Pushing the hyperpolarizability to the limit

We use numerical optimization to find a one-dimensional potential energy function that yields the largest hyperpolarizability, which we find is within 30% of the fundamental limit. Our results reveal insights into the character of the potential energy functions and wave functions that lead to the largest hyperpolarizability. We suggest that donor-acceptor molecules with a conjugated bridge with many sites of reduced conjugation to impart conjugation modulation may be the best paradigm for making materials with huge hyperpolarizabilities that approach the fundamental limit.     

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.     

关于"太阳在银河系中所受引力与到银心距离r的关系"的讨论

讨论了银道面内的引力场强分布和太阳在银河系中所受引力与到银心距离r的关系，指出引力场强g并不是与r的平方成反比，这是由于银河系的大小和形状不能忽略造成的．强调了万有引力定律的适用条件．     

On the connection between the solutions to the Dirac and Weyl equations and the corresponding electromagnetic four-potentials

In this work we study in detail the connection between the solutions to the Dirac and Weyl equations and the associated electromagnetic four-potentials.First,it is proven that all solutions to the Weyl equation are degenerate,in the sense that they correspond to an infinite number of electromagnetic four-potentials.As far as the solutions to the Dirac equation are concerned,it is shown that they can be classified into two classes.The elements of the first class correspond to one and only one four-potential,and are called non-degenerate Dirac solutions.On the other hand,the elements of the second class correspond to an infinite number of four-potentials,and are called degenerate Dirac solutions.Further,it is proven that at least two of these fourpotentials are gauge-inequivalent,corresponding to different electromagnetic fields.In order to illustrate this particularly important result we have studied the degenerate solutions to the forcefree Dirac equation and shown that they correspond to massless particles.We have also provided explicit examples regarding solutions to the force-free Weyl equation and the Weyl equation for a constant magnetic field.In all cases we have calculated the infinite number of different electromagnetic fields corresponding to these solutions.Finally,we have discussed potential applications of our results in cosmology,materials science and nanoelectronics.     

On the covariantization of the chiral constraints

We show that a complete covariantization of the chiral constraint in the Floreanini-Jackiw necessitates an infinite number of auxiliary Wess-Zumino fields other-wise the covariantization is only partial and unable to remove the nonlocality in the chiral boson operator. We comment on recent works that claim to obtain covariantization through the use of Batalin-Fradkin-Tyutin method, that uses just one Wess-Zumino field.     

On the verification of the applicability of the orthotropic plate wave theory to paper

In the literature one basic work can be found that describes an attempt to verify the applicability of the orthotropic plate wave theory to paper. In the present study we have repeated the key experiment and also modified the original experimental set-up to be able to make new complementary measurements. The performed verification attempt is based on a key experiment in which an ultrasonic resonance method is used. When it is applied to paper, a second resonance can be observed in addition to the one that originates from the asymmetric A0 mode. The result of the verification experiment is conclusive only if the source of this second resonance is the symmetric S0 mode. Our results show that the second resonance is not generated by the S0 mode. Instead, they indicate that the source is a longitudinal wave propagating in the thickness direction of the paper. We therefore conclude that the applicability of the orthotropic plate wave theory to paper cannot be verified by performing the key experiment that is described in the literature.     

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.     

Effect of the electric conductivity on the drift velocity of the cholesteric fingers of the second type in confined geometry

We show that the drift velocity of the cholesteric fingers of the second species in ac electric field strongly depends on the conductivity of the liquid crystal chosen and exponentially vanishes above a cutoff frequency we found to be equal (within a numerical factor close to 1) to the charge relaxation frequency of the sample. We further show that the drift velocity is proportional to the applied electric field, provided that the confinement ratio is kept constant.     

On the standard form of the Bloch equation

The requirement is often made in non-equilibrium statistical mechanics that a transport equation should be derived as that which governs the subdynamics relative to a (small) part of a (large) conservative dynamical system close to equilibrium. We show that such a requirement on the Markovian relaxation of a 1/2-spin imposes that this process be described by a Bloch equation of a very specific form, which we call standard. We show that this reduced dynamics is quasi-free if, and only if, the relaxation time is maximally anisotropic.Research supported in part by NSF grant MCS 76-07286     

Life at the end of the universe?

Tipler has claimed in a recent scientific paper [1] that life could exist until the very end of a universe that recollapses to a final fireball in the future—including the Planck era when quantum gravity dominates. His article is one of a number that have excited general interest because of some strong claims made on the basis of this type of argument about life in the future (indeed it has even been claimed [2,3] that this type of mathematical-physical argument can prove that Resurrection of the Dead will take place!). We point out that the underlying argument of Tipler's paper runs into problems on two quite different grounds. Firstly, it assumes a flat space information theory result and makes other technical assumptions about information processing, which invalidate the immediate technical argument. However at least as important is the fact that the argument is unsustainable because physical mechanisms required to make coherent information processing possible would not be able to operate under the extreme physical conditions that would occur towards the end of the universe.Editor's note: This paper, although related to cosmology, does not fall within the scope of material generally published in theG.R.G. Journal. It is a direct rebuttal of an article that appeared inPhysics Letters B. The editors of that journal felt that their journal was an inappropriate place for the rebuttal. A second journal, for reasons which remain unclear, after having the article in their possession for many months, still had not decided whether to publish or not, so it was withdrawn. The editorial board of theG.R.G. Journal felt that a scientific answer to the original article should appear, and so have offered the authors space in this journal.     

Adam and the Ants: On the Influence of the Optimization Algorithm on the Detectability of DNN Watermarks

As training Deep Neural Networks (DNNs) becomes more expensive, the interest in protecting the ownership of the models with watermarking techniques increases. Uchida et al. proposed a digital watermarking algorithm that embeds the secret message into the model coefficients. However, despite its appeal, in this paper, we show that its efficacy can be compromised by the optimization algorithm being used. In particular, we found through a theoretical analysis that, as opposed to Stochastic Gradient Descent (SGD), the update direction given by Adam optimization strongly depends on the sign of a combination of columns of the projection matrix used for watermarking. Consequently, as observed in the empirical results, this makes the coefficients move in unison giving rise to heavily spiked weight distributions that can be easily detected by adversaries. As a way to solve this problem, we propose a new method called Block-Orthonormal Projections (BOP) that allows one to combine watermarking with Adam optimization with a minor impact on the detectability of the watermark and an increased robustness.     

On the covariance of the Fokker-Planck equation

We study the covariance of the Fokker-Planck equation under general gross variables transformations by means of Riemann differential geometry using an affine connection Γ^?_μν unsymmetric in their lower indices and without assuming that the covariant derivative of the diffusion tensor D^μν_;? be zero. We come to the conclusion that to achieve our aim we only need the value of the contraction Γ^?_?ν, all other components of the affine connection remaining completely arbitrary. We argue, therefore, that the most economic way of presenting the covariance of the Fokker-Planck equation is by means of exterior differential calculus. As an application we study physical systems under detailed balance showing that for them the irreversible part of the contravariant drift vector, that is then uniquely determined, is related only to a symmetric tensor while its reversible component is exclusively related to an antisymmetric tensor. A criticism of a compact Fokker-Planck equation is also included.     

Correcting the concept of denseness for the bootstrap

One way of stating the bootstrap theory is to say that hadrons are ‘dense’. In order for this to have a truly physical meaning, and in order for the abstract idea of infinite cardinality to be rigorously self-consistent, it is necessary to redefine the concept of denseness to mean that size is increasing as velocity.     

Representation of the spin in the Dirac equation for the electron

The conventional interpretation of the spin matrices contained in the Dirac equation for the electron is considered to be mostly unintelligible in the operational sense. It is shown that it appears that the interpretation is often illogical. The necessity of a more comprehensible interpretation of the concerned equation is implied.     

On the Energy-loss in the CERENKOV Radiation

The object of this paper is to find the electromagnetic field and the rate of increase of the field energy due to a pair of charged particles soon after their creation. It is shown that in case of the CERENKOV radiation, there is a constant rate of increase of the field energy. The power spectrum is similar to that obtained in the usual formulation, where the particles are assumed to be moving with uniform velocity since infinite past.     

On the equivalence of the Fröhlich and the Bloch approaches to the electron-phonon coupling

It is shown that the Fröhlich approach for calculating electron-phonon coupling constants based on wave functions moving with the vibrating atoms can be set on a rigorous basis. This approach and the Bloch approach are shown to lead to the same physical results provided that one stays within the adiabatic approximation and considers both first and second order vertices (in the harmonic approximation). Advantages of the Fröhlich approach in past and in possible future calculations are discussed.     

Some insight into the acoustics of the didjeridu

The Australian didjeridu is a unique and interesting instrument. Despite the fact that the bore shape is almost random in nature and varies considerably across different instruments, the didjeridu timbre is readily recognizable. This is also true despite the fact that the player can manipulate the timbre more than in most wind instruments, by changing the shape of his vocal tract. In this study we examine the didjeridu spectrum in detail, in order to determine the characteristics that are similar across different instruments, those that are constant for a given instrument, and those that are readily influenced by the player. To this end we recorded and analyzed the sounds of eight instruments of different quality, all of them played across a range of timbres. Examining the resultant spectra, along with the resonance frequencies of these instruments, leads to a number of interesting conclusions. One of these is that the random nature of the instrument bore is actually conducive to creating its typical timbre. We also give a preliminary explanation of the differences between good and poor instruments.     

On the predictability of the positions of the convergence zones in the ocean

The disagreement between the experimental and calculated positions of the first convergence zone are known from many publications. The most probable cause for such a disagreement, namely, the incorrect specification of the input data for the calculations, is considered. The lack of simultaneity between the hydrological surveys of the region and the acoustic experiments is emphasized. The experimental data obtained by the author in five ocean regions are presented. These data characterize the diurnal variability of the distance from the source to the nearest boundary of the convergence zone. The relations proposed by different researchers for calculating the sound speed from the temperature, salinity, and hydrostatic pressure are analyzed. It is shown that these relations lead to a substantial difference in the estimated depth dependence of the hydrostatic gradient of the sound speed. The position of the first convergence zone is calculated for the propagation conditions determined by vertical temperature and salinity profiles with the subsequent recalculation of these profiles into sound speed profiles by using eight different formulas known from the literature. It is shown that different formulas lead to different values of the distance to the first zone; this difference is substantially greater than that between the calculations and experiment. The necessity of improving the recalculation relations in view of the experimental data on sound propagation in natural oceanic waveguides, including the data on the actual positions of the convergence zones, is emphasized.