The Mass and Size of Photons in the 5-Dimensional Extended Space Model

We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth additional coordinate, the interval S is used. This value is constant under the usual Lorentz transformations in M, but it changes when the transformations in the extended space G are used. We call this model the Extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. In the ESM, gravity and electromagnetism are combined in one field. In the ESM, a photon can have a nonzero mass and this mass can be either positive or negative. It is also possible to establish in the frame of ESM connection between mass of a particle and its size.

Unique Solution of Integral Equations via Intuitionistic Extended Fuzzy b-Metric-Like Spaces

In this manuscript,our goal is to introduce the notion of intuitionistic extended fuzzy b-metric-like spaces.We establish some fixed point theorems in this setting.Also,we plot some graphs of an example of obtained result for better understanding.We use the concepts of continuous triangular norms and continuous triangular conorms in an intuitionistic fuzzy metric-like space.Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions.Triangular conorms are known as dual operations of triangular norms.The obtained results boost the approaches of existing ones in the literature and are supported by some examples and applications.

A Closure for Isotropic Turbulence Based on Extended Scale Similarity Theory in Physical Space

The closure of a turbulence field is a longstanding fundamental problem, while most closure models are introduced in spectral space. Inspired by Chou＇s quasi-normal closure method in spectral space, we propose an analytical closure model for isotropic turbulence based on the extended scale similarity theory of the velocity structure function in physical space. The assumptions and certain approximations are justified with direct numerical simulation. The asymptotic scaling properties are reproduced by this new closure method, in comparison to the classical Batchelor model.

Optimal Maintenance Modeling for Systems with Multiple Non-Identical Units Using Extended DSSP Method

In the optimal maintenance modeling, all possible maintenance activities and their corresponding probabilities play a key role in modeling. For a system with multiple non-identical units, its maintenance requirements are very complicated, and it is time-consuming, even omission may occur when enumerating them with various combinations of units and even with different maintenance actions for them. Deterioration state space partition (DSSP) method is an efficient approach to analyze all possible maintenance requirements at each maintenance decision point and deduce their corresponding probabilities for maintenance modeling of multi-unit systems. In this paper, an extended DSSP method is developed for systems with multiple non-identical units considering opportunistic, preventive and corrective maintenance activities for each unit. In this method, different maintenance types are distinguished in each maintenance requirement. A new representation of the possible maintenance requirements and their corresponding probabilities is derived according to the partition results based on the joint probability density function of the maintained system deterioration state. Furthermore, focusing on a two-unit system with a non-periodical inspected condition-based opportunistic preventive-maintenance strategy;a long-term average cost model is established using the proposed method to determine its optimal maintenance parameters jointly, in which “hard failure” and non-negligible maintenance time are considered. Numerical experiments indicate that the extended DSSP method is valid for opportunistic maintenance modeling of multi-unit systems.

Assessment of Model Predictive Control Performance Criteria

The current highly competitive environment has driven industries to operate with increasingly restricted profit margins. Thus, it is imperative to optimize production processes. Faced with this scenario, multivariable predictive control of processes has been presented as a powerful alternative to achieve these goals. Moreover, the rationale for implementation of advanced control and subsequent analysis of its post-match performance also focus on the benefits that this tool brings to the plant. It is therefore essential to establish a methodology for analysis, based on clear and measurable criteria. Currently, there are different methodologies available in the market to assist with such analysis. These tools can have a quantitative or qualitative focus. The aim of this study is to evaluate three of the best current main performance assessment technologies： Minimum Variance Control-Harris Index; Statistical Process Control （Cp and Cpk）; and the Qin and Yu Index. These indexes were studied for an alumina plant controlled by three MPC （model predictive control） algorithms （GPC （generalized predictive control）, RMPCT （robust multivariable predictive control technology） and ESSMPC （extended state space model predictive controller）） with different results.

Quantum corrections to the thermodynamics and phase transition of a black hole surrounded by a cavity in the extended phase space

In the extended phase space,we investigate the rainbow gravity-corrected thermodynamic phenomena and phase structure of the Schwarzschild black hole surrounded by a spherical cavity.The results show that rainbow gravity has a very significant effect on the thermodynamic phenomena and phase structure of the black hole.It prevents the black hole from total evaporation and leads to a remnant with a limited temperature but no mass.Additionally,we restore the P-V criticality and obtain the critical quantities of the canonical ensemble.When the temperature or pressure is smaller than the critical quantities,the system undergoes two Hawking-Page-like phase transitions and one first-order phase transition,which never occurs in the original case.Remarkably,our findings demonstrate that the thermodynamic behavior and phase transition of the rainbow SC black hole surrounded by a cavity in the extended phase space are analogous to those of the Reissner–Nordstr?m anti-de Sitter black hole.Therefore,rainbow gravity activates the effect of electric charge and cutoff factor in the evolution of the black hole.

Thermodynamics and weak cosmic censorship conjecture of charged AdS black hole in the Rastall gravity with pressure

Treating the cosmological constant as a dynamical variable,we investigate the thermodynamics and weak cosmic censorship conjecture(WCCC)of a charged AdS black hole(BH)in the Rastall gravity.We determine the energy momentum relation of charged fermion at the horizon of the BH using the Dirac equation.Based on this relation,it is shown that the first law of thermodynamics still holds as a fermion is absorbed by the BH.However,the entropy of both the extremal and near-extremal BH decreases in the irreversible process,which means that the second law of thermodynamics is violated.Furthermore,we verify the validity of the WCCC by the minimum values of the metric function h(r)at its final state.For the extremal charged AdS BH in the Rastall gravity,we find that the WCCC is always valid since the BH is extreme.While for the case of near-extremal BH,we find that the WCCC could be violable in the extended phase space(EPS),depending on the value of the parameters of the BH and their variations.

Dynamical time versus system time in quantum mechanics

Properties of an operator representing the dynamical time in the extended parameterization invariant formulation of quantum mechanics are studied. It is shown that this time operator is given by a positive operator measure analogously to the quantities that are known to represent various measurable time operators. The relation between the dynamical time of the extended formulation and the best known example of the system time operator, i.e., for the free one- dimensional particle, is obtained.

Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space

Based on the Melnikov method,we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations.Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause temporal chaos only when the perturbation amplitude is above a critical value,which involves the angular momentum J.Under the spatial perturbation,however,it is found that spatial chaos always occurs,independent of the perturbation amplitude.

A New Interpretation of the Higgs Vacuum Potential Energy Based on a Planckion Composite Model for the Higgs

We present a new interpretation of the Higgs field as a composite particle made up of a positive, with, a negative mass Planck particle. According to the Winterberg hypothesis, space, i.e., the vacuum, consists of both positive and negative physical massive particles, which he called planckions, interacting through strong superfluid forces. In our composite model for the Higgs boson, there is an intrinsic length scale associated with the vacuum, different from the one introduced by Winterberg, where, when the vacuum is in a perfectly balanced state, the number density of positive Planck particles equals the number density of negative Planck particles. Due to the mass compensating effect, the vacuum thus appears massless, chargeless, without pressure, energy density, or entropy. However, a situation can arise where there is an effective mass density imbalance due to the two species of Planck particle not matching in terms of populations, within their respective excited energy states. This does not require the physical addition or removal of either positive or negative Planck particles, within a given region of space, as originally thought. Ordinary matter, dark matter, and dark energy can thus be given a new interpretation as residual vacuum energies within the context of a greater vacuum, where the populations of the positive and negative energy states exactly balance. In the present epoch, it is estimated that the dark energy number density imbalance amounts to, , per cubic meter, when cosmic distance scales in excess of, 100 Mpc, are considered. Compared to a strictly balanced vacuum, where we estimate that the positive, and the negative Planck number density, is of the order, 7.85E54 particles per cubic meter, the above is a very small perturbation. This slight imbalance, we argue, would dramatically alleviate, if not altogether eliminate, the long standing cosmological constant problem.

On the Cosmic Evolution of the Quantum Vacuum Using Two Variable G Models and Winterberg’s Thesis

We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G-1, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.

Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter

We obtain an exact solution for spherically symmetric Letelier AdS black holes immersed in perfect fluid dark matter(PFDM).Considering the cosmological constant as the positive pressure of the system and volume as its conjugate variable,we analyze the thermodynamics of our black holes in the extended phase space.Owing to the background clouds of strings parameter(a)and the parameter endowed with PFDM(β),we analyze the Hawking temperature,entropy,and specific heat.Furthermore,we investigate the relationship between the photon sphere radius and phase transition for the Letelier AdS black holes immersed in PFDM.Through the analysis,with a particular condition,non-monotonic behaviors are found between the photon sphere radius,impact parameter,PFDM parameter,temperature,and pressure.We can regard the changes in both the photon sphere radius and impact parameter before and after phase transition as the order parameter;their critical exponents near the critical point are equal to the same value,1/2,similar to that in ordinary thermal systems.This indicates that a universal relation of gravity may exist near the critical point for a black hole thermodynamic system.

Hawking-Page phase transitions of charged AdS black holes surrounded by quintessence

Hawking-Page phase transitions between the thermal anti-de Sitter vacuum and charged black holes surrounded by quintessence are studied in the extended phase space.The quintessence field,with the state parameter-1<w<-1/3,modifies the temperature and the Gibbs free energy of a black hole.The phase transition temperature Thp and the Gibbs free energy G are first analytically investigated for the special case of w=-2/3,and then,the results of numerical simulations are shown for general w.The phase transition temperature Thp increases with pressure and decreases with electric potential.In addition,Thp significantly decreases owing to the quintessence field,which generates negative pressure around the black hole.