Two-dimensional topological gravity and intersection theory on the moduli space of holomorphic bundles

We define a two-dimensional topological Yang-Mills theory for an arbitrary compact simple Lie group. This theory is defined in terms of intersection theory on the moduli space of flat connections on a two-dimensional surface and corresponds physically to a two-dimensional reduction and truncation of four-dimensional topological Yang-Mills theory. Two-dimensional topological Yang-Mills theory defines a topological matter system and may be naturally coupled to two-dimensional topological gravity. This topological Yang-Mills theory is also closely related to Chern-Simons gauge theory in 2 + 1 dimensions. We also discuss a relation between SL (2, ) Chern-Simons theory and two-dimensional topological gravity.     

Nonlinear classical theory of electromagnetism

A topological theory of electric charge is given. Einstein's criteria for the completion of classical electromagnetic theory are summarized and their relation to quantum theory and the principle of complementarity is indicated. The inhibiting effect that this principle has had on the development of physical thought is discussed. Developments in the theory of functions on nonlinear spaces provide the conceptual framework required for the completion of electromagnetism. The theory is based on an underlying field which is a continuous mapping of space-time into points on the two-sphere.     

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.     

Quantum free Yang-Mills on the plane

We construct a free-probability quantum Yang-Mills theory on the two dimensional plane, determine the Wilson loop expectation values, and show that this theory is the N=∞ limit of U(N) quantum Yang-Mills theory on the plane. Our model provides an example of a stochastic geometry, motivated by quantum field theory, based on free probability theory.     

Scalar-tensor theories of gravitation: Foundations and prospects

A generalization of Einstein's theory is discussed in which the gravitation is described by a tensor and a scalar field. The theory is more consistent with Mach's principle and less reliant on absolute properties of space. The modification involves a violation of the “strong principle of equivalence” on which Einstein's theory is based. In the original version of this new theory, the “constant” of gravitationG is varying and particle masses are fixed. Later on another version of the theory was given in whichG is truly a constant and the particle masses vary. The two versions are related by a conformal transformation. The physical and mathematical foundations of this theory have been discussed and the field equations have been derived. The astrophysical and cosmological consequences of the theory have been elaborately reviewed.     

Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.     

Extended thermodynamics of real gases with dynamic pressure: An extension of Meixnerʼs theory

Basing on the recent theory of extended thermodynamics of dense gases, we study a thermodynamic theory of gases with the energy transfer from molecular translational mode to internal modes as an extension of Meixner?s theory. We focus our attention on the simplest case with only one dissipative process due to the dynamic pressure. The dispersion relation for sound derived from the present theory is compared with that from Meixner?s theory. Kinetic theoretical basis of the present approach is also discussed.     

MULTIMODE THEORY OF WHISPERING-GALLERY-MODE MICROSPHERE LASER

A multimode theory of whispering-gallery-mode microsphere laser is developed based on the linear and nonlinear semiclassical theory of the microsphere laser. The average photon-number of each lasing mode and the pumping level requirement for multimode coexistence are derived. The comparison between the theory and experimental results shows that the theory can be used to treat the practical problems on microsphere laser.     

Covariant open string field theory on multiple Dp-branes

We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind(BFSS) matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya(IKKT) matrix model.The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in(p+1)-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.     

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.     

Electron transport in rectangular quantum wells

Experimental results on low-field and high-field electron transport in rectangular quantum wells are reviewed. The related theory is presented and the experimental results are examined in the light of the theory. It is concluded that although some experimental results are available and the theory of transport has been developed, numerical agreement between theory and experiments has not yet been reached. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.     

微小颗粒的光散射数值模拟

简单介绍了以经典Mie理论为基础的光散射测量技术在颗粒直径和颗粒浓度测量中广泛的应用。分别以Mie理论和离散偶极子近似理论(DDA)为基础, 用数值计算方法分析了球型颗粒的光散射特性，给出了微小颗粒对平行入射光散射的强度函数和散射偏振度的数值计算方法。得到了强度函数和偏振度随相关物理参量变化的三维图，为微小颗粒散射研究提供了一种三维视图。计算结果表明：当尺度参量x＜4时，2种方法所得结果差异不大；随尺度参量增大，2种方法所得结果出现较大差异。与经典Mie理论相比，由于离散偶极子近似理论可以解决各种形状的颗粒散射问题，其应用前景更广泛。     

Changing topology and nontrivial homotopy

A method is proposed for extending the path integral to a sum over paths which change topology. This is used to show that topological contributions to a field theory path integral arising from nontrivial homotopy on the background space are completely determined in the free theory. The method is applied to extend (“third quantize”) field theory to backgrounds which change topology (e.g. string theory) and to show that topological contributions from nontrivial homotopy of field histories in the target space are completely determined by the field theory on a fixed background.     

Fractional Dynamical Systems: Recent Trends in Theory and Applications

In this EPJ Special Topics issue selected contributions on some recent developments in the theory and applications of fractional dynamical systems are presented. Results on topics involving fundamental theory, qualitative theory, iterative methods and numerous applications of fractional-order equations are reported.     

Nanophotonic light-trapping theory for solar cells

Conventional light-trapping theory, based on a ray-optics approach, was developed for standard thick photovoltaic cells. The classical theory established an upper limit for possible absorption enhancement in this context and provided a design strategy for reaching this limit. This theory has become the foundation for light management in bulk silicon PV cells, and has had enormous influence on the optical design of solar cells in general. This theory, however, is not applicable in the nanophotonic regime. Here we develop a statistical temporal coupled-mode theory of light trapping based on a rigorous electromagnetic approach. Our theory reveals that the standard limit can be substantially surpassed when optical modes in the active layer are confined to deep-subwavelength scale, opening new avenues for highly efficient next-generation solar cells.     

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.     

Fluctuating hydrodynamics for a rarefied gas based on extended thermodynamics

We develop a theory of fluctuating hydrodynamics based on extended thermodynamics through studying the 13-variable theory for a monatomic rarefied gas as a representative case. After analyzing the relationship between the present theory and the Landau-Lifshitz theory, we discuss the hierarchy structure of the hydrodynamic fluctuations.     

Unification of the quantum and classical theories of methyl NMR.

The existing low and high temperature theories of methyl NMR are not linked because two conditions imposed on state functions in the low temperature theory are not compatible with the classical rotations on which the high temperature theory is based. The conditions do not occur in a geometrical theory of quantum phenomena in which particles and waves have separate roles. When applied to methyl dynamics, this theory covers the whole temperature range.     

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.