Set the controls for the heart of the Sun

In this paper we describe experiments conducted with high-power lasers that are attempting to replicate, for a very short time and in miniature, conditions found in the Sun. Experiments to date have reached conditions in the outer part of the Sun. To reach the Sun's centre requires compression of material to very much greater than solid density and heating to over ten million degrees. To achieve this, a new class of experiments and a new generation of high-power lasers are required.     

Violations of the Pauli principle and the interior of the sun

The consequences of a violation of the Pauli principle for the physics of the solar interior are explored. It is found that a bound state of two protons becomes possible. This leads to an increase in the rate of hydrogen burning in the sun. Because a very large cross section for this reaction is in clear contradiction with the theory of stellar structure when compared with observations of solar luminosity, radius and mechanical oscillations, stringent limits on a violation of the Pauli principle in the two nucleon system can be given. However, a very small violation of the Pauli principle in the two nucléon system might solve the longstanding solar neutrino problem.     

Relaxing the clustering condition in the derivation of the KMS property

We consider as in [1] an infinite dynamical system idealized as aC*-algebra acted upon by time-translation automorphisms. We show that a stationary state of such a system which is stable for local perturbations of the dynamics and is clustering in time, either gives rise to a one-sided energy spectrum or is a KMS state. The clustering property assumed here is weaker than the one assumed in [1]. The new proof makes explicit use of spectral properties of clustering states.Supported by the Norwegian Research Council for Science and Humanities.     

On the numerical solution of the biharmonic equation in the plane

The biharmonic equation arises in a variety of problems in applied mathematics, most notably in plane elasticity and in viscous incompressible flow. Integral equation methods are natural candidates for the numerical solution of such problems, since they discritize the boundary alone, are easy to apply in the case of free or moving boundaries, and achieve superalgebraic convergence rates on sufficiently smooth domains, regardless of shape. In this paper, we follow the work of Mayo and Greenbaum and make use of the Sherman-Lauricella integral equation which is a Fredholm equation with bounded kernel. We describe a fast algorithm for the evaluation of the integral operators appearing in that equation. When combined with a conjugate gradient like algorithm, we are able to solve the discretized integral equation in an amount of time proportional to N, where N is the number of nodes in the discretization of the boundary.     

On the possibility to optimize the gain of the Compton laser

The gain of the Compton laser is derived in the case when the direction of propagation of the amplified wave does not coincide with the direction of motion of an electron beam. The optimum geometry of the experiment is found. Numerical estimations are presented, which show that there is a possibility to achieve a noticeable amplification in the ultra-violet region using a CO₂ laser as a pump.     

Confronting the MSSM and the NMSSM with the discovery of a signal in the two photon channel at the LHC

We confront the discovery of a boson decaying into two photons, as reported recently by ATLAS and CMS, with the corresponding predictions in the Minimal Supersymmetric Standard Model (MSSM) and the Next-to-Minimal Supersymmetric Standard Model (NMSSM). We perform a scan over the relevant regions of parameter space in both models and evaluate the MSSM and NMSSM predictions for the dominant Higgs production channel and the photon–photon decay channel. Taking into account the experimental constraints from previous direct searches, flavor physics, electroweak measurements as well as theoretical considerations, we find that a Higgs signal in the two photon channel with a rate equal to, or above, the SM prediction is viable over the full mass range 123?M _H ?127 GeV, both in the MSSM and the NMSSM. We find that besides the interpretation of a possible signal at about 125 GeV in terms of the lightest $\mathcal {CP}$ -even Higgs boson, both the MSSM and the NMSSM permit also a viable interpretation where an observed state at about 125 GeV would correspond to the second-lightest $\mathcal {CP}$ -even Higgs boson in the spectrum, which would be accompanied by another light Higgs with suppressed couplings to W and Z bosons. We find that a significant enhancement of the γγ rate, compatible with the signal strengths observed by ATLAS and CMS, is possible in both the MSSM and the NMSSM, and we analyse in detail different mechanisms in the two models that can give rise to such an enhancement. We briefly discuss also our predictions in the two models for the production and subsequent decay into two photons of a $\mathcal {CP}$ -odd Higgs boson.     

On the NLO QCD corrections to the production of the heaviest neutral Higgs scalar in the MSSM

We present a calculation of the two-loop top–stop–gluino contributions to Higgs production via gluon fusion in the MSSM. By means of an asymptotic expansion in the heavy particle masses, we obtain explicit and compact analytic formulas that are valid when the Higgs and the top quark are lighter than stops and gluino, without assuming a specific hierarchy between the Higgs mass and the top mass. Being applicable to the heaviest Higgs scalar in a significant region of the MSSM parameter space, our results complement earlier ones obtained with a Taylor expansion in the Higgs mass, and can be easily implemented in computer codes to provide an efficient and accurate determination of the Higgs production cross section.     

On the Locality of the No Hair Conjecture and the Measure of the Universe

We reanalize the recently proposed proof by Jensen and Stein-Schabes [1] of the No Hair Theorem for inhomogeneous spacetimes, putting a special emphasis on the asymptotic behaviour of the shear and curvature. We conclude that the theorem only holds locally and estimate the minimum size a region should be in order for it to inflate. We discuss in some detail the assumptions used in the theorem. In the last section we speculate about the possible measure of the set of spacetimes that would undergo inflation.     

On the theory of the Buckingham effect

We apply general arguments (based on spatial transformation properties, intrinsic symmetry and dimensional analysis) to the theory of the Buckingham effect (electric-field–gradient-induced birefringence in a gas). These yield, in a simple manner, the temperature-dependent and temperature-independent terms in the birefringence (each to within a numerical factor), and also the expression, derived by Buckingham and Longuet-Higgins, for the effective quadrupole centre of a molecule. We show in addition how the calculation of the two numerical factors can be simplified in our approach.     

Contributions of the cornea and the lens to the aberrations of the human eye

The relative contributions of optical aberrations of the cornea and the crystalline lens to the final image quality of the human eye were studied. The aberrations of the entire eye were obtained from pairs of double-pass retinal images, and the aberrations of the cornea were obtained from videokeratographic data. Third-order spherical aberration and coma were significantly larger for the cornea than for the complete eye, indicating a significant role of the lens in compensating for corneal aberrations. In a second experiment retinal images were recorded in an eye before and after we neutralized the aberrations of the cornea by having the subjects wear swimming goggles filled with saline water, providing a direct estimate of the optical performance of the crystalline lens.     

Influence of the thickness of the liquid layer on the ratio of the dimensions of a convection cell

A theory is developed for a new type of transition — a change in the ratio of the longitudinal and transverse dimensions of a convection cell as the thickness of a liquid layer is varied. A sudden change in the ratio of the cell dimensions takes place because of a change in the predominant mechanism for excitation of convection. The governing influence of buoyancy forces gives way to one of thermocapillary forces, and they in turn give way to the influence of thermoelectric forces for yet thinner layers. As the layer thickness is reduced gradually at a fixed external heating, the ratio of the dimensions will take on the values 0.7, 0.65, and 1, respectively. Zh. Tekh. Fiz. 68, 7–11 (November 1998)     

On the role of the Killing tensor in the Einstein-Maxwell theory

It is shown that when a four dimensional source-free Einstein-Maxwell space-time admits a group of motions leaving the electromagnetic field unchanged a linear relation exists between two Maxwell fields and the covariant derivative of a Killing vector. For the case in which the two electromagnetic fields are related by a duality rotation it is seen that a purely geometric form of Einstein's equations may be derived. The behaviour of these under a class of quasi conformal transformations of the metric is shown to lead to Harrison's theorem.     

Unraveling the symmetry of the hole states near the Fermi level in the MgB2 superconductor

We use x-ray absorption spectroscopy (XAS) and electron energy loss spectroscopy (EELS) to study the fine structure at the K edge of boron in MgB(2). We observe in XAS a peak of width 0.7 eV at the edge threshold, signaling a narrow energy region with empty boron p states near the Fermi level. The changes in the near edge structure observed in EELS with direction of the momentum transfer imply that these states have p(x)p(y) symmetry. Our observations are consistent with electronic structure calculations indicating a narrow energy window of empty p(x)p(y) states that falls to zero at 0.8 eV above the Fermi level. The disappearance of the p(x)p(y) feature in EELS at grain boundaries suggests that this signature may become powerful in probing superconductivity at nanoscale.     

On the reversibility of the Meissner effect and the angular momentum puzzle

It is generally believed that the laws of thermodynamics govern superconductivity as an equilibrium state of matter, and hence that the normal-superconductor transition in a magnetic field is reversible under ideal conditions. Because eddy currents are generated during the transition as the magnetic flux changes, the transition has to proceed infinitely slowly to generate no entropy. Experiments showed that to a high degree of accuracy no entropy was generated in these transitions. However, in this paper we point out that for the length of times over which these experiments extended, a much higher degree of irreversibility due to decay of eddy currents should have been detected than was actually observed. We also point out that within the conventional theory of superconductivity no explanation exists for why no Joule heat is generated in the superconductor to normal transition when the supercurrent stops. In addition we point out that within the conventional theory of superconductivity no mechanism exists for the transfer of momentum between the supercurrent and the body as a whole, which is necessary to ensure that the transition in the presence of a magnetic field respects momentum conservation. We propose a solution to all these questions based on the alternative theory of hole superconductivity. The theory proposes that in the normal-superconductor transition there is a flow and backflow of charge in direction perpendicular to the phase boundary when the phase boundary moves. We show that this flow and backflow explains the absence of Joule heat generated by Faraday eddy currents, the absence of Joule heat generated in the process of the supercurrent stopping, and the reversible transfer of momentum between the supercurrent and the body, provided the current carriers in the normal state are holes.     

On the Quantum Dynamic Theory of the MIT Output Coupler for the Bose-Einstein Condensation

A linear quantum dynamic theory for output coupler of Bose-Einstein condensed atoms in a trap is considered with the Bogoliu bov approximation in the thermodynamical limit based on the recent MIT experiment (Phys. Rev. Lett. 78 (1997) 582) for atomic laser. In evolution of total system, the solution of the many-body problem shows a factorization of dynamic process, i.e., the wave function initially prepared in a direct product of a vacuum state and a coherent state remains in a direct product of coherent states at any instance. Physically, this factorizable structure predicts that an ideal condensate in the trap will remain in such a condensate state after the radiation frequency interaction while the output-coupler pulse of atoms forms a macroscopic quantum state in a propagating mode, i.e., the atomic laser.     

Study of the cavitation region and the evolution of the acoustic spectrum

An experimental setup and a technique for measuring the transient period before a stationary cavitation in a liquid by the evolution of the cavitation noise spectrum are described. The time dependences of harmonic amplitudes both near the radiator and outside the cavitation region are presented. From the form of these dependences, the characteristic transient periods preceding the stage of a fully developed cavitation in water and in transformer oil are calculated. A formal scheme for describing the cavitation region is proposed.     

On the rotational dynamics of the rattleback

The rattleback is a very popular science toy shown to students all over the world to demonstrate the nontriviality of rotational motion. When spun on a horizontal table, this boat-shaped object behaves in a peculiar way. Although the object appears symmetric, the dynamics of its motion seem very asymmetric. When spun in the preferred direction, it spins smoothly, whereas in the other direction it starts to oscillate wildly. The oscillation soon dies out and the rattleback starts to spin in the preferred way. We will construct and go through an analytical model capable of explaining this behaviour in a simple and intelligible way. Although we aim at a semi-pedagogical treatise, we will study the details only when they are necessary to understand the calculation. After presenting the calculations we will discuss the physical validity of our assumptions and take a look at more sophisticated models requiring numerical analysis. We will then improve our model by assuming a simple friction force.     

On the nature of the step-like transition in the UP-USe system

Neutron diffraction experiments on the solid solution UP_0.9Se_0.1 indicate that the step-like transition occurring at low temperature in the UP-USe system is of the same nature as in UAs and UP. It corresponds to a transition from a collinear single-k structure to a non-collinear double-k structure.     

Determination of the exact solutions to the inhomogeneous burgers equation with the use of the darboux transformation

A method of determining the exact solutions to the Burgers equation on the basis of the Darboux transformation is described. It is shown that a single application of the Darboux transformation to the homogeneous Burgers equation transforms the latter into the inhomogeneous equation describing acoustic wave propagation against transonic flow in the de Laval nozzle. In this case, the contraction ratio of the nozzle is fixed and determined by the viscosity coefficient of the medium. Based on the exact solution of the homogeneous Burgers equation, for the aforementioned problem of the flow in the nozzle, all the possible regular steady-state solutions are presented and the evolution of nonstationary solutions is investigated. The algorithm of a multiple Darboux transformation, which allows an increase in the strength of inhomogeneity, i.e., in the contraction ratio of the nozzle, is determined. This approach leads to a discrete set of possible contraction ratios at which exact solutions can be obtained. The Crum’s theorem is used to derive a formula that allows determination of the exact solutions to the inhomogeneous Burgers equation from the solutions to the homogeneous heat transfer equation. It is noted that, in fact, the proposed algorithm of the multiple Darboux transformation makes it possible to decrease the viscosity coefficient of the medium in a discrete way.     

Role of the near-electrode regions in the formation of the volume discharge heterogeneity in nitrogen in the pin-to-plane configuration

The development of streamers and sparks in nitrogen at atmospheric pressure in the pin-to-plane electrode configuration is studied in experiments and theoretical calculations. It is demonstrated that the near-electrode regions play the decisive role in streamer initiation. At a negative pin voltage, a spark is formed in the absence of fast primary streamers. At a positive pin voltage, streamer build-up is initiated by the current spots on the anode that result from the development of the ionization instabilities in the anode region. The calculations show that the formation of the current spot on the anode leads to a redistribution of the electric field in the vicinity of the anode, so that a single avalanche is transformed into a streamer under the conditions when the known criterion for streamer breakdown (the Meek-Raether criterion) is not satisfied. Original Text ? Astro, Ltd., 2006.