Classical Evolution Research Articles

Hydrodynamic Interpretation of Generic Squeezed Coherent States: A Kinetic Theory

The hydrodynamic interpretation of quantum mechanics treats a system of particles in an effective manner. In this work, we investigate squeezed coherent states within the hydrodynamic interpretation. The Hamiltonian operator in question is time dependent, n-dimensional and in quadratic order. We start with deriving a phase space Wigner probability distribution and an associated equilibrium entropy for the squeezed coherent states. Then, we decompose the joint phase space distribution into two portions: a marginal position distribution and a momentum distribution that is conditioned on the post-selection of positions. Our conditionally averaged momenta is shown to be equal to the Bohm's momenta whose connection to the weak measurements is already known. We also keep track of the corresponding classical system evolution by identifying shear, magnification and rotation components of the symplectic phase space dynamics. This allows us to pinpoint which portion of the underlying classical motion appears in which quantum statistical concept. We show that our probability distributions satisfy the Fokker-Planck equations exactly. They can be used to decompose the equilibrium entropy into the missing information in positions and in momenta as in the Sackur-Tetrode entropy of the classical kinetic theory. Eventually, we define a quantum pressure, a quantum temperature and a quantum internal energy which are related to each other in the same fashion as in the classical kinetic theory. We show that the quantum potential incorporates the kinetic part of the internal energy and the fluctuations around it. This allows us to suggest a quantum conditional virial relation. In the end, we show that the kinetic internal energy is linked to the fractional Fourier transformer part of the underlying classical dynamics similar to the case where the energy of a quantum oscillator is linked to its Maslov index.

Application of Fuzzy Immune Algorithm and Soft Computing in the Design of 2‐DOF PID Controller

To solve the difficulty in selecting the crossover probability and mutation probability in genetic algorithms, a fuzzy immune algorithm based on adaptive estimation of crossover probability and mutation probability in a fuzzy reasoning system is proposed, and it is used in the parameter optimization design of a two‐degree‐of‐freedom PID controller. According to the experiment and simulation results, classic genetic algorithm evolution tends to halt after 37 generations, with a fitness value of 7.135, whereas fuzzy genetic algorithm evolution tends to stop after 20 generations, with a fitness value of 7.486. The 2‐DOF PID controller that was created can give the system strong target value following and interference suppression features at the same time.

Disconnection-Mediated migration of interfaces in microstructures: II. diffuse interface simulations

The motion of interfaces is an essential feature of microstructure evolution in crystalline materials. While atomic-scale descriptions provide mechanistic clarity, continuum descriptions are important for understanding microstructural evolution and upon which microscopic features it depends. We develop a microstructure evolution simulation approach that is linked to the underlying microscopic mechanisms of interface migration. We extend the continuum approach describing the disconnection-mediated motion of interfaces introduced in Part I [Han, Srolovitz and Salvalaglio, 2021] to a diffuse interface, phase-field model suitable for large-scale microstructure evolution. A broad range of numerical simulations showcases the capability of the method and the influence of microscopic interface migration mechanisms on microstructure evolution. These include, in particular, the effects of stress and its coupling to interface migration which arises from disconnections, showing how this leads to important differences from classical microstructure evolution represented by mean curvature flow.

Influence of RE (Pr3+, Er3+, Nd3+) doping on structural, vibrational and enhanced persistent photocatalytic properties of ZnO nanostructures

Rare earth (RE- Pr, Er and Nd) doped ZnO nanostructures were prepared through simple wet chemical precipitation route. The RE doping induced interesting morphological transition from spherical to flower like structures were analyzed. The X-ray diffraction (XRD) measurements revealed that the prepared materials were of highly crystalline in nature and RE dopant ions did not altered the crystal structure of ZnO. The microstrain of ZnO was altered with respect to the nature of dopants. In the case of the Pr doped ZnO, X-ray photoelectron spectroscopy (XPS) analysis confirmed that the dopant (Pr) ions successfully substituted in the ZnO lattice. Raman spectra revealed RE doping induced lower energy side shift and variation in intensity of the peaks related to the characteristic phonon modes of ZnO. In the case of Nd doped ZnO nanostructures, dopant induced suppression in classical Raman modes and evolution of multiphonon related modes were identified. Optical diffuse reflectance spectral (DRS) measurements, along with the characteristic excitonic band of ZnO, other bands associated to the transitions of 4f energy levels related to the RE ions were observed. The partially filled 4f orbitals led to the enhanced photocatalytic activity in RE doped ZnO nanostructures. The observed enhanced photocatalytic activity in RE doped ZnO when compared to bare ZnO was discussed. The decolorization efficiency of MB ensued the following order 96 > 94 > 86 > 78% for ZnErO, ZnNdO, ZnPrO and ZnO, respectively.

Abstract 12626: Valvosoft Non-Invasive Ultrasound Therapy (NIUT) in Patients With Severe Symptomatic Aortic Valve Stenosis: First-in-Human Study - Twelve-Months Safety Update

Background: While aortic valve replacements (AVR) generally present favorable outcomes in severe calcific aortic stenosis (CAS), not all patients are eligible for an invasive treatment.Cardiawave © developed a novel non-invasive ultrasound therapy (NIUT) device, Valvosoft, to treat CAS. A prospective first-in-human study was conducted in two centers (Hôpital Européen Georges-Pompidou, France and Heart Center, Amphia Hospital, Netherlands) in 10 patients and a second study (University Clinical Center of Serbia) involving brain-MRI in 4 patients. All patients had symptomatic severe CAS and were ineligible for SAVR or TAVR according to local heart teams. Methods: Transthoracic NIUT was delivered on all 14 patients with Valvosoft. Clinical and echocardiographic evaluation was performed at baseline, discharge, 1-, 3-, 6- and 12-months follow-up (FUP). Additionally, the 4 patients of the second study had a brain-MRI performed before and after treatment. Results: Patients were advanced in age (82.4±5.3 years) with severe comorbidities (57% with heart failure and 50% with coronary heart disease). No adverse events (AE) occurred during the procedure other than isolated ventricular extrasystoles. No serious AE were adjudicated by a Clinical Event Committee (CEC) as device- or procedure-related at 1-month FUP. No death, stroke or transient ischemic attack or deterioration of neurological status were observed at 1-month FUP.During 12-months FUP, 5 deaths were reported (between 2 to 7 months after the procedure), all were adjudicated by CEC as non-procedure related. The survival rate was 100%, 93%, 79%, 64% at 1-, 3-, 6 and 12-months (to compare to the classic natural evolution of the disease survival rate of 94%, 73%, 73%, 54% respectively). No sign of cerebrovascular accident was detected in any of the 4 patients who had a brain-MRI before and after treatment. Conclusions: NIUT was feasible and safe in this small cohort of very frail, severe symptomatic CAS patients with severe comorbidities. Brain-MRIs performed before and after treatment ruled out silent cerebrovascular events. The survival rate of this cohort suggests that NIUT is beneficial for these patients and serves an unmet medical need.

Using Optimisation Meta-Heuristics for the Roughness Estimation Problem in River Flow Analysis

Climate change threats make it difficult to perform reliable and quick predictions on floods forecasting. This gives rise to the need of having advanced methods, e.g., computational intelligence tools, to improve upon the results from flooding events simulations and, in turn, design best practices for riverbed maintenance. In this context, being able to accurately estimate the roughness coefficient, also known as Manning’s n coefficient, plays an important role when computational models are employed. In this piece of research, we propose an optimal approach for the estimation of ‘n’. First, an objective function is designed for measuring the quality of ‘candidate’ Manning’s coefficients relative to specif cross-sections of a river. Second, such function is optimised to return coefficients having the highest quality as possible. Five well-known meta-heuristic algorithms are employed to achieve this goal, these being a classic Evolution Strategy, a Differential Evolution algorithm, the popular Covariance Matrix Adaptation Evolution Strategy, a classic Particle Swarm Optimisation and a Bayesian Optimisation framework. We report results on two real-world case studies based on the Italian rivers ‘Paglia’ and ‘Aniene’. A comparative analysis between the employed optimisation algorithms is performed and discussed both empirically and statistically. From the hydrodynamic point of view, the experimental results are satisfactory and produced within significantly less computational time in comparison to classic methods. This shows the suitability of the proposed approach for optimal estimation of the roughness coefficient and, in turn, for designing optimised hydrological models.

Nonequilibrium effects on one-norm geometric correlations and the emergence of a pointer-state basis in the weak- and strong-coupling regimes

Correlations in the open quantum systems manifest a rich phenomenology under the influence of various physical sources of noise. We theoretically study the dynamics of quantum correlations and their classical counterparts in a two-qubit system, measured by one-norm geometric quantifiers. We consider both qubits are initially prepared in the arbitrary $X$-type states and locally subjected to nonequilibrium dephasing environments with non-Markovian and nonstationary statistical features. We then explore the effects of nonequilibrium on the abrupt changes in the evolution of geometric correlations in the weak- and strong-coupling regimes. Particularly, in the weak-coupling regime, we show that the environmental nonequilibrium feature can efficiently control the appearance of double-sudden transitions and the decay rate in geometric quantum correlation dynamics. However, in the strong-coupling case, we show that the nonequilibrium nature can prolong the interval for the frozen quantum correlation and suppresses the number of multiple sudden changes in its decay rate. Moreover, the abrupt change from decay to a constant regime in classical correlation evolution reveals the emergence of the pointer-state basis. We show that the pointer-state basis appearance can be retarded in the weak-coupling case when the environment deviates from equilibrium. However, in a strong-coupling regime, we observe the metastable pointer-states basis characterized by multiple, successive sudden transitions in classical correlation dynamics. Remarkably, we unveil that the nonequilibrium feature may suppress the apparition of the metastable pointer-states basis.

Therapeutic potential of ibuprofen inhalation for COVID-19 pneumonia: Report of two first cases

No specific and effective antiviral treatment has been approved for COVID-19 so far. Systemic corticosteroid and remdesivir have shown to decrease mortality in COVID-19 patients, but mortality still is elevated. We propose that nebulized hypertonic ibuprofen solution which has bactericidal, virucidal, mucolytic and anti-inflammatory properties to be used for COVID-19 pneumonia and prevent the classical evolution to respiratory failure and mechanical respiration. We report here the first two cases of the COVID-19 pneumonia successfully treated with nebulized hypertonic ibuprofen solution (NaIHS). Rationale of the treatment is to mitigate the local inflammation with inhaled NIH that stays in the lung and may inhibit proliferation of the virus, inflammation and successfully reverts the hypoxia observed in these clinical cases. Mild adverse events were observed. Larger and further studies are warranted to confirm the result of these cases. Keywords: hypertonic ibuprofen solution; inhalation; coronavirus disease 2019.

Nonsingular cosmological models with strong gravity in the past

In scalar-tensor Horndeski theories, nonsingular cosmological models---bounce and genesis---are problematic because of potential ghost and/or gradient instabilities. One way to get around this obstacle is to send the effective Planck mass to zero in the asymptotic past (``strong gravity in the past''). One may suspect that this feature is a signal of a strong coupling problem at early times. However, the classical treatment of the cosmological background is legitimate, provided that the strong coupling energy scale remains at all times much higher than the scale associated with the classical evolution. We construct various models of this sort, namely (i) bouncing Universe which proceeds through inflationary epoch to kination (expansion within general relativity, driven by massless scalar field); (ii) bouncing Universe with kination stage immediately after bounce; (iii) combination of genesis and bounce, with the Universe starting from flat space-time, then contracting and bouncing to the expansion epoch; (iv) ``standard'' genesis evading the strong coupling problem in the past. All these models are stable, and perturbations about the backgrounds are not superluminal.

Random generators of Markovian evolution: A quantum-classical transition by superdecoherence.

Continuous-time Markovian evolution appears to be manifestly different in classical and quantum worlds. We consider ensembles of random generators of N-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties. We then show how the two types of generators can be related by superdecoherence. In analogy with the mechanism of decoherence, which transforms a quantum state into a classical one, superdecoherence can be used to transform a Lindblad operator (generator of quantum evolution) into a Kolmogorov operator (generator of classical evolution). We inspect spectra of random Lindblad operators undergoing superdecoherence and demonstrate that, in the limit of complete superdecoherence, the resulting operators exhibit spectral density typical to random Kolmogorov operators. By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. Furthermore, we define an inverse procedure of supercoherification that is a generalization of the scheme used to construct a quantum state out of a classical one. Finally, we study microscopic correlation between neighboring eigenvalues through the complex spacing ratios and observe the horseshoe distribution, emblematic of the Ginibre universality class, for both types of random generators. Remarkably, it survives both superdecoherence and supercoherification.

Generator functions and their applications

We had introduced so called generators functions to precisely follow the regularity of analytic solutions of Navier-Stokes equations earlier (see Grenier and Nguyen [Ann. PDE 5 (2019)]. In this short note, we give a short presentation of these generator functions and use them to construct analytic solutions to classical evolution equations, which provides an alternative way to the use of the classical abstract Cauchy-Kovalevskaya theorem (see Asano [Proc. Japan Acad. Ser. A Math. Sci. 64 (1988), pp. 102–105], Baouendi and Goulaouic [Comm. Partial Differential Equations 2 (1977), pp. 1151–1162], Caflisch [Bull. Amer. Math. Soc. (N.S.) 23 (1990), pp. 495–500], Nirenberg [J. Differential Geom. 6 (1972), pp. 561–576], Safonov [Comm. Pure Appl. Math. 48 (1995), pp. 629–637]).

Design Scalability Study of the Γ-Shaped Piezoelectric Harvester Based on Generalized Classical Ritz Method and Optimization

This paper studies the design scalability of a Γ-shaped piezoelectric energy harvester (ΓEH) using the generalized classical Ritz method (GCRM) and differential evolution algorithm. The generalized classical Ritz method (GCRM) is the advanced version of the classical Ritz method (CRM) that can handle a multibody system by assembling its equations of motion interconnected by the constraint equations. In this study, the GCRM is extended for analysis of the piezoelectric energy harvesters with material and/or orientation discontinuity between members. The electromechanical equations of motion are derived for the PE harvester using GCRM, and the accuracy of the numerical simulation is experimentally validated by comparing frequency response functions for voltage and power output. Then the GCRM is used in the power maximization design study that considers four different total masses—15 g, 30 g, 45 g, 60 g—to understand design scalability. The optimized ΓEH has the maximum normalized power density of 23.1 × 103 kg·s·m−3 which is the highest among the reviewed PE harvesters. We discuss how the design parameters need to be determined at different harvester scales.

Density perturbations in axionlike particles: Classical versus quantum field treatment

Axions and axion-like particles are bosonic quantum fields. They are often assumed to follow classical field equations due to their high degeneracy in the phase space. In this work, we explore the disparity between classical and quantum field treatments in the context of density and velocity fields of axions. Once the initial density and velocity field are specified, the evolution of the axion fluid is unique in the classical field treatment. However, in the quantum field treatment, there are many quantum states consistent with the given initial density and velocity field. We show that evolutions of the density perturbations for these quantum states are not necessarily identical and, in general, differ from the unique classical evolution. To illustrate the underlying physics, we consider a system of large number of bosons in a one-dimensional box, moving under the gravitational potential of a heavy static point-mass. We ignore the self-interactions between the bosons here. Starting with homogeneous number density and zero velocity field, we determine the density perturbations in the linear regime in both quantum and classical field theories. We find that classical and quantum evolutions are identical in the linear regime if only one single-particle state is occupied by all the bosons and the self-interaction is absent. If more than one single-particle states are occupied, the density perturbations in quantum evolutions differ from the classical prediction after a certain time which depends upon the parameters of the system.

Time and Evolution in Quantum and Classical Cosmology

We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators the classical evolution is reproduced. We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.

Abstract dynamical systems: Remarks on symmetries and reduction

In this paper, we review how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions.

Euclidean LQG dynamics: an electric shift in perspective

Loop quantum gravity (LQG) is a non-perturbative attempt at quantization of a classical phase space description of gravity in terms of SU(2) connections and electric fields. As emphasized recently Ashtekar and Varadarajan (2020 arXiv:2012.12094 [gr-qc]), on this phase space, classical gravitational evolution in time can be understood in terms of certain gauge covariant generalizations of Lie derivatives with respect to a spatial SU(2) Lie algebra valued vector field called the electric shift. We present a derivation of a quantum dynamics for Euclidean LQG which is informed by this understanding. In addition to the physically motivated nature of the action of the Euclidean Hamiltonian constraint so derived, the derivation implies that the spin labels of regulating holonomies are determined by corresponding labels of the spin network state being acted upon thus eliminating the ‘spin j-ambiguity’ pointed out by Perez. By virtue of Thiemann’s seminal work, the Euclidean quantum dynamics plays a crucial role in the construction of the Lorentzian quantum dynamics so that our considerations also have application to Lorentzian LQG.

Can scale-dependent cosmology alleviate the H0 tension?

Scale-dependence is a common feature to all effective models of quantum gravity. In this paper, a cosmological model based on the scale-dependent scenario of gravity is presented. It is argued that such models, where the scale-dependence appears as a correction to the classical ΛCDM evolution, have the potential of addressing the tensions between early and late time measurements of H0. After defining criteria to parametrize this tension, we perform a numerical scan over the parameter space of the scale-dependent model, subject to these criteria. In this analysis, it is found that, indeed, the tension can be released.

Geochemistry Study of Cross-castic Magma Alkalinity Evolution

DOI:10.17014/ijog.8.2.177-196The discrimination of magmatic alkalinity is a classic study that has never stopped for the past ninety years. Various methodologies have been developed since Shand’s classification using the method of alumina saturation to approach silica saturation and the methodology without involving alumina and silica such as K2O vs. Na2O and others, while the aim is to find out the evolution of alkalinity during the magmatic differentiation. The classical magmatic alkalinity evolution has been known as a castic magma alkalinity evolution, where the initial magma in the form of magma-X(a) will evolve along the stages of differentiation and remain a derivative of the initial magma {magmaX(a)}. The same philosophy is also explained in the ternary AFM diagram. Is the magmatic differentiation, followed by fractional crystallization, always an evolution of alkalinity based on caste? This question often raises current debates. This study takes the example of cogenetic volcanic and albitites. The application of the cogenetic volcanic using the selected diagram, which is ‘Three in one an overlaid diagram’. The output of the diagram presents the differentiation of magma which based on the evolution of Mg-series and Fe-series in a discontinuous branch of Bowen 1922 that can take place the castic and cross-castic, e.g. (a) from Mg-series to Mg-series {castic}, (b) from Mg-series to Feseries {cross-castic}, (c) from high-Mg tholeiitic basalt to calc-alkaline series {cross-castic}, (d) from Fe-series to Fe-series {castic}. While the evolution of magmatic alkalinity based on the continuous branch and refer to Trapezoid model generally occurring a cross-castic, e.g. (A) from sodic calc-alkaline to sodic alkaline-calcic, (B) from sodic calc-alkaline to shoshonitic alkaline-calcic, (C) from sodic calc-alkaline to potassic calc-alkaline, (D) from potassic calc-alkaline to shoshonitic alkaline-calcic, (E) sodic alkaline-calcic to sodic alkaline/peralkaline, (F) shoshonitic alkaline-calcic to potassic/ultrapotassic alkaline-calcic (cross-castic in subalkaline), (G) shoshonitic/potassic alkalinecalcic to shoshonitic/potassic alkaline/peralkaline. In this study, Fossa delle Felci volcanics (Italy) shows the evolution of magma from Mg-series to Mg-series, but the evolution of alkalinity of magma reveals the cross-caste (from sodic calc-alkaline to shoshonitic alkaline-calcic). Salak volcanics (Western Jawa) shows the evolution of magma from the Mg-series to Fe-series (cross-castic), and also the cross-castic in the evolution of alkalinity from sodic calc-alkaline to alkaline-calcic. Gothara albitites (India) clearly reveal the sodic-rich alkaline, which the magma generates from the evolution of sodic alkaline-calcic to sodic alkaline without the presence of potassic.

Gain-saturation-induced self-sustained oscillations in non-Hermitian optomechanics

We explore the classical dynamics of a non-Hermitian compound optomechanical system. By resorting to the method used in laser theory, we derived the classical dynamical equations of the system which incorporate the gain saturation effect of the gain medium. By simulating the classical evolutions of the system, we find that as long as the initial state of the cavities is not in the vacuum state the gain medium will amplify the light energy stored initially in the system and drive the mechanical oscillator into self-sustained oscillation although there is no extra optical drive for the system. Self-sustained oscillation can be formed in both the nonlinear $PT$ symmetry and $PT$ symmetry-broken phase. We also find that the oscillation amplitudes of the mechanical oscillator are more sensitive to the gain saturation of the gain medium than the gain coefficient. Multistability of the self-sustained oscillation also appears in our model. Our paper provides a deeper insight into the influence of non-Hermiticity on the dynamics of optomechanical systems and a tool for device applications.

Quantum manipulation through finite fluctuations for a generalized parametric oscillator using a lie algebra representation

In this paper, we focus on the effects of temporally compact fluctuations on the parameters m(t) (mass), (frequency), and (spatial dilation coefficient), for the generalized Caldirola-Kanai Hamiltonian. We propose an algorithm such that given control over the timing of repeated compact fluctuations, one can produce any time-evolution associated with complete parameter control of the generalized Caldirola-Kanai Hamiltonian. Computational simplicity is achieved in this endeavor using a faithful representation of the Hamiltonian’s associated Lie algebra. Further simplification occurs as a result of using unitarity conditions for the time-evolution operator. We apply our analysis to the effects of Dirac delta fluctuations in mass and frequency, both separately and simultaneously. We also numerically demonstrate control of the generalized Caldirola-Kanai system for the case of timed Gaussian fluctuations in the mass term. Furthermore, we use the faithful Lie algebra representation to show that any unitary evolution of this generalized Caldirola-Kanai system is given by the squeeze operator multiplied with a phase factor. We also show that the classical evolution of a probabilistic Gaussian phase space distribution and the evolution of the Wigner function of a coherent state in the quantum Caldirola-Kanai system are identical.