The Mathematical Basis for Physical Laws

Laws of mechanics, quantum mechanics, electromagnetism, gravitation and relativity are derived as “related mathematical identities” based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. This probability formalism is necessary because continuous variables are not precisely observable. These demonstrations explain why these laws must have the forms previously discovered through experiment and empirical deduction. Indeed, the very existence of electric, magnetic and gravitational fields is predicted by these purely mathematical constructions. Furthermore these constructions incorporate gravitation into special relativity theory and provide corrected definitions for coordinate time and proper time. These constructions then provide new insight into the relationship between manifold geometry and gravitation and present an alternative to Einstein’s general relativity theory.     

K–K excitations on as “primary” superfields

We show that the K–K spectrum of IIB string on is described by “twisted chiral” superfields, naturally described in “harmonic superspace”, obtained by taking suitable gauge singlets polynomials of the D3-brane boundary superconformal field theory.To each p-order polynomial is associated a massive K–K short representation with states. The quadratic polynomial corresponds to the “supercurrent multiplet” describing the “massless” bulk graviton multiplet.     

Testable scenario for relativity with minimum length

I propose a general class of spacetimes whose structure is governed by observer-independent scales of both velocity (c) and length (Planck length), and I observe that these spacetimes can naturally host a modification of FitzGerald–Lorentz contraction such that lengths which in their inertial rest frame are bigger than a “minimum length” are also bigger than the minimum length in all other inertial frames. With an analysis in leading order in the minimum length, I show that this is the case in a specific illustrative example of postulates for relativity with velocity and length observer-independent scales.     

On the theory of temporal aberrations for cathode lenses

A new approach to the theory of temporal aberration for cathode lenses is given in the present paper. A definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0ε_z1ε_0max) is considered. A new method to calculate the temporal aberration coefficients of cathode lenses named “direct integral method” is also presented. The “direct integral method” gives new expressions of the temporal aberration coefficients which are expressed in integral forms. The difference between “direct integral method” and “τ-variation method” is that the “τ-variation method” needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the “direct integral method” only needs to carry out the integral calculation for all of these temporal aberration coefficients of second order.All of the formulae of the temporal aberration coefficients deduced from “direct integral method” and “τ-variation method” have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solutions and the solutions of temporal aberration coefficients of the first and second order are the same as with the analytical solutions. Although some forms of the results seem different, but they can be transformed into the same form. Thus, it can be concluded these two methods given by us are equivalent and correct, but the “direct integral method” is related to solve integral equations, which is more convenient for computation and could be suggested for use in practical design.     

Thomas Fermi limit of Bose-jellium

The thermodynamic limit of charged bosons in a background that contracts according to Thomas-Fermi scaling is considered. The theory reduces to a mean field theory with the mean field determined by a “Thomas-Bose” equation. The Bose condensation of this system shows some special features.     

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

Quantum interference rectifier

Electron transport in bent quantum wire in the presence of a magnetic field which is orthogonal to the system plane is considered. Possible constructions of “quantum interference switch” and “quantum interference rectifier” are suggested.     

Novel comprehension of “common path” principle

The idea of “common path” has been widely applied in optical instrument design for 30 years and even today. But the meaning of “common path” has not yet been explained clearly and sometimes confusion has been created. In this paper an “adaptive principle” is proposed and recommended on optical instrument system. It suggests that the designer not only arranges the measurement system to obtain measurement signal but also sets a channel to give prediction of noise or disturbance in real time or short term. Such a recommendation is based on the recent studies on nonlinear dynamics and atmospheric disturbance by means of experiments as well as theoretical analysis.     

Absolutely Continuous Spectrum for the Isotropic Maxwell Operator with Coefficients that are Periodic in Some Directions and Decay in Others

The purpose of this paper is to prove that the spectrum of an isotropic Maxwell operator with electric permittivity and magnetic permeability that are periodic along certain directions and tending to a constant super-exponentially fast in the remaining directions is purely absolutely continuous. The basic technical tools is a new “operatorial” identity relating the Maxwell operator to a vector-valued Schrödinger operator. The analysis of the spectrum of that operator is then handled as in [3,4].     

Nucleation and growth mechanism for flame synthesis of MoO2 hollow microchannels with nanometer wall thickness

The growth and morphological evolution of molybdenum-oxide microstructures formed in the high temperature environment of a counter-flow oxy-fuel flame using molybdenum probes is studied. Experiments conducted using various probe retention times show the sequence of the morphological changes. The morphological row begins with micron size objects exhibiting polygonal cubic shape, develops into elongated channels, changes to large structures with leaf-like shape, and ends in dendritic structures. Time of probe–flame interaction is found to be a governing parameter controlling the wide variety of morphological patterns; a molecular level growth mechanism is attributed to their development. This study reveals that the structures are grown in several consecutive stages: material “evaporation and transportation”, “transformation”, “nucleation”, “initial growth”, “intermediate growth”, and “final growth”. XRD analysis shows that the chemical compositions of all structures correspond to MoO₂.     

Physics versus Semantics: A Puzzling Case of the Missing Quantum Theory

A case for the project of excising of confusion and obfuscation in the contemporary quantum theory initiated and promoted by David Deutsch has been made. It has been argued that at least some theoretical entities which are conventionally labelled as “interpretations” of quantum mechanics are in fact full-blooded physical theories in their own right, and as such are falsifiable, at least in principle. The most pertinent case is the one of the so-called “Many-Worlds Interpretation” (MWI) of Everett and others. This set of idea differs from other “interpretations” since it does not accept reality of the collapse of Schrödinger’s wavefunction. A survey of several important proposals for discrimination between quantum theories with and without wavefunction collapse appearing from time to time in the literature has been made, and the possibilities discussed in the framework of a wider taxonomy.     

Deformed “commutative” Chern–Simons’ system

Noncommutative Chern–Simons’ system is non-perturbatively investigated at a full deformed level. A deformed “commutative” phase space is found by a non-canonical change between two sets of deformed variables of noncommutative space. It is explored that in the “commutative” phase space all calculations are similar to the case in commutative space. Spectra of its energy and angular momentum of the Chern–Simons’ system are obtained at the full deformed level. The noncommutative–commutative correspondence is clearly showed. Formalism for the general dynamical system is briefly presented. Some subtle points are clarified.     

Moving Observers in an Isotropic Universe

This paper considers how the motion of an observer in an isotropic universe may be determined by measurements. This provides a means to identify inertial frames, yielding a simple resolution to the twins paradox of relativity theory in such a universe. We propose that isotropy is a requirement for a frame to be inertial; this makes it possible to relate motion to the large scale structure of the universe.     

Belting and pop, nonclassical approaches to the female middle voice: Some preliminary considerations

There is a commonly perceived difference in the sound produced in the approximate range D₄-D₅ by female singers in the western opera and concert tradition, on the one hand, and certain other styles, including rock, pop, folk, and some Broadway musicals, on the other. The term “belting” is sometimes used to refer to at least one approach to such “nonclassical” singing. In this study, based on spectrographic, electroglottographic, and sub- and supraglottal pressure measurements on representative voices of the “operatic” and “nonclassical” tradition, acoustic and laryngeal differences between the two traditions are described, and an objective, specific definition of “belting” is offered.     

What the inflaton might tell us about RHIC/LHC

Topical phenomena in high-energy physics related to collision experiments of heavy nuclei (“Little Bang”) and early universe cosmology (“Big Bang”) involve far-from-equilibrium dynamics described by quantum field theory. One example concerns the role of plasma instabilities for the process of thermalization in heavy-ion collisions. The reheating of the early universe after inflation may exhibit rather similar phenomena following a tachyonic or parametric resonance instability. Certain universal aspects associated to nonthermal fixed points even quantitatively agree, and considering these phenomena from a common perspective can be fruitful.     

Three-dimensional diffuse optical imaging of hand joints: System description and phantom studies

In this paper we describe a three-dimensional (3D) continuous wave (CW) diffuse optical tomography (DOT) system and present 3D volumetric reconstruction studies using this DOT system with simple phantom models that simulate hand joints. The CCD-based DOT system consists of 64×64 source/detector fiber optic channels, which are arranged in four layers, forming a cylindrical fiber optic/tissue interface. Phantom experiments are used to evaluate system performance with respective to axial spatial resolution, optical contrast and target position for detection of osteoarthritis where cartilage is the primary target region of interest. These phantom studies suggest that we are able to quantitatively resolve a 2 mm thick “cartilage” and qualitatively resolve a 1 mm thick “cartilage” using our 3D reconstruction approach. Our results also show that optical contrast of 3:1–7:1 between the “disease cartilage” and normal cartilage can be quantitatively recovered. Finally, the target position along axial direction on image reconstruction is studied. All the images are obtained using our 3D finite-element-based reconstruction algorithm.     

Feasibility of “intermittent” active control of combustion instabilities in liquid fueled combustors using a “smart” fuel injector

This paper describes an experimental investigation of the feasibility of an “intermittent” active control approach for suppressing combustion instabilities in liquid fueled combustors. The developed controller employs a “smart” fuel injector that can modify the spray properties in response to changes in combustor operating conditions. This action weakens or breaks up the coupling between the combustion process and combustor acoustic modes oscillations, thus preventing the excitation of large amplitude instabilities. This approach differs significantly from previously proposed active control methods, both in concept and implementation, as it requires only “intermittent” modification of the combustion process by a single control action as opposed to the continuous action required by most other active control methods. The “smart” fuel injector used in this study consisted of a double-staged, air-assisted atomizer in which counter swirling, primary (inner stage) and secondary (outer stage) air streams were supplied to the injector through separate sets of tangentially oriented orifices. Control of the ratio of air mass flow rates supplied to these two stages, by use of a diverter valve, resulted in significant changes in the spray shape and its axial, tangential, and radial velocity components. This variation in spray properties of the “smart” injector was characterized for different values of the inner to outer air flow rate ratio in cold flow tests with a PDPA system. These results were then correlated with the characteristics of the “intermittently” controlled combustor. Measured quantities included the instability amplitudes, axial dependence of the mean and oscillatory heat release amplitudes, and the characteristics of the recirculation zones, which were all shown to depend on the fuel spray properties. The results of this study demonstrate the feasibility of using “smart” fuel injectors with capabilities for varying the combustion process characteristics to reduce the amplitudes of detrimental combustion instabilities in real engines to acceptable levels.     

Interband tunneling depopulation in type-II InAs/GaSb cascade laser heterostructure

An exact analytical representation has been obtained for electron eigenstates in the full isotropic 8-band Kane model and applied to calculate the depopulation rate of the lower lasing state in the active region of a type-II intersubband cascade laser. We show that interband tunneling rate takes its maximum value when the depopulated states belong to the upper of the coupled electron- and hole-like subbands in the “leaky window” of the broken-gap InAs/GaSb heterostructure.     

Beyond nanosizing: an approach to shape analysis of fluorescent nanostructures by SMI-microscopy

Using spatially modulated illumination (SMI) light microscopy it is possible to measure the sizes of fluorescent structures that have an extension far below the conventional optical resolution limit (“subresolution size”). Presently, the sizes are determined as the object extension along the optical axis of the SMI microscope. For this, however, “a priori” assumptions on the fluorochrome distribution (“shape”) within the examined fluorescent structure have to be made. Usually it is assumed that the fluorochrome follows a Gauss-distribution or a spherical distribution. In this report we overcome the necessity to make an assumption on the shape of the fluorochrome distribution. We introduce two new experimentally obtained parameters which allow the determination of a shape measure to describe the spatial distribution of the fluorescent dye. This becomes possible by independent measurements with different excitation wavelengths. As an example, we present shape parameter measurements on individual fluorescent microspheres with a nominal geometrical diameter (“size”) of 190 nm. In the case investigated, the experimental shape correlated well with a homogeneous fluorochrome distribution (“spherical shape”) but not with a variety of other “shapes”.