On unconstrained SU(2) gluodynamics with theta angle

The Hamiltonian reduction of classical SU(2) Yang–Mills field theory to the equivalent unconstrained theory of gauge invariant local dynamical variables is generalized to the case of nonvanishing -angle. It is shown that for any -angle the elimination of the pure gauge degrees of freedom leads to a corresponding unconstrained non-local theory of self-interacting second rank symmetric tensor fields, and that the obtained classical unconstrained gluodynamics with different -angles are canonically equivalent as on the original constrained level. Received: 16 November 2001 / Published online: 5 April 2002     

Assessing auditory distance perception using virtual acoustics

In most naturally occurring situations, multiple acoustic properties of the sound reaching a listener's ears change as sound source distance changes. Because many of these acoustic properties, or cues, can be confounded with variation in the acoustic properties of the source and the environment, the perceptual processes subserving distance localization likely combine and weight multiple cues in order to produce stable estimates of sound source distance. Here, this cue-weighting process is examined psychophysically, using a method of virtual acoustics that allows precise measurement and control of the acoustic cues thought to be salient for distance perception in a representative large-room environment. Though listeners' judgments of sound source distance are found to consistently and exponentially underestimate true distance, the perceptual weight assigned to two primary distance cues (intensity and direct-to-reverberant energy ratio) varies substantially as a function of both sound source type (noise and speech) and angular position (0 degrees and 90 degrees relative to the median plane). These results suggest that the cue-weighting process is flexible, and able to adapt to individual distance cues that vary as a result of source properties and environmental conditions.     

Thermodynamic coefficients of ideal Fermi gas

We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non-relativistic ideal Fermi gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio, and others are explicitly expressed through the derivatives. We demonstrate correct ideal Boltzmann gas and low-temperature Fermi gas asymptotes and derive corrections to thermodynamic functions for these limiting cases. Numerical computations of thermodynamic properties of ideal Fermi gas can be accurately performed using the developed freely available Python module ifg .     

Fission fragment mass yields of Th to Rf even-even nuclei

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.     

On periodic solvable groups having automorphisms with nilpotent fixed point groups

Letp be a prime,G a periodic solvablep′-group acted on by an elementary groupV of orderp ². We show that ifC _G(v) is abelian for eachv ∈V ^# thenG has nilpotent derived group, and ifp=2 andC _G(v) is nilpotent for eachv ∈V ^# thenG is metanilpotent. Earlier results of this kind were known only for finite groups.     

Finely holomorphic functions and quasi-analytic classes

We study the set of functions in quasi-analytic classes and the set of finely holomorphic functions. We show that no one of these two sets is contained in the other.LetI denote the set of complex functionsf: for which there exists a quasi-analytic classC{M _n} containingf. Let denote the set of complex functionsf: for which there exist a fine domainU containing the real line and a function finely holomorphic onU satisfyingf(x)= (x) for allx . The power of unique continuation is incomparable in these two cases (I\ is non-empty, \I is non-empty).Research supported by the grant No. 201/93/2174 of Czech Grant Agency and by the grant No. 354 of Charles University.     

Unit squares intersecting all secants of a square

LetS be a square of side lengths>0. We construct, for any sufficiently larges, a set of less than 1.994s closed unit squares whose sides are parallel to those ofS such that any straight line intersectingS intersects at least one square ofS. It disproves L. Fejes Tóth's conjecture that, for integrals, there is no such configuration of less than 2s−1 unit squares. Supported by “Deutsche Forschungsgemeinschaft”, Grant We 1265/2-1.     

Approximation of convex bodies by simplices

This paper deals with the following kind of approximation of a convex bodyQ in Euclidean space E ⁿ by simplices: which is the smallest positive numberh _S(Q) such thatS ₁ Q S ₂ for a simplexS ₁ and its homothetic copyS ₂ of ratioh _S(Q). It is shown that ifS ₀ is a simplex of maximal volume contained inQ, then a homothetic copy ofS ₀ of ratio 13/3 containsQ.     

Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations

We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S¹. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H¹(S¹), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then lim_tT* w(t,·) exists in C¹(S¹) but vanishes at some point. We show further that if T* > (1 + √3)/16π² √3 then T* = ∞ and lim_t∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc.     

Seeing the Unseen: Experimental Observation of Magnetic Anapole State Inside a High-Index Dielectric Particle

The existence of non-radiating electromagnetic sources attracts much attention in photonic community and gives rise to extensive discussions of various applications in lasing, medical imaging, sensing, and nonlinear optics. In this article, the existence of magnetic anapole states (or magnetic-type non-radiating sources) characterized by a suppressed magnetic dipole radiation in a dielectric cylindrical particle is theoretically predicted and experimentally demonstrated. The specific features of the magnetic anapole state under ideal conditions are identified, followed by a demonstration of how their existence can be detected in practical structures. The concept is valid in various frequency bands from visible range for nanoparticles to microwave range for millimeter size objects. The experimental study is performed in microwave frequency range which allows not only to measure the far-field (scattered field) characteristics, but also to probe the peculiar field profile directly inside the dielectric particle. The experimental results agree well with the analytical ones and pave the way to detect and identify nontrivial different-type anapole states.