A singular conformal spacetime

The infinite cosmological “constant” limit of the de Sitter solutions to Einstein’s equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which constitutes a new example of maximally-symmetric spacetime. Grounded on its geometric and thermodynamic properties, some speculations are made in connection with the primordial universe.     

Observable geometric phase induced by a cyclically evolving dissipative process

In [1], a new way to generate an observable geometric phase on a quantum system by means of a completely incoherent phenomenon has been proposed. The basic idea is to force the ground state of the system to evolve cyclically by “adiabatically” manipulating the environment with which it interacts. The specific scheme analyzed in [1], consisting of a multilevel atom interacting with a broadband squeezed vacuum bosonic bath whose squeezing parameters are smoothly changed in time along a closed loop, is here solved in a more direct way. This new solution emphasizes how the geometric phase at the ground state of the system is indeed due to a purely incoherent dynamics.     

On drift,diffusion and geometry

We present some reflections on the links between drift, diffusion and geometry. For this purpose, we examine different sources of “diffusion models”, in physics and in mathematics. We observe that diffusion processes may arise from original models either deterministic, or random but where dynamics and noise are clearly delineated. In the end, we get a diffusion process where noise and dynamics (“drift”) are generally intimately entangled in a second-order partial differential operator. We focus on the following questions. Are there implicit geometric structures to properly define a diffusion? How are drift/dynamics and diffusion mixed? Are there geometric structures needed to separate drift and diffusion? We stress the importance of recurrent differential geometric structures – connections and Riemannian metrics – needed to properly define a “diffusion term” and also to separate drift from diffusion.     

A general dynamic synthesis for structures with discrete substructures

This paper presents a substructure synthesis method for the dynamic simulation of complex structures, where the structures consist of an assemblage of discrete substructures. An analogy between distributed and discrete structures is extensively invoked. To stimulate the motion of discrete substructures, the concept of “admissible vectors” is introduced, where admissible vectors represent the discrete counterpart of admissible functions for distributed substructures. The individual substructures are forced to act as a whole structure by imposing certain geometric compatibility on internal boundaries shared by any two substructures. A numerical example illustrating the method is presented.     

The physics of amorphous and nanocrystalline hard magnetic materials

The magnetic properties of amorphous and nanocrystalline hard magnetic materials are summarized. The reduction of the “effective” anisotropy field due to exchange coupling in nanocrystalline materials is demonstrated. This leads experimentally as well as theoretically to a remanence enhancement and to a reduced coercivity. Also the domain structure shows the effect of exchange coupling. Nd–Fe–Al is taken as an example of a new “amorphous” hard magnetic material. For magnetostrictive materials the possibility of reducing the anisotropy in nanocrystalline samples without loosening the high magnetostriction is discussed.     

Magneto-dimensional resonance. Pseudospin phase and hidden quantum number

The Schrödinger operator for a spinless charge inside a layer with parabolic confinement profile and homogeneous magnetic field is considered. The Lorentz (cyclotron) and the confinement frequencies are assumed to be equal to each other. After inclination of the layer normal from the magnetic field direction there appears a pseudospin su(2)-field removing the resonance degeneracy of Landau levels. Under deviations of the layer surface from the plane shape, a longitudinal geometric current is created. In circulations around surface warping, there is a nontrivial quantum phase transition generated by an element of the π₁-homotopy group and a hidden degree of freedom (spectral degeneracy) associated with a “charge” of geometric poles on the layer. The quantization rule contains an additional parity index related to the algebraic number of geometric poles and the Landau level number. The resonance pseudospin phase-shift represents an example of general Aharonov–Bohm type topologic phenomena in quantum (semiclassical or adiabatic) systems with delta-function singularities in symplectic structure.     

The “paradox” of a brake pad

By the example of a brake pad, a typical error is illustrated, i.e., the fact that the initial conditions should be reconsidered upon finding that there is no solution of the static problem in a certain region of parameters (incorrect in the sense of Hadamard). For example, it turns out that the conditions of disk rotation in the positive direction cannot be implemented in the domain of parameters leading to a “paradox.” In this region, the “brake-pad” mechanism is transformed into the “wedge stopper” mechanism.     

Those Wonderful Pioneer Years of SSRL: A Personal Reflection

It is a rare moment in the history of science when a new capability is born that transforms our ability to “see” what is happening in the world in which we live. The use of the light emitted from accelerating electrons as they are bent by magnetic fields that was pioneered at SSRL in the 1970s is not just another example of this, but arguably is the most important development in the history of science in enabling us to “see” the world of electrons and atoms. There is, in addition, a special feature of the new capability enabled by synchrotron radiation: it is likely to remain, in the future, the best way to see the microscopic world forever. This is because the light used to “see” does not only have all the intensity one needs, but also because all its properties can be adjusted so as to provide the ideal illumination for the particular thing one wants to “see.” Thus, literally what was born at SSRL, which has since then been and will be continually improved, will forever provide our species the ability to “see” and understand the microscopic world in which we live.     

Salt fingers in double-diffusive systems

“Salt fingering”, the phenomenon of the double-diffusive convection has been studied experimentally. We prepared a system with vertical density variation, which contains salt and sugar solutions, separated one from the other. The “salt fingers” appear at the interface between these layers of salt and sugar solutions. The “salt fingers” have been observed by means of shadowgraph technique.With the aid of a computer and the video-capture technique, it was possible for the first time to conduct a detailed investigation of the phenomenon. The geometric characteristics of the “salt fingers” such as form, length and width have been investigated.The way in which these quantities depend on the salinity and sugar concentrations, as well as the thickness of the salt and sugar layers has been verified experimentally. We also verified the predicted form of dependence of the average “salt fingers” width on its vertical length.     

Solution of the scalar wave equation over very long distances using nonlinear solitary waves: Relation to finite difference methods

The linear wave equation represents the basis of many linear electromagnetic and acoustic propagation problems. Features that a computational model must have, to capture large scale realistic effects (for over the horizon or “OTH” radar communication, for example), include propagation of short waves with scattering and partial absorption by complex topography. For these reasons, it is not feasible to use Green’s Function or any simple integral method, which neglects these intermediate effects and requires a known propagation function between source and observer. In this paper, we describe a new method for propagating such short waves over long distances, including intersecting scattered waves. The new method appears to be much simpler than conventional high frequency schemes: Lagrangian “particle” based approaches, such as “ray tracing” become very complex in 3-D, especially for waves that may be expanding, or even intersecting. The other high frequency scheme in common use, the Eikonal, also has difficulty with intersecting waves.Our approach, based on nonlinear solitary waves concentrated about centroid surfaces of physical wave features, is related to that of Whitham [1], which involves solving wave fronts propagating on characteristics. Then, the evolving electromagnetic (or acoustic) field can be approximated as a collection of propagating co-dimension one surfaces (for example, 2-D surfaces in three dimensions). This approach involves solving propagation equations discretely on an Eulerian grid to approximate the linear wave equation. However, to propagate short waves over long distances, conventional Eulerian numerical methods, which attempt to resolve the structure of each wave, require far too many grid cells and are not feasible on current or foreseeable computers. Instead, we employ an “extended” wave equation that captures the important features of the propagating waves. This method is first formulated at the partial differential equation (PDE) level, as a wave equation with an added “confining” term that involves both a positive and a negative dissipation. Once we have the stable PDE, the discrete formulation is simply a multidimensional PDE with (stable) perturbations caused by the discretization. The resulting discrete solution can then be low order and very simple and yet remain stable over arbitrarily long times. When discretized and solved on an Eulerian grid, this new method allows far coarser grids than required by conventional resolution considerations, while still accounting for the effects of varying atmospheric and topographic features. An important point is that the new method is in the same form as conventional discrete wave equation methods. However, the conventional solution eventually decays, and only the “intermediate asymptotic” solution can be used. Simply by adding an extra term, we show that a nontrivial true asymptotic solution can be obtained. A similar solitary wave based approach has been used successfully in a different problem (involving “Vorticity Confinement”), for a number of years.     

An alternative to quantum theory

In a recent paper we have shown that continuous sets of resonances (as expressed by the nonvanishing of the kinetic collision operator) result in divergences in the traditional unitary transformation theory in addition to the usual ultraviolet divergences. Therefore, relaxation processes and lifetimes cannot be eliminated by unitary transformations diagonalizing the Hamiltonian. For this reason, we introduce a more general transformation theory based on nonfactorizable superoperators which “block diagonalize” the Hamiltonian superoperator and eliminate the divergence of the unitary transformation. This leads to a new concept of “observables” which are represented in general by operators which are both noncommuting and nondistributive. For example, to a single energy level we now associate a set of numbers corresponding to a probability distribution whose width is determined by the lifetime of the state. This new approach incorporates dissipation into the frame of quantum mechanics. It leads directly to a number of predictions such as the existence of a new anomalous Lamb shift dependent on lifetime as well as the appearance of a broken “time symmetry” in the structure of the energy spectrum. As this symmetry breaking depends on the arrow of time (thermodynamic equilibrium is approached in our future and not in our past) which is a property of our universe as a whole, we may call this new effect the “cosmological” Lamb shift. Of course subsequent experiments will have to explore the existence of this effect. Other consequences of this approach are briefly mentioned and will be developed in subsequent papers.     

The elemental composition of Stradivari's musical instruments: new results through non‐invasive EDXRF analysis

During recent decades, many researchers have tried to understand the main influences on the extraordinary sound and beauty of the masterpieces made by the ancient violin makers. This is still a challenge for many others today. Mainly because of a lack of written historical documents, the rediscovery of some of the ancient violin‐making processes was made possible thanks to scientific analyses performed on their materials by means of diagnostic techniques. However, understanding which substances were adopted is a very hard task, because the analyses are influenced by many factors: for example, alterations, wear, retouches, and the heterogeneity of materials. This paper presents some new EDXRF results collected on eight‐stringed musical instruments made by Antonio Stradivari between 1669 and 1734 (“Clisbee” 1669, “Hellier” 1679, “Ford‐Rougemont” 1703, “Joachim‐Ma” 1714, “Russian Federation” viola 1715, “Cremonese” 1715, “Vesuvius” 1727, and “Scotland” 1734) and now preserved at the Museo del Violino in Cremona. A brief comparison with a modern violin made by Simone Ferdinando Sacconi (“Hellier copy” 1941), one of the most eminent violin makers of the 20th century and one of the greatest experts on Stradivari's work, is also provided. This represents the first comparative analysis of a wide number of ancient musical instruments made by the same violin maker over an extended period. A non‐destructive and non‐invasive approach was followed to (a) understand the elemental composition differences between the best conserved and most worn‐out surfaces; (b) check if there are elemental similarities among the finishing materials of violins made in different years by the same violin maker; (c) give new suggestions about the materials used. To distinguish the best conserved areas from the worn‐out ones, a preliminary investigation by UV‐induced fluorescence photography was performed. In addition, stereomicroscopic observations and Fourier transform infrared spectroscopy (FTIR) analyses were performed on selected areas to validate the hypotheses. The results, in some cases comparable with previous research on Stradivari instruments, have increased the pool of information about materials and treatments adopted in the Stradivari workshop.     

二维金属光子晶体的带结构研究

采用一种新的平面波展开法研究金属光子晶体的带结构，即在传统平面波展开法的基础上，将“原问题”拓展，引入一个“新问题”，通过求解“新问题”得到“原问题”的带结构，并论证了它们之间的关系.为了准确求解“新问题”，引入辅助函数，将其色散关系等价为一个积分微分本征方程，求解这个本征方程得到“新问题”的带结构，从而由此导出“原问题”的带结构.最后，以正方晶格二维金属光子晶体为例，进行数值计算，得到了满意的结果. 关键词： 金属光子晶体 平面波展开法 带结构 正方晶格     

Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures

Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell’s equations is made to obey “inclined” boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of “entanglement” of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lüneburg lens.     

Revisiting the Darmois and Lichnerowicz junction conditions

What have become known as the “Darmois” and “Lichnerowicz” junction conditions are often stated to be equivalent, “essentially” equivalent, in a “sense” equivalent, and so on. One even sees not infrequent reference to the “Darmois–Lichnerowicz” conditions. Whereas the equivalence of these conditions is manifest in Gaussian-normal coordinates, a fact that has been known for close to a century, this equivalence does not extend to a loose definition of “admissible” coordinates (coordinates in which the metric and its first order derivatives are continuous). We show this here by way of a simple, but physically relevant, example. In general, a loose definition of the “Lichnerowicz” conditions gives additional restrictions, some of which simply amount to a convenient choice of gauge, and some of which amount to real physical restrictions, away from strict “admissible” coordinates. The situation was totally confused by a very influential, and now frequently misquoted, paper by Bonnor and Vickers, that erroneously claimed a proof of the equivalence of the “Darmois” and “Lichnerowicz” conditions within this loose definition of “admissible” coordinates. A correct proof, based on a strict definition of “admissible” coordinates, was given years previous by Israel. It is that proof, generally unrecognized, that we must refer to. Attention here is given to a clarification of the subject, and to the history of the subject, which, it turns out, is rather fascinating in itself.     

A transport-phase-transition as a solution of a simplified extended Peierls-Boltzmann equation

We investigate a simple example of a “transport-phase-transition” in a phonon system (linear chain) including a localized mode. For increasing (decreasing) energy flux there is a critical value Φ_cu(Φ_cl) for which the local excitation “jumps” from the “thermodynamic” to a nonthermodynamic branch (or vice versa). Noteworthy is the “hysteresis” and the fact that only an additional relaxation path creates stability.     

苹果轻微机械损伤高光谱图像无损检测

无损检测是高光谱遥感应用研究热点之一。苹果在采摘、运输过程中易发生轻微机械损伤而影响其品质。使用高光谱成像系统分别采集54个轻微损伤的“黄香蕉”与“烟台富士”苹果可见-近红外波段(400~1 000 nm)的图像,提取苹果损伤区域的均值波谱曲线,对其进行最小噪声分离变换和基于几何顶点端元原理提取端元波谱,计算损伤区域波谱和端元波谱的光谱角,构建了端元提取光谱角苹果轻微机械损伤检测模型。通过设定光谱角阈值分别检测“黄香蕉”与“烟台富士”苹果轻微机械损伤,并与MNF变换、PCA方法检测精度进行对比分析,结果表明EESA模型检测苹果轻微机械损伤的精度最高,检测正确率分别达到94.44%和90.07%。