Sound wave motion in pipes having time-variant ambient temperature

The classical time-invariant acoustic waveguide theory is extended by allowing for temporal variations of the speed of sound. Essentially, what distinguishes the present theory from the classical waveguide theory is that, while the latter predicts stable waves for all frequencies, the present theory predicts that stable waves may occur only in certain frequency bands. Implication of the theory for engine exhaust pipes is discussed.     

The critical supersaturations predicted by nucleation theory

A general set of equations is derived for calculating the supersaturation required to obtain a given rate of nucleation. This set is general enough to encompass all the present theories, the classical theory, the Lothe-Pound theory, the Reiss-Katz-Cohen theory, a recent theory by H. Reiss, and any other theory which includes a size-dependent correction to the classical theory. Comparison of these predictions is made for various substances.     

Dynamic non-linear response of beams subjected to impact loads

A non-linear theory is presented for plane deformation of beams which allows for longitudinal stretching as well as for cross-sectional stretching and shearing. The exact strain measures for this theory are also deduced. The longitudinal and flexural motions are coupled in the theory. If the cross section is constrained from stretching, the resulting theory may be classified as a non-linear Timoshenko beam theory. The equations of the latter theory are used to study the motion of beams under impact loads.     

The refined theory of deep rectangular beams based on general solutions of elasticity

The problem of deducing one-dimensional theory from two-dimensional theory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the refined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two examples, it is shown that the new theory provides better results than Levinson’s beam theory when compared with those obtained from the linear theory of elasticity.     

On the Foundations of Superstring Theory

Superstring theory is an extension of conventional quantum field theory that allows for stringlike and branelike material objects besides pointlike particles. The basic foundations on which the theory is built are amazingly shaky, and, equally amazingly, it seems to be this lack of solid foundations to which the theory owes its strength. We emphasize that such a situation is legitimate only in the development phases of a new doctrine. Eventually, a more solidly founded structure must be sought. Although it is advertised as a “candidate theory of quantum gravity”, we claim that string theory may not be exactly that. Rather, just like quantum field theory itself, it is a general mathematical framework for a class of theories. Its major flaw could be that it still embraces a Copenhagen view on the relation between quantum mechanics and reality, while any “theory of everything”, that is, a theory for the entire cosmos, should do better than that.     

Violation of Locality Beyond Bell's Theorem for Multiparticle Perfect Correlations

We present the analogous inequalities of Bell's inequality for N-qubit system predicted respectively by realistic theory, quantum mechanics, local theory, local realistic theory, and local quantum theory on the same Bell-type joint experiment. It is shown that quantum mechanics can be interpreted by hidden-variable theories while being incompatible to any local theory. A necessary condition for the separability of N-qubit system is derived.     

Introduction to string theory and conformal field theory

A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.     

Nonlocal character of the Rastall model

The discussion of whether quantum theory is compatible with the locality idea that no causal influence can act outside the forward light cone has recently been tightly linked to the corresponding question for a much simpler model theory that enjoys all of the pertinent properties of quantum theory but is much easier to fully comprehend. It is shown here that, contrary to recent claims, the model theory is incompatible with the locality idea mentioned above. The logical structure of the argument, which is similar to the one employed for quantum theory, is discussed.     

Interpretation of the d-parameters,occurring in the Mayants-Averbukh theory of infrared intensity,in terms of the bond dipole moment concept: Equivalence with the valence-optical theory in the zeroth approximation for linear and planar molecules

From a comparison with the valence-optical theory of infrared intensity in the zeroth approximation, it is suggested that the d-parameters (elements of the effective charge tensor D_n⁰ of a bond) occurring in the Mayants-Averbukh theory can be expressed in terms of bond dipole moment components and their derivatives with respect to components of the Cartesian bond displacement vector. With this interpretation, which may be suitable for practical application, the Mayants-Averbukh theory formally appears as a combination of the “special” and the generalized valence-optical theory. In particular, it is found that for linear molecules the Mayants-Averbukh theory is equivalent to the “special” valence-optical theory in the zeroth approximation. For planar molecules the Mayants-Averbukh theory is equivalent to the generalized valence-optical theory (zeroth approximation) for in-plane modes and to the “special” valence-optical theory for out-of-plane modes.     

Comparative Study on Large and Small Signal Theory for Intensity Modulation Response of Semiconductor Lasers Including Higher-Order Dispersion Terms

In this article, the comparison of large signal theory and small signal theory has been done with dispersive propagation of optical signal with IMDD (Intensity Modulation Direct Detection) systems for semiconductor lasers with higher-order dispersion terms. The expressions for an exact large signal theory and small signal theory including higher-order dispersion terms for propagation of an optical wave with sinusoidal amplitude and frequency modulation in a dispersive fiber have been derived. It is observed that small signal theory is more sensitive compared to large signal theory in terms of intensity modulation/direct detection systems. Also, it is reported that for large signal analysis the higher-order effects of dispersion can be ignored, whereas for small signal theory, the higher-order effects can be ignored for lower modulation frequencies only. The variation in the transfer function for various values of modulation indices are greater for small signal analysis than for large signal analysis. Also, as the intensity modulation index is increased, there is a decrease in the value of transfer function. The large signal model approximates the small signal model for lower values of the intensity modulation index.     

The refined theory of transversely isotropic piezoelectric rectangular beams

The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur’e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.     

Gaseous ion mobility and diffusion in electric fields of arbitrary strength

In a previous paper we presented the first kinetic theory of gaseous ion mobility which is valid for electric fields of arbitrary strength and for arbitrary ion-neutral interaction potentials and mass ratios. In this paper we extend this theory to gaseous ion diffusion and systematize it so as to greatly decrease the effort involved in computing high approximations to the transport coefficients. Analytical results in low approximation are discussed, as are scaling rules for ion mobilities and diffusion coefficients. An extensive study of the convergence of the successive approximations of this theory is given for model systems, from which it is concluded that the theory is accurate, particularly in third and higher approximation, when applied to ion mobility and mean kinetic energy. When applied to diffusion, the theory is less successful in some circumstances, but it is still the best general theory currently available.     

A new rectangular beam theory

A new theory for beams of rectangular cross-section which includes warping of the cross-sections is presented in the present work. By satisfying the shear-free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required. It is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in Timoshenko beam theory provided that for the Timoshenko equation the shear coefficient is taken to be $\text{5}\text{6}$; this value lies within the range of values, 0·822–0·870, appearing in the literature for the beam of rectangular cross-section. Results for two typical static examples are given for both the new theory and Timoshenko beam theory. These results are compared with the solutions of the comparable problems in the linear theory of elasticity. For the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while Timoshenko beam theory underestimates the shear correction term by 20%. For the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution.     

Comparative Study on Large and Small Signal Theory for Intensity Modulation Response of Semiconductor Lasers Including Higher-Order Dispersion Terms

In this article, the comparison of large signal theory and small signal theory has been done with dispersive propagation of optical signal with IMDD (Intensity Modulation Direct Detection) systems for semiconductor lasers with higher-order dispersion terms. The expressions for an exact large signal theory and small signal theory including higher-order dispersion terms for propagation of an optical wave with sinusoidal amplitude and frequency modulation in a dispersive fiber have been derived. It is observed that small signal theory is more sensitive compared to large signal theory in terms of intensity modulation/direct detection systems. Also, it is reported that for large signal analysis the higher-order effects of dispersion can be ignored, whereas for small signal theory, the higher-order effects can be ignored for lower modulation frequencies only. The variation in the transfer function for various values of modulation indices are greater for small signal analysis than for large signal analysis. Also, as the intensity modulation index is increased, there is a decrease in the value of transfer function. The large signal model approximates the small signal model for lower values of the intensity modulation index.     

Mixed-system brain dynamics: Neural memory as a macroscopic ordered state

The paper reviews the current situation regarding a new theory of brain dynamics put forward by the authors in an earlier publication. Motivation for the theory is discussed in terms of two issues: the long-standing problem of accounting for the stability and nonlocal properties of memory, and the experimental and theoretical evidence against the classical theory of brain action. It is shown that the new theory provides an explanation and a conceptually unifying framework for phenomena of brain action that resist classical explanation. Further independent experiments provide strong additional support for the theory. The fact that this theory incorporates quantum mechanisms in an essential way is considered to be of wide scientific interest in view of the unique status of the brain in relation to the physical, biological, and mental orders in nature.     

On the relation between Brueckner theory and Jastrow theory of nuclear matter

The two- and three-hole-line contributions to the ground state energy as calculated from Brueckner theory are derived from a cluster expansion followed by variation of the trial function. The implications of that derivation both for Brueckner theory and for Jastrow theory are worked out in detail. It is argued that the Jastrow theory is able to give simpler methods to calculate the ground state energy which may be of the same accuracy as current Brueckner calculations. It is shown that the single-particle potential of Brueckner theory is intimately related to a subsidiary condition used in the variation of the trial function. The main steps which have to be taken in a derivation of the general hole-line expansion from Jastrow theory are indicated. It is shown that the hole-line expansion is not a cluster expansion in the sense of Jastrow theory, and an interpretation is given of the “self-consistent choice” of the single-particle potential advocated in Brueckner theory.     

The properties of conformal blocks,the AGT hypothesis,and knot polynomials

Various properties of correlators of the two-dimensional conformal field theory are discussed. Specifically, their relation to the partition function of the four-dimensional supersymmetric theory is analyzed. In addition to being of interest in its own right, this relation is of practical importance. For example, it is much easier to calculate the known expressions for the partition function of supersymmetric theory than to calculate directly the expressions for correlators in conformal theory. The examined representation of conformal theory correlators as a matrix model serves the same purpose. The integral form of these correlators allows one to generalize the obtained results for the Virasoro algebra to more complicated cases of the W algebra or the quantum Virasoro algebra. This provides an opportunity to examine more complex configurations in conformal field theory. The three-dimensional Chern–Simons theory is discussed in the second part of the present review. The current interest in this theory stems largely from its relation to the mathematical knot theory (a rather well-developed area of mathematics known since the 17th century). The primary objective of this theory is to develop an algorithm that allows one to distinguish different knots (closed loops in three-dimensional space). The basic way to do this is by constructing the so-called knot invariants.     

Applied validity of effortless method for design of sinusoidal surface microstructure

With the purpose of easily analyzing and designing the transmittance performance of a sinusoidal surface microstructure, the validity of effortless methods including scalar diffraction theory and effective medium theory has been evaluated quantitatively by the comparison of diffraction efficiencies predicted from scalar theory and effective indices theory, respectively, with exact results calculated with the rigorous vector method of Fourier modal method. Generally speaking, when the normalized period of surface microstructure is less than ten wavelengths of the incident light the scalar diffraction theory is believed to be inaccurate for designing and analyzing the diffraction efficiency of surface microstructure. But, in this paper, it is found that scalar diffraction theory can be used for predicting transmittance of the optical elements when the normalized period is more than three wavelengths of incident light within the error less than 5% at normal incidence. In addition, it is generally recognized that the effective medium theory is inaccurate for analyzing periodic surface microstructure when the normalized period is more than a tenth of the wavelength of incident light. However, the results in this study shows that effective medium theory is accurate as only zero-order waves are to propagate through the surface profiles, which the maximum difference between zero-order effective indices method and rigorous vector method reaches to 1%. Besides, the limitation of both simplified theories is dependent on not only the normalized period of a surface microstructure but also the normalized groove depth. Therefore, the range of applied validity of scalar theory and effective medium theory is expanded quantitatively compared to that of previous inaccuracy application for more easily designing and analyzing a sinusoidal surface microstructure.