生成RbH(Х1Σ+,ν″=0～2)振动态。研究了RbH(Х1Σ+)高位振动态与H2,N2间的碰撞弛豫过程,利用泛频泵浦分别激发Х1Σ+(ν″=0)至Х1Σ+(ν″=15～22)各振动态,检测激光激发Х1Σ+(ν″)至A1Σ+(ν′),测量A1Σ+(ν′)的时间分辨激光感应荧光光谱,利用Stern-Volmer方程,得到振动能级ν″的总的弛豫速率系数kν(H2)。在H2和N2的混合气体中,总弛豫速率系数kν(H2+N2)与α(H2的摩尔配比)成直线的关系,其斜率为kν(H2)-kν(N2),而截距为kν(N2)。对于ν″<18主要发生单量子弛豫(Δν=1)过程,kν(H2)和kν(N2)与振动量子数ν″均成线性增加关系。对于ν″≥18,多量子弛豫(Δν≥2)过程及共振振动-振动转移起重要作用。对于RbH(ν″=21)+N2(0),测量ν″=16的布居数时间演化轮廓,在20μs内有一个锐锋,在100～200μs内有一个较低的宽峰,锐锋相应于RbH(ν″=21)+N2(0)→RbH(ν″=16)+N2(1)的共振转移过程,而宽峰是由相继的单量子过程产生的。     

A-twisted heterotic Landau–Ginzburg models

In this paper, we apply the methods developed in recent work for constructing A-twisted (2, 2) Landau–Ginzburg models to analogous (0, 2) models. In particular, we study (0, 2) Landau–Ginzburg models on topologically non-trivial spaces away from large-radius limits, where one expects to find correlation function contributions akin to (2, 2) curve corrections. Such heterotic theories admit A- and B-model twists, and exhibit a duality that simultaneously exchanges the twists and dualizes the gauge bundle. We explore how this duality operates in heterotic Landau–Ginzburg models, as well as other properties of these theories, using examples which renormalization-group flow to heterotic nonlinear sigma models as checks on our methods.     

Depression of quasiparticle density of states at zero energy in la1. 9Sr0.1Cu1-xZnxO (4)

We have measured low-temperature specific heat C(T,H) of La 1.9Sr 0. 1Cu 1-xZn xO (4) ( x = 0, 0.01, and 0.02) in both zero and applied magnetic fields. A pronounced dip of C/T below 2 K was observed in Zn-doped samples, which is absent in the nominally clean one. If the origin of the dip in C/T is electronic, the quasiparticle density of states N(E) in Zn-doped samples may be depressed below a small energy scale E0. The present data can be well described by the model N(E) = N(0)+alphaE(1/2), with a nonzero N(0) and positive alpha. Magnetic fields depress N(0) and lead to an increase in E0, while leaving the energy dependence of N(E) unchanged. This novel depression of N(E) below E0 in impurity-doped cuprates cannot be reconciled with the semiclassical self-consistent approximation model. Discussions in the framework based on the nonlinear sigma model field theory and other possible explanations are presented.