On the Possibility of the Implicit Renormalization of the Casimir Energy

We propose a procedure for renormalizing the Casimir energy that makes the steps that are used in the standard renormalization procedure, that is, regularization, subtraction, and deregularization, implicit. The proposed procedure is based on the calculation of a set of convergent sums, each of which is related to the initial divergent sum of the non-renormalized Casimir energy. Next, we construct a system of linear equations that relates this set of convergent sums to the renormalized Casimir energy. The unknown renormalized Casimir energy is obtained as a result of solving this system of equations. In this case, both the calculations of the convergent sums and the subsequent solution of the system of linear equations are performed with a certain (generally speaking, arbitrary) ordered accuracy; thus, the result is also approximate. The proposed procedure is, first, more computationally effective than the standard one, and, second, applicable not only to the problems where a transcendental equation for the spectrum can be written, but also to the problems where the spectrum is known only numerically.     

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)     

Finding the impedance of the organ of Corti

Measurements of the nonlinear response of the basilar membrane to a pure tone are shown to have a simple form for moderate membrane velocities: V(x,f;Vu)/Vu approximately [V(x,f)/Vu]v(x,f), f less than or equal to fc(x), where the response V is the velocity of the membrane at measurement position x, Vu is the umbo velocity, f is the frequency of the stimulus, and fc(x) is the local characteristic frequency. The frequency dependence of the functions v(x,f) and V(x,f) is determined from the data, and v(x,f) and ln V(x,f) are shown to be analytic functions in the lower half of the complex frequency plane, with Re [v(x,f)] a monotonically increasing function of f at fixed x. The linear limit of basilar membrane motion is characterized by a transfer function T(x,f) = (V/V1)v/(1-v), estimated by extrapolating V(x,f;Vu)/Vu to a small membrane velocity V1.T(x,f) and ln T(x,f) are shown to be analytic functions in the lower half of the complex frequency plane. The inverse of the amplitude of the transfer function, which has both a deep dip at f approximately fc(x) and a broad shoulder at lower frequencies, bears a striking resemblance to the neural threshold tuning curve. The functional form of T(x,f) is used to deduce the equation governing the motion of a section of the organ of Corti. Each section acts like a negatively damped harmonic oscillator stabilized at time t by a feedback force proportional to the velocity at the previous time t-tau. The time delay tau is proportional to the oscillator period [tau approximately 1.75/fc(x)]. Like a laser, the organ of Corti pumps energy into harmonic traveling waves. Unlike the laser, the direction of energy flow abruptly reverses as the traveling wave approaches the point of maximum membrane velocity [fc(x) approximately f]. All accumulated wave energy is then pumped back into a small section of the organ of Corti where transduction presumably occurs. Outer hair cells are conjectured to be active elements contributing to the negative damping and feedback of the cochlear amplifier.     

Application of the method of collective coordinates the the quantisation of the two-dimensional higgs model

A comprehensive analysis of the application of the method of collective coordinates to the two dimensional Higgs model is given. First the instanton solution is derived, and the geometry of configuration space, and the construction of Schrodinger wave functionals are discussed. It is then explicitly verified that the Goldstone mode is the projection of the vacuum state onto the generator of the broken symmetry. The elimination of this Goldstone mode by means of the unitary gauge condition is demonstrated to the the crucial point in the construction of a consistent perturbation procedure. The parameter of the broken symmetry group is then used as the collective coordinate for field configurations around a minimum of the interaction. Throughout, the discussion is sufficiently detailed in order to facilitate the application of the method to other fields.     

On the nature of the nearest singularities of the free energy in the neighborhood of a critical point

Algebraic functions are used to provide an example of multiple-valued functions which coincide with a model (single-valued) free energy on one sheet of the Riemann surface in the neighborhood of a critical point. For the case of homogeneous free energies andα=α′=0, there are enough conditions to determine the behavior of the nearest singularities (branch points) to the critical point of the algebraic function. If no other singularities are present these branch points would represent the spinodal line. The particular exponents of the two-dimensional Ising model are used to provide a specific example.     

Analysis of the sensitivity to the electrochemical potential of the width of a metallic nanoconstriction

In relation to a metallic nanowire in the presence of an electrochemical potential, the sensitivity to this potential of the nanowire width is evaluated by defining and calculating a suitable parameter that can be regarded as a normalized gradient, this gradient being the derivative of the above-mentioned width with respect to the electrochemical potential.     

Analysis of the Topology of the Kerr Metric

The equations of motion of a test particle are integrated for the field of a rotating Kerr black hole (BH) (in accordance with [1]). Due to the lack of analytical transformations for the Carter–Penrose diagrams (CPDs) for the Kerr metric, the topology of the Kerr BH is studied by analytical investigation of the equations of motion. Transformations for the CPDs for the Reisner–Nordström metric are analyzed. The problem of boundary conditions for the Reisner–Nordström topology is analyzed. A solution to this problem of boundary conditions is proposed. It is proved that, in the Reisner–Nordström topology, only one way to go to another universe is possible. For the Kerr topology, the possibility of the existence of an alternative transition to another universe that does not coincide with the universe for the ordinary transition is found. This alternative transition is performed through a surface with a zero radial coordinate (zero radius). Initial conditions for the falling particle are found that correspond to an alternative transition to another universe. The tidal forces acting on a falling body in the Kerr metric are estimated, and the possibility of the transition of the body to other universes without being destroyed by tidal forces is proved.     

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.     

Application of the structured illumination method to study the topography of the sole of the foot during a walk

The structured illumination technique consists of projecting a fringe system onto a 3D object from a well defined space point, which results in a pattern that depends on the characteristic of the projected fringes, the viewpoint and the illuminated object morphology. Therefore, the structured illumination method enables to determine the topography of 3D objects. To implement this technique we set up an optoelectronic array that allows studying the sole of the foot during a walk. The method consists of projecting a Ronchi grid and capturing the images generated on the foot by a CCD camera. These obtained images are graphically processed and fringes converted into vectors. A depending algorithm on the experimental setup allows obtaining, from those vectors data, cotes for a discrete profile plotting of the studied object. The method enables the quantitative determination of the sole topography during the walk. Qualitatively, it can be used for diagnosis and control of deformation and injuries caused by accidents or illnesses. It can be introduced in the primary attention health system to study a great number of patients, due to its simplicity and low cost installation, and for being a non-invasive technique.     

Role of the null space of the DRM in the performance of modulated polarimeters

Imaging polarimeters infer the spatial distribution of the polarization state of the optical field as a function of time and/or wavelength. A polarimeter indirectly determines the polarization state by first modulating the intensity of the light field and then demodulating the measured data to infer the polarization parameters. This Letter considers passive Stokes parameter polarimeters and their inversion methods. The most widely used method is the data reduction matrix (DRM), which builds up a matrix equation that can be inverted to find the polarization state from a set of intensity measurements. An alternate strategy uses linear system formulations that allow band limited reconstruction through a filtering perspective. Here we compare these two strategies for overdetermined polarimeters and find that design of the null space of the inversion operator provides degrees of freedom to optimize the trade off between accuracy and signal-to-noise ratio. We further describe adaptive filtering techniques that could optimize the reconstruction for a particular experimental configuration. This Letter considers time-varying Stokes parameters, but the methods apply equally to polarimeters that are modulated in space or in wavelength.     

Effect of the architecture of the left ventricle on the speed of the excitation wave in muscle fibers

It is known that preferential paths for the propagation of an electrical excitation wave in the human ventricular myocardium are associated with muscle fibers in tissue. The speed of the excitation wave along a fiber is several times higher than that across the direction of the fiber. To estimate the effect of the architecture and anisotropy of the myocardium of the left ventricle on the process of its electrical activation, we have studied the relation between the speed of the electrical excitation wave in a one-dimensional isolated myocardial fiber consisting of sequentially coupled cardiomyocytes and in an identical fiber located in the wall of a threedimensional anatomical model of the left ventricle. It has been shown that the speed of a wavefront along the fiber in the three-dimensional myocardial tissue is much higher than that in the one-dimensional fiber. The acceleration of the signal is due to the rotation of directions of fibers in the wall and to the position of the excitation wavefront with respect to the direction of this fiber. The observed phenomenon is caused by the approach of the excitable tissue with rotational anisotropy in its properties to a pseudoisotropic tissue.     

On the nature of a*kak and the emergence of the Born rule

This paper is intended to show that a review in the concept of the game theoretical utility, the revised utility to be applied to the definition of the utility of a wave function representing an object subsystem relative to its observer subsystem, both within an isolated system, leads to the emergence of Max Born's rule as a profit under a von Neumann good measure game.     

Constraining the topology of the universe

The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar temperature patterns along each circle. We restrict the search to back-to-back circle pairs, and to nearly back-to-back circle pairs, as this covers the majority of the topologies that one might hope to detect in a nearly flat universe. We do not find any matched circles with radius greater than 25 degrees. For a wide class of models, the nondetection rules out the possibility that we live in a universe with topology scale smaller than 24 Gpc.     

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.     

Revisiting the scaling of the specific heat of the three-dimensional random-field Ising model

We revisit the scaling behavior of the specific heat of the three-dimensionalrandom-field Ising model with a Gaussian distribution of the disorder. Exact ground statesof the model are obtained using graph-theoretical algorithms for different strengths?? = 268 ³ spins. By numerically differentiating the bond energywith respect to h, a specific-heat-like quantity is obtained whosemaximum is found to converge to a constant in the thermodynamic limit. Compared to aprevious study following the same approach, we have studied here much larger system sizeswith an increased statistical accuracy. We discuss the relevance of our results under theprism of a modified Rushbrooke inequality for the case of a saturating specific heat.Finally, as a byproduct of our analysis, we provide high-accuracy estimates of thecritical field h_c =2.279(7) and the critical exponent of the correlation exponentν =1.37(1), in excellent agreement to the most recent computations in theliterature.     

On the theory of the condensed states of heteropolymers

The collapse (globulization) of an ideal heteropolymer chain under the action of an external attractive field is considered. The problem of the collapse of different types of primary structures, including mobile, periodic, large-block, and statistical structures, is formulated. It is shown that for a random heteropolymer, the mathematical image of the globular state is the chain-length independence of the probability distribution of a random thermal distribution function of the end monomer coordinates. The free energy per monomer of a chain in a globular state and local densities of monomers of all types are shown to be a self-averaging quantities. An exactly solvable model is proposed for a globule formed by a statistical heteropolymer chain. In this model, different types of monomers are attracted to different centers by linear elastic forces with identical elastic constants. The modulus of elasticity is obtained for a heteropolymer globule with respect to the attraction of different types of monomers in different directions. It is shown that this modulus is higher for a short-periodic polymer than for a statistical one.     

The reduction of the sorting bias in the eigenvalues of the diffusion tensor.

One of the most intrinsic quantities when measuring the diffusion properties of a system is the set of principal diffusivities, which represents diffusion along the fibre axes. System noise is a well-known cause of systematic sorting bias when closely spaced diffusivities are ordered according to their magnitude and leads to their inaccurate estimation. This paper describes a new method for the ordering of the principal diffusivities in which local fibre directional coherence was used as a basis for sorting. The method was applied and tested in computer simulations and experimental data acquired in an isotropic water phantom and healthy human brain. Our results demonstrate that this method leads to significant reduction in the sorting bias in comparison to other techniques and thus a more accurate estimation of the eigenvalues. The method is advantageous over other proposed alternatives to the conventional magnitude sorting method because it is not reliant on a large region-of-interest averaging scheme.     

Influence of the polarisation of the medium on the radiation of channeled particles

The theory of the electromagnetic radiation from channeled particles is developed with inclusion of a virtual photon interaction with the crystal. Simple estimates are made for the spectral and angular distribution of the radiation. It is shown that the polarisation of the medium may lead to a drastic shrinking of the frequency range allowed for the radiation. The possibility of an increase of the transverse energy of a particle caused by radiation is predicted.     

Morphological modification of the surface of polymers by the replication of the structure of anodic aluminum oxide

Anodic aluminum oxide films have been used as stamps to modify polymer materials in order to create superhydrophobic surfaces. Using polyethylene terephthalate, it has been shown that a high replication degree leads to a strong increase in the water wetting contact angle (up to 174°). However, the inverse situation is observed for the case of low replication degrees: hydrophilization of the surface occurs, which can be explained by a change of the Cassie-Baxter wetting mechanism to the Wenzel mechanism.     

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.