Space-time Phase Research Articles

Energy-Space-Time Plateau-Rayleigh Instability, Quantum Phenomenon & the Fundamental Interactions

In general, fluids in motion or at rest tend to minimize their surface area due to their surface tension. It is shown that kinetic energy flow through space-time experience the same Plateau-Rayleigh instability observed in fluid dynamics. Energy, space-time act like fluids, and the space-time reaction to the energy action is the equivalent of an interface tension between energy and space-time. Energy cannot continuously flow through space-time due to an energy-space-time Plateau-Rayleigh instability, space-time compression (contraction) on kinetic energy direction of motion induces an energy wave like motion (a space-time compression wave acting as kinetic energy waveguide), the particle or energy packet must follow when moving through space-time, the reason for the observed wave - particle duality. Quantum phenomenon is simply a consequence of the space-time compression on kinetic energy direction of motion. Kinetic energy and space-time are fluids and energy quanta can reach a critical point when energy quanta can change from linear to circular motion and assume a spherically symmetrical shape (the minimum surface area possible to minimize the tension at the space-time energy interface) and so it condensates as mass energy. It is shown that energy quanta to mass transformation occurs via Plateau–Rayleigh energyspace-time instability and it is governed by an energy-space-time Young-Laplace equation. Electric field lines are described as space contraction energy shock waves induced by a dynamic space-time phase transition at maximum kinetic energy space- time interface tension which is the “charge”. Space-time always reacts to the presence of energy and that reaction is the interface tension at the energy-space-time boundary: gravitational & electric energy fields are consequences of energyspace-time interface tension (at either rest or kinetic energy boundary) also governed by an energy-space-time instability Young-Laplace equation. Gravitational constant G and the fine structure constant ∝ are respectively, the energy interface field’s interaction constants. The Strong force is a consequence of a direct contact between the nucleon's energy-space-time interface tension fields and has no interaction constant. The range and variation in the strength of the Strong force is due to Heisenberg’s uncertainty principle

Study of Nonlinear Evolution of Spacetime Fluctuations in Quantum Gravity Inflation for Deriving Primordial Spectrum

We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special conformal invariance. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs at a dynamical scale of about 1017 GeV. We show that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. The goal of this research is to derive the spectra of scalar fluctuations at the phase transition point, that is, the primordial spectra. A system of nonlinear evolution equations for the fluctuations is derived from the quantum gravity effective action. The running coupling constant is then expressed by a time-dependent average following the spirit of the mean field approximation. In this paper, we determine and examine various nonlinear terms, not treated in previous studies such as the exponential factor of the conformal mode. These contributions occur during the early stage of inflation when the amplitude is still large. Moreover, in order to verify their effects concretely, we numerically solve the evolution equation by making a simplification to extract the most contributing parts of the terms in comoving momentum space. The result indicates that they serve to maintain the initial scale invariance over a wide range beyond the comoving Planck scale. This is a challenge toward the derivation of the precise primordial spectra, and we expect in the future that it will lead to the resolution of the tensions that have arisen in cosmology.

A new approximation for bienergy and biangle of particles with extended Darboux frame in Minkowski spacetime

ABSTRACT This work is motivated by recent researches in particles and their bienergy in different types of geometric structures and applied physical spacetime phases. In this paper, we define a new approach of bienergy and biangle with Sasaki metric in Minkowski spacetime. Moreover, we use the ED-frame method for bienergy and biangle of first and second kind fields. We study the bienergy and biangle for the extended Darboux frame (ED-frame) fields of first and second kind on some hypersurfaces in Minkowski spacetime. Also, we obtain main results as a new relationship for biangle and bienergy of the particle on the hypersurface in Minkowski spacetime. We get new geometric properties of some graphics with the bienergy and biangle. Finally, we determine a new relationship for biangle and bienergy of the particle on the hypersurface in Minkowski spacetime.

Bifurcation analysis based on new macro two-velocity difference model

Based on the new macroscopic two-velocity difference model, this paper analyzes the linear stability of the new model and studies the nonlinear bifurcation theory. First, the linear stability analysis method is used to study the stability conditions of the shock wave in the model. Then, considering the long wave model in the coarse-grained scale, the reduced perturbation method is used to analyze the characteristics of the traffic flow in the metastable region, and the solitary wave solution of the Korteweg-de Vries (KdV) equation in the metastable region is derived. In addition, by using the bifurcation analysis method, the type, and stability of the equilibrium solution are discussed and the existing conditions of the saddle-node bifurcation are proven. Then, taking the saddle-node bifurcation as the starting point, we draw the density space-time diagram and phase plane diagram of the system. It is proven that the newly proposed model can describe complex traffic phenomena such as stop-and-go and sudden changes in stability, which is of great help to solve traffic congestion.

Electron mass singularities in semileptonic kaon decays

We show that recent improvements in the $O(\alpha)$ long-distance quantum electrodynamics (QED) corrections to the radiative inclusive $K_{e3}$ decay rate using the Sirlin representation are free from infrared divergences and collinear electron mass singularities in the limit $m_e\rightarrow0$, as predicted by the Kinoshita-Lee-Nauenberg theorem. We also verify that in massless QED with the simultaneous dimensional regularization of QED photon infrared divergences and electron mass singularities leads to the same result for the inclusive rate in the limit of four space-time dimensions. The equivalence of the two approaches results in part from an interesting interplay between a small chirality-breaking effect in the massless electron limit and the generalization of space-time algebra and phase space integrals to $d>4$ dimensions. Our finding supports the small theoretical uncertainty claimed for $K_{e3}$ radiative inclusive rates and reaffirms its utility in precision unitarity tests of the quark mixing matrix.

Amplification and Manipulation of Nonlinear Electromagnetic Waves and Enhanced Nonreciprocity using Transmissive Space-Time-Coding Metasurface.

A novel amplifier‐based transmissive space‐time‐coding metasurface is presented to realize strongly nonlinear controls of electromagnetic (EM) waves in both space and frequency domains, which can manipulate the propagation directions and adjust enhancements of nonlinear harmonic waves and break the Lorenz reciprocity due to the nonreciprocity of unilateral power amplifiers. By cascading the power amplifier between patches placed on two sides of the metasurface, the metasurface can transmit the spatial EM waves in the forward direction while blocking it in the backward direction. Two status of power amplifier biased at the standard working voltage and zero voltage are represented as codes “1” and “0,” respectively. By periodically setting adequate code sequences and proportions in the temporal dimension, according to the space‐time coding strategy, the amplitudes and phases of the harmonic transmission coefficients can be adjusted in a programmable way. A metasurface prototype is fabricated and measured in the microwave frequency to validate the concept and feasibility. The experimental results show good agreement with the theoretical predictions and numerical simulations. The proposed metasurface can achieve controllable harmonic power enhancements for flexibly configuring the power intensities in space, which enlarge and manipulate the quality of transmitting signals.

Second-harmonic generation and the conservation of spatiotemporal orbital angular momentum of light

Light with spatiotemporal orbital angular momentum (ST-OAM) is a recently discovered type of structured and localized electromagnetic field. This field carries characteristic space-time spiral phase structure and transverse intrinsic OAM. In this work, we present the generation and characterization of the second-harmonic of ST-OAM pulses. We uncovered the conservation of transverse OAM in a second-harmonic generation process, where the space-time topological charge of the fundamental field is doubled along with the optical frequency. Our experiment thus suggests a general ST-OAM nonlinear scaling rule - analogous to that in conventional OAM of light. Furthermore, we observe that the topology of a second-harmonic ST-OAM pulse can be modified by complex spatiotemporal astigmatism, giving rise to multiple phase singularities separated in space and time. Our study opens a new route for nonlinear conversion and scaling of light carrying ST-OAM with the potential for driving other secondary ST-OAM sources of electromagnetic fields and beyond.

A new boundary element algorithm for a general solution of nonlinear space-time fractional dual-phase-lag bio-heat transfer problems during electromagnetic radiation

The main aim of this paper is to propose a new boundary element method (BEM) formulation for solving the nonlinear space-time fractional dual-phase-lag bio-heat transfer problems during electromagnetic radiation. Due to the advantages of BEM, such as not requiring a discretization of the interior of the treated region and providing a low RAM and CPU time. BEM is therefore a flexible and efficient tool for modeling bio-heat transfer problems. The efficiency of our proposed methodology has been improved by applying the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and CPU time. Numerical results are depicted graphically to show the effects of time-fractional derivative order and space-fractional derivative order on the nonlinear temperature distributions. The numerical results also show the significant differences between the nonlinear temperature distributions of the classical Fourier, single-phase-lag, and dual-phase-lag bio-heat conduction models. To demonstrate the validity and accuracy of the proposed BEM methodology, numerical solutions for two-dimensional (2D) special case of the nonlinear space-time fractional dual phase lag bio-heat transfer problems are obtained and compared to experimental, Legendre wavelet collocation method (LWCM) and Fractional order Legendre functions and Galerkin method (FOLFs-GM).

Analogy between freezing lakes and the cosmic radiation era

An equation describing a one-dimensional model for the freezing of lakes is shown to be formally analogous to the Friedmann equation of cosmology. The analogy is developed and used to speculate on the change between two hypothetical "spacetime phases" in the early universe.

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell's mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith's theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires $C^1$-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-$\alpha$ method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton-Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

An efficient space-time phase field discretization for ferroelectrics

Recent developments of phase field model based on the Ginzburg–Landau theory have provided an unprecedented look at the formation of polarization domain structures and rich phenomena of polarization behaviors in nanoscale ferroelectrics under electrical and mechanical multi-fields. However, the phase field simulations are often computationally expensive. One of the major reasons behind this inefficiency is due to the complex spatio-temporal effects on the dynamical behavior of polarization. In this work, an efficient scheme with error control and adaptive time-stepping is introduced to the phase field model in the context of Ginzburg–Landau theory. The proposed time adaptivity algorithm is based on the discrete maximum norm of the difference in numerical solutions at three consecutive time steps. In addition, the energy stability of the proposed scheme is demonstrated. Several benchmarks of convergence tests are presented to validate the model. The performance of proposed technique is illustrated through numerical examples involving behaviors of polarization in complex ferroelectric nanostructures in three dimensions.

Drift wave in strong collisional dusty magnetoplasma

The study about the wave mechanism of magnetized dusty plasmas has important value to related experiment, industrial processing and exploring celestial space. The linear and nonlinear fluctuation characteristics of the nonuniform magnetized dust plasma system are researched in this paper. For the homogeneous external magnetic field and the nonuniform environment with density and temperature gradients, a two-dimensional nonlinear dynamic magnetoplasma equation is derived considering the strong impact between dust and neutral particles. The linear dispersion relation is obtained by the linearized method. There are both the damping wave causing by strong collision and the harmonic wave by particle drift. Employing the typical numerical parameters for analysis, the results display that the quantum parameter modifies the system lengths; the real wave frequency is proportion to the drift frequency; the imaginary wave frequency has complex relationship with the collision frequency between dust and neutrals, and the collision of particles causes the dissipation effects to the system. Besides, the analytical solutions of drift shock wave and explosive wave are solved by function change method. The variation about the electrostatic potential with the main physical parameters is discussed in detail. It is shown that the strength of the electrostatic shock wave and the width of the explosive wave increase with increasing the dust density and magnetic field intensity, decrease with increasing the collision frequency, change with the drift velocity. When the space-time phase is small, the electrostatic potential changes quickly; once big enough, the potential tends to be stable value and reaches stable state eventually. Finally, the stability of the system is discussed. It is found that the dusty charge, quantum parameter, drift velocity all appear in the disturbed solution. All these results in the paper show that the strong collision effect, quantum effect, particle drift and magnetic field all play important role to the generation, evolution and stability of drift waves.

The LHC Drell–Yan measurements as a constraint for the noncommutative space-time

The LHC measurements of the differential cross section of the Drell–Yan process is used to constrain the noncommutative space-time (NCST) phase space. A χ2 method is utilized to exclude the part of the parameters space which is not consistent with the LHC measurements. Depending on other NCST parameters, the scale can be pushed up to ΛNC > 655 GeV. The effect of other parameters is also investigated. To our knowledge, it is the first time that a detailed statistical analysis is performed to compare the NCST results with the Hadron Collider measurements.

Learning the space-time phase diagram of bacterial swarm expansion

Coordinated dynamics of individual components in active matter are an essential aspect of life on all scales. Establishing a comprehensive, causal connection between intracellular, intercellular, and macroscopic behaviors has remained a major challenge due to limitations in data acquisition and analysis techniques suitable for multiscale dynamics. Here, we combine a high-throughput adaptive microscopy approach with machine learning, to identify key biological and physical mechanisms that determine distinct microscopic and macroscopic collective behavior phases which develop as Bacillus subtilis swarms expand over five orders of magnitude in space. Our experiments, continuum modeling, and particle-based simulations reveal that macroscopic swarm expansion is primarily driven by cellular growth kinetics, whereas the microscopic swarming motility phases are dominated by physical cell-cell interactions. These results provide a unified understanding of bacterial multiscale behavioral complexity in swarms.

Axion electrodynamics from Infeld–van der Waerden formalisms

In this paper, we will explore the spacetime phase structure inside the Infeld–van der Waerden formalisms, showing that Maxwell’s theory in this scenario leads to an axion-like phase electrodynamics, which suggests that this phase may originate the axion field.

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Hořava–Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.

A Multi-relay Cooperative Communication Using Space Time Spatial Phase Coding Based on OFDM

Among schemes to obtain diversity gain, space-time block code (STBC) and spatial phase coding (SPC) have been widely studied for the cooperative wireless relaying system. However, conventional STBC has a problem that cannot deal with change in the number of relays due to low throughput. In this paper, we propose a SPC that multi-relay transmission is possible and a space-time spatial phase coding (STSPC) using the proposed SPC scheme and STBC. The STSPC scheme provides improved bit error rate performance and full rate.

Superconducting and Antiferromagnetic Phases of Space-Time

A correspondence between the SO5 theory of high-TC superconductivity and antiferromagnetism, put forward by Zhang and collaborators, and a theory of gravity arising from symmetry breaking of a SO5 gauge field is presented. A physical correspondence between the order parameters of the unified SC/AF theory and the generators of the gravitational gauge connection is conjectured. A preliminary identification of regions of geometry, in solutions of Einstein’s equations describing charged-rotating black holes embedded in de Sitter space-time, with SC and AF phases is carried out.

Spatial correlation properties of coherent array beams modulated by space-time random phase

The coherent array beams modulated by space-time random phase will produce a time-variant speckle field, i.e. partially coherent light field. The spatial correlation properties of the light field are investigated in detail. The analytical expressions of far-field intensity expectation, covariance and spatial correlation function are derived firstly. From the formulae, the effects of array geometry, the elements number, and the cycle number of phase modulation on the spatial correlation properties, including transverse coherence length, correlation coefficient are discussed. Numerical simulations are provided as auxiliary means to illustrate the analysis results.

A new 2D/3D Phase Unwrapping Strategy of Differential Interferograms SAR

3D space-time phase unwrapping is a major problem in many disciplines including SAR interferometry, where elevation models and displacement measurements can be obtained after phase unwrapping and removing the ambiguity modulo 2π. The unwrapping of these phases can be performed in two different approaches, the first is to place the differential phases in the 2D plane and the second approach is to unwrap the phase taking into account the phase discontinuity in the time series. The latter quantifies the space-time deformation. In this context, we propose a strategy of 3D phase unwrapping which focuses on two methods: the first one is based on locating and tracking the unwrapping path of the best quality three-dimensional factor and the second method enables to unwrap the phase voxels regardless of the path avoiding the lines and planes cut. The proposed strategy has been tested on a series of simulated interferograms to show the use of voxel phase unwrapping 3D versus the 2D unwrapping (pixel to pixel temporally). It is then applied to the differential interferogram generated from a series of ERS1/ERS2 radar images acquired over a region of southern Algeria affected by the problem of land subsidence and the presence of scalable tectonic faults.