The locality problem in quantum measurements

The locality problem of quantum measurements is considered in the framework of the algebraic approach. It is shown that contrary to the currently widespread opinion one can reconcile the mathematical formalism of the quantum theory with the assumption of the existence of a local physical reality determining the results of local measurements. The key quantum experiments: double-slit experiment on electron scattering, Wheeler’s delayed-choice experiment, the Einstein-Podolsky-Rosen paradox, and quantum teleportation are discussed from the locality-problem point of view. A clear physical interpretation for these experiments, which does not contradict the classical ideas, is given.     

Quantitative wave–particle duality and sensitivity of phase measurements

We approach the quantification theory of the wave–particle duality restricting ourselves to a qubit entangled with its environment. We use the notion of the conditional expectation value and conditional variance to provide an alternative derivation of the well-known “strong” inequality for the which-way knowledge and quantum-erasure visibility.     

A thermal flux-diffusing model for complex networks and its applications in community structure detection

We introduce a thermal flux-diffusing model for complex networks. Based on this model, we propose a physical method to detect the communities in the complex networks. The method allows us to obtain the temperature distribution of nodes in time that scales linearly with the network size. Then, the local community enclosing a given node can be easily detected for the reason that the dense connections in the local communities lead to the temperatures of nodes in the same community being close to each other. The community structure of a network can be recursively detected by randomly choosing the nodes outside the detected local communities. In the experiments, we apply our method to a set of benchmarking networks with known pre-determined community structures. The experiment results show that our method has higher accuracy and precision than most existing globe methods and is better than the other existing local methods in the selection of the initial node. Finally, several real-world networks are investigated.     

Effect of local field fluctuations on orientational ordering in random-site dipole systems

Some peculiarities of dipole ordering in systems with uniaxial or cubic anisotropy with an arbitrary degree of dilution are analyzed in terms of random local field theory. The approach takes into account the effect of thermal and spatial fluctuations of the local fields acting on each particle from its neighbors with an accuracy corresponding to that of the Bethe-Paierls pair clusters approach. We show that ferromagnetic (ferroelectric) structure for uniaxial Ising dipoles distributed on a simple cubic lattice is intrinsically unstable against the fluctuations of the local fields for any concentration of the dipoles. This result is quite different from the prediction of the mean-field theory which implies the possibility of ferromagnetic ordering as a metastable state in field-cooled experiments. The local field fluctuations do not exclude, however, antiferromagnetic ordering above a certain critical concentration. Ferromagnetic ordering is possible for other types of lattice geometries and for an amorphous-like dipole distribution above a certain critical concentration. A simple physical explanation of such behavior is given based on the specific angular dependence of the dipole-dipole interaction that results in a relatively high value of the local field second moment for simple cubic lattice.     

Implicit subgrid-scale modeling by adaptive deconvolution

A new approach for the construction of implicit subgrid-scale models for large-eddy simulation based on adaptive local deconvolution is proposed. An approximation of the unfiltered solution is obtained from a quasi-linear combination of local interpolation polynomials. The physical flux function is modeled by a suitable numerical flux function. The effective subgrid-scale model can be determined by a modified-differential equation analysis. Discretization parameters which determine the behavior of the implicit model in regions of developed turbulence can be adjusted so that a given explicit subgrid-scale model is recovered to leading order in filter width. Alternatively, improved discretization parameters can be found directly by evolutionary optimization. Computational results for stochastically forced and decaying Burgers turbulence are provided. An assessment of the computational experiments shows that results for a given explicit subgrid-scale model can be matched by computations with an implicit representation. A considerable improvement can be achieved if instead of the parameters matching an explicit model discretization parameters determined by evolutionary optimization are used.     

Ab initio electron theory for hard-magnetic rare-earth-transition-metal intermetallics

For the development of new hard-magnetic materials a better understanding of the physical mechanisms which determine the intrinsic magnetic material parameters are of invaluable importance. In this review it is demonstrated that the modern ab initio electron theory yields a considerable help in this direction and may provide data on quantities which are hard to determine reliably by experiments. As an example, theoretical results are reported for the intrinsic magnetic material parameters (local magnetic moments, local magnetic hyperfine fields, crystal-field parameters and effective exchange interactions) of the series R₂Fe₁₄B (R = rare earth).     

Magnetic field compensation for field-cycling NMR Relaxometry in the ULF band

In setting up field-cycling experiments aimed to study physical phenomena in the low-field region, magnetic field contributions from external sources (earth’s field, environment, other magnets, etc.) become important. Indeed, a compensation of these contributions has successfully been used for the application of field-cycling methods to nuclear magnetic relaxation and double resonance experiments. This feature becomes relevant in samples where local fields are stronly averaged due to motional narrowing, on the ground that relaxation experiments can therefore be extended to lower fields. Compensation of external contributions is also crucial for the study of kinky processes related to internal local fields. In this article we outline NMR field-cycling experiments aimed to detect and quantify the external net magnetic field sensed by the spin-system. Both parallel and normal components with respect to the high-field Zeeman axis can be determined separately by using different experimental protocols.     

A theoretical approach to local attenuation measurements of shear waves by MRE. Preliminary experimental results

An essential highlight of the presented method is the employment of Magnetic Resonance Elastography (MRE) for local measurements of the attenuation of elastic shear waves introduced into a biological sample. Such a measurement can be accomplished by combining the MRE method with those methods, in which collective displacement of spins is induced by external physical factors, such as variable electric field, strong magnetic field gradient or longitudinal elastic wave. A theoretical basis of the method involving external factors and results of preliminary experiments have been presented in this paper.     

Investigation of thermal and deformation properties of quartzite in a temperature range of polymorphous α-β transition by neutron diffraction and acoustic emission methods

The results of combined application of the neutron diffraction and acoustic emission methods for investigation of the physical properties of synthetic quartz and natural quartzite in a temperature range of α-β transition are given. In experiments, the quartzite sample was exposed to heating and uniaxial compression. Changes of the lattice spacings in quartzite were measured in a temperature range 540–620°C. On the basis of these measurements, the inner inner stresses are evaluated and found to exceed the applied stresses by several times. It is found that after the phase transition is finished, short bursts of acoustic emission (AE) occur which are two orders of magnitude more intense than the acoustic emissions produced by thermal cracking of the sample while the sample is heating up to the transition temperatures. An assumption is made that the anomalous behavior of the physical properties of quartz-containing rocks under relatively low pressures near the transition temperature can cause the formation of strong concentrators of local stresses comparable with the breaking point of the material, thereby initiating microcracking.     

Optical manipulation of complex molecular systems by high density green photons: experimental and theoretical evidence

The recent revolution in modern optical techniques revealed that light interaction with matter generates a force, known as optical force, which produces material properties known in physics as optical matter. The basic technique of the domain uses forces exerted by a strongly focused beam of light to trap small objects and subsequently to manipulate their local structures. The purpose of this paper is to develop an alternative approach, using irradiations with high-density-green-photons, which induce electric dipoles by polarization effects. The materials used for the experiments were long carbon chains which represent the framework of biological macromolecules. The physical techniques used to reveal the locally induced molecular arrangements were: dynamic viscosity, zeta potential, chemiluminescence, liquid chromatography; mass spectrometry, and Raman and infrared spectroscopy. The principal result of our experiments was the detection of different molecular arrangements within the mixture of alkane chains, generated by our optical manipulations. This induced “optical matter” displayed two material properties: antioxidant effects and large molecular aggregation effects. In order to bring the experimental results in relation with theory, we developed a physical model and the interacting force between polarizable bodies was computed. By numerical calculations stable structures for N = 6 and N = 8 particles were obtained.     

Pattern formation in mixtures of ultracold atoms in optical lattices

Regular pattern formation is ubiquitous in nature; it occurs in biological, physical, and materials science systems. Here we propose a set of experiments with ultracold atoms that show how to examine different types of pattern formation. In particular, we show how one can see the analog of labyrinthine patterns (so-called quantum emulsions) in mixtures of light and heavy atoms (that tend to phase separate) by tuning the trap potential and we show how complex geometrically ordered patterns emerge (when the mixtures do not phase separate), which could be employed for low-temperature thermometry. The complex physical mechanisms for the pattern formation at zero temperature are understood within a theoretical analysis called the local density approximation.     

Dynamics of a locally distorted impurity in a host crystal with displacive phase transition

We study the dynamic behaviour of a soft displacive impurity in a host crystal undergoing a displacive phase transition. The impurity-induced localized mode and the dynamic autocorrelation function of the impurity below the local freezing temperature are investigated in mean-field approximation (MFA). Furthermore, we give a physical interpretation of the MFA result of the local freezing-out, and discuss the fluctuation behaviour of various types of impurities in relation to recent experiments.     

Mechanical normal forms of knots and flat knots

We describe a series of physical experiments with knotted resilient wires and observe that ambient isotopy classes of knots with a small number of crossing have unique normal forms (corresponding to minima of the energy of the wire). We then describe local moves that the wire knots can perform (Reidemeister moves, Markov moves, the Whitney trick). Further, we consider flat knots (i.e. wire knots squeezed between parallel planes) and prove theorems about their mathematical models.     

Hölder exponents of irregular signals and local fractional derivatives

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/local Hölder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyze the pointwize behaviour of irregular signals and functions.     

Delayed-Choice Experiments and the Metaphysics of Entanglement

Delayed-choice experiments in quantum mechanics are often taken to undermine a realistic interpretation of the quantum state. More specifically, Healey has recently argued that the phenomenon of delayed-choice entanglement swapping is incompatible with the view that entanglement is a physical relation between quantum systems. This paper argues against these claims. It first reviews two paradigmatic delayed-choice experiments and analyzes their metaphysical implications. It then applies the results of this analysis to the case of entanglement swapping, showing that such experiments pose no threat to realism about entanglement.     

Physics-Informed Neural Networks for Solving Coupled Stokes–Darcy Equation

In this paper, a grid-free deep learning method based on a physics-informed neural network is proposed for solving coupled Stokes–Darcy equations with Bever–Joseph–Saffman interface conditions. This method has the advantage of avoiding grid generation and can greatly reduce the amount of computation when solving complex problems. Although original physical neural network algorithms have been used to solve many differential equations, we find that the direct use of physical neural networks to solve coupled Stokes–Darcy equations does not provide accurate solutions in some cases, such as rigid terms due to small parameters and interface discontinuity problems. In order to improve the approximation ability of a physics-informed neural network, we propose a loss-function-weighted function strategy, a parallel network structure strategy, and a local adaptive activation function strategy. In addition, the physical information neural network with an added strategy provides inspiration for solving other more complicated problems of multi-physical field coupling. Finally, the effectiveness of the proposed strategy is verified by numerical experiments.