scholarly journals The spectrum of the Hamiltonian with a PT-symmetric periodic optical potential

2017 ◽  
Vol 15 (01) ◽  
pp. 1850008 ◽  
Author(s):  
O. A. Veliev
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Optical Potential ◽  
Mathematical Proof ◽  
Hill Operator ◽  
The Real ◽  
The Hill ◽  
Degeneration Point

We give a complete description, provided with a mathematical proof, of the shape of the spectrum of the Hill operator with potential [Formula: see text], where [Formula: see text] We prove that the second critical point [Formula: see text], after which the real parts of the first and second bands disappear, is a number between [Formula: see text] and [Formula: see text]. Moreover, we prove that [Formula: see text] is the degeneration point for the first periodic eigenvalue. Besides, we give a scheme by which one can find arbitrary precise value of the second critical point as well as the [Formula: see text]th critical points after which the real parts of the [Formula: see text]th and [Formula: see text]th bands disappear, where [Formula: see text]

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

Numerical Approach for Real Gas Simulations: Part II — Flow Simulation for Supercritical CO2 Centrifugal Compressor

2017 ◽  
Author(s):  
Swati Saxena ◽  
Ramakrishna Mallina ◽  
Francisco Moraga ◽  
Douglas Hofer
Keyword(s):  
Critical Point ◽  
Centrifugal Compressor ◽  
Supercritical Co2 ◽  
Operating Conditions ◽  
Inlet Guide Vane ◽  
Thermodynamic Quantities ◽  
3D Flow ◽  
Real Gas ◽  
The Real ◽  
Operating Range

This paper is presented in two parts. Part I (Tabular fluid properties for real gas analysis) describes an approach to creating a tabular representation of the equation of state that is applicable to any fluid. This approach is applied to generating an accurate and robust tabular representation of the RefProp CO2 properties. Part II (this paper) presents numerical simulations of a low flow coefficient supercritical CO2 centrifugal compressor developed for a closed loop power cycle. The real gas tables presented in part I are used in these simulations. Three operating conditions are simulated near the CO2 critical point: normal day (85 bar, 35C), hot day (105 bar, 50 C) and cold day (70 bar, 20C) conditions. The compressor is a single stage overhung design with shrouded impeller, 155 mm impeller tip diameter and a vaneless diffuser. An axial variable inlet guide vane (IGV) is used to control the incoming swirl into the impeller. An in-house three-dimensional computational fluid dynamics (CFD) solver named TACOMA is used with real gas tables for the steady flow simulations. The equilibrium thermodynamic modeling is used in this study. The real gas effects are important in the desired impeller operating range. It is observed that both the operating range (minimum and maximum volumetric flow rate) and the pressure ratio across the impeller are dependent on the inlet conditions. The compressor has nearly 25% higher operating range on a hot day as compared to the normal day conditions. A condensation region is observed near the impeller leading edge which grows as the compressor operating point moves towards choke. The impeller chokes near the mid-chord due to lower speed of sound in the liquid-vapor region resulting in a sharp drop near the choke side of the speedline. This behavior is explained by analyzing the 3D flow field within the impeller and thermodynamic quantities along the streamline. The 3D flow analysis for the flow near the critical point provides useful insight for the designers to modify the current compressor design for higher efficiency.

A Markov Prediction-Based Privacy Protection Scheme for Continuous Query

2019 ◽  
Vol 28 (09) ◽  
pp. 1950147
Author(s):  
Lei Zhang ◽  
Jing Li ◽  
Songtao Yang ◽  
Yi Liu ◽  
Xu Zhang ◽  
...  
Keyword(s):  
Privacy Protection ◽  
Location Privacy ◽  
Mathematical Proof ◽  
Security Analysis ◽  
Continuous Query ◽  
The Real ◽  
Protection Scheme ◽  
Whole Process ◽  
Prediction Scheme ◽  
Location Privacy Protection

The query probability of a location which the user utilizes to request location-based service (LBS) can be used as background knowledge to infer the real location, and then the adversary may invade the privacy of this user. In order to cope with this type of attack, several algorithms had provided query probability anonymity for location privacy protection. However, these algorithms are all efficient just for snapshot query, and simply applying them in the continuous query may bring hazards. Especially that, continuous anonymous locations which provide query probability anonymity in continuous anonymity are incapable of being linked into anonymous trajectories, and then the adversary can identify the real trajectory as well as the real location of each query. In this paper, the query probability anonymity and anonymous locations linkable are considered simultaneously, then based on the Markov prediction, we provide an anonymous location prediction scheme. This scheme can cope with the shortage of the existing algorithms of query probability anonymity in continuous anonymity locations difficult to be linked, and provide query probability anonymity service for the whole process of continuous query, so this scheme can be used to resist the attack of both of statistical attack as well as the infer attack of the linkable. At last, in order to demonstrate the capability of privacy protection in continuous query and the efficiency of algorithm execution, this paper utilizes the security analysis and experimental evaluation to further confirm the performance, and then the process of mathematical proof as well as experimental results are shown.

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

Spectral properties of the Hill operator

2016 ◽  
Vol 99 (3-4) ◽  
pp. 598-602 ◽  
Author(s):  
A. G. Baskakov ◽  
D. M. Polyakov
Keyword(s):  
Spectral Properties ◽  
Hill Operator ◽  
The Hill

scholarly journals A method to estimate statistical errors of properties derived from charge-density modelling

2018 ◽  
Vol 74 (3) ◽  
pp. 170-183 ◽  
Author(s):  
Bertrand Fournier ◽  
Benoît Guillot ◽  
Claude Lecomte ◽  
Eduardo C. Escudero-Adán ◽  
Christian Jelsch
Keyword(s):  
Charge Density ◽  
Least Squares ◽  
Critical Point ◽  
Critical Points ◽  
Property Values ◽  
Density Model ◽  
Interaction Energies ◽  
Topological Properties ◽  
A Charge ◽  
Density Modelling

Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with theMoProsoftware. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties ofanyproperty related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely availableMoProprogram dedicated to charge-density refinement and modelling.

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