scholarly journals Presenting Different Time Steps, at the Start of Inflation, Using Kiefer Density Matrix, for the Use of an Inflaton, in Determining Different Conceivable Time Intervals for Time Flow Analysis

2021 ◽  
Author(s):  
Andrew W Beckwith
Keyword(s):  
Quantum Gravity ◽  
Density Matrix ◽  
Early Universe ◽  
Flow Analysis ◽  
Initial Time ◽  
Time Step ◽  
Time Intervals ◽  
Time Flow ◽  
Loop Approximation ◽  
Gravity Interpretation

We are using the book “Towards Quantum Gravity with an article by Claus Kiefer as to a quantum gravity interpretation of the density matrix in the early universe. The density matrix we are using is a one loop approximation, with inflaton value and potential terms, like V(phi) using the Padmanabhan values one can expect if the scale factor is a ~ a(Initial) times t ^ gamma , from early times . In doing so, we isolate out presuming a very small initial time step candidates initial time values which are from a polynomial for time values due to the Kiefer Density value.

The universe created from vacuum in the quantum-gravity interpretation of Brans-Dicke’s theory

1989 ◽  
Vol 104 (4) ◽  
pp. 467-473
Author(s):  
Liu Liao ◽  
Fan Li ◽  
Huang Chao-guang
Keyword(s):  
Quantum Gravity ◽  
Gravity Interpretation ◽  
The Universe

scholarly journals ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xingjie Helen Li ◽  
Fei Lu ◽  
Felix X.-F. Ye
Keyword(s):  
Large Time ◽  
Gradient System ◽  
Numerical Schemes ◽  
Time Step ◽  
Inference Problem ◽  
Time Dynamics ◽  
Efficient Simulation ◽  
Time Flow ◽  
Ergodic Measures ◽  
Locally Lipschitz

<p style='text-indent:20px;'>Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient simulation of both short-time dynamics and large-time statistics. However, locally Lipschitz SDEs often require special treatments such as implicit schemes with small time-steps to accurately simulate the ergodic measures. We introduce a framework to construct inference-based schemes adaptive to large time-steps (ISALT) from data, achieving a reduction in time by several orders of magnitudes. The key is the statistical learning of an approximation to the infinite-dimensional discrete-time flow map. We explore the use of numerical schemes (such as the Euler-Maruyama, the hybrid RK4, and an implicit scheme) to derive informed basis functions, leading to a parameter inference problem. We introduce a scalable algorithm to estimate the parameters by least squares, and we prove the convergence of the estimators as data size increases.</p><p style='text-indent:20px;'>We test the ISALT on three non-globally Lipschitz SDEs: the 1D double-well potential, a 2D multiscale gradient system, and the 3D stochastic Lorenz equation with a degenerate noise. Numerical results show that ISALT can tolerate time-step magnitudes larger than plain numerical schemes. It reaches optimal accuracy in reproducing the invariant measure when the time-step is medium-large.</p>

scholarly journals Performance and uncertainties of TSS stormwater sampling strategies from online time series

2018 ◽  
Vol 78 (6) ◽  
pp. 1407-1416
Author(s):  
Santiago Sandoval ◽  
Jean-Luc Bertrand-Krajewski ◽  
Nicolas Caradot ◽  
Thomas Hofer ◽  
Günter Gruber
Keyword(s):  
Time Series ◽  
Suspended Solids ◽  
Sampling Strategy ◽  
Sampling Strategies ◽  
Sampling Errors ◽  
Time Step ◽  
Sewer System ◽  
Time Intervals ◽  
Combined Sewer ◽  
One Year

Abstract The event mean concentrations (EMCs) that would have been obtained by four different stormwater sampling strategies are simulated by using total suspended solids (TSS) and flowrate time series (about one minute time-step and one year of data). These EMCs are compared to the reference EMCs calculated by considering the complete time series. The sampling strategies are assessed with datasets from four catchments: (i) Berlin, Germany, combined sewer overflow (CSO); (ii) Graz, Austria, CSO; (iii) Chassieu, France, separate sewer system; and (iv) Ecully, France, CSO. A sampling strategy in which samples are collected at constant time intervals over the rainfall event and sampling volumes are pre-set as proportional to the runoff volume discharged between two consecutive sample leads to the most representative results. Recommended sampling time intervals are of 5 min for Berlin and Chassieu (resp. 100 and 185 ha area) and 10 min for Graz and Ecully (resp. 335 and 245 ha area), with relative sampling errors between 7% and 20% and uncertainties in sampling errors of about 5%. Uncertainties related to sampling volumes, TSS laboratory analyses and beginning/ending of rainstorm events are reported as the most influent sources in the uncertainties of sampling errors and EMCs.

The renormalization group in perturbative quantum gravity

2021 ◽  
pp. 488-493
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Minimal Subtraction Scheme ◽  
Loop Approximation ◽  
Renormalization Group Equations ◽  
Gauge Fixing ◽  
Perturbative Renormalization ◽  
Fourth Derivative ◽  
Perturbative Quantum ◽  
The One

This is a short chapter summarizing the main results concerning the renormalization group in models of pure quantum gravity, without matter fields. The chapter starts with a critical analysis of non-perturbative renormalization group approaches, such as the asymptotic safety hypothesis. After that, it presents solid one-loop results based on the minimal subtraction scheme in the one-loop approximation. The polynomial models that are briefly reviewed include the on-shell renormalization group in quantum general relativity, and renormalization group equations in fourth-derivative quantum gravity and superrenormalizable models. Special attention is paid to the gauge-fixing dependence of the renormalization group trajectories.

Performance Evaluation of Gear Pump by 2D Unsteady CFD Analysis

2013 ◽  
Author(s):  
K. Anil Kumar ◽  
N. Balamuralikrishnan
Keyword(s):  
Mass Flow ◽  
Transient Flow ◽  
Flow Analysis ◽  
Adverse Pressure Gradient ◽  
Implant Design ◽  
Gear Pump ◽  
Time Step ◽  
Design Synthesis ◽  
Angular Velocities ◽  
Rotation Motion

Gas Turbine development activities have been associated with development of different pumps and its allied subsystems used for fuel supply and lubrication oil supply at different engine operating condition. 2D transient flow analysis of a Dual pump has been carried out in an environment with an adverse pressure gradient to map important parameters like pressure, velocity, mass flow and effect of slip. Three achievable close tolerances were selected and carried out the analysis. Finally identified tolerance to be maintained during manufacturing based on the analysis. A moving dynamic mesh concept was adopted because of its capability to facilitate solving transient flow problem and motion of the domain boundaries. A simulated motion control was decided based on the time step, angular velocities of gears rotation motion and coded through a User defined function (UDF) to give angular momentum. Each analysis was carried out for 180 degree of rotation. The main parameter mass flow rate was monitored for different speed and outlet pressures. A validation experimental test was carried out at one rpm thus build up a confidence in implant design synthesis to meet challenges in future.

scholarly journals Investigation of Zero Moment Point in a Partially Filled Liquid Vessel Subjected to Roll Motion

2020 ◽  
Vol 10 (11) ◽  
pp. 3992
Author(s):  
Muhammad Usman ◽  
Muhammad Sajid ◽  
Emad Uddin ◽  
Yasar Ayaz
Keyword(s):  
Autonomous Vehicles ◽  
Center Of Mass ◽  
Flow Analysis ◽  
Liquid Interface ◽  
Liquid Region ◽  
Time Step ◽  
Two Phase ◽  
Zero Moment Point ◽  
Zero Moment ◽  
Air Liquid Interface

Liquid-handling robots are designed to dispense sub-microliter quantities of fluids for applications including laboratory tests. When larger amounts of liquids are involved, sloshing must be considered as a parameter affecting stability, which is of significance for autonomous vehicles. The measurement and quantification of slosh in enclosed volumes poses a challenge to researchers who have traditionally resorted to tracking the air–liquid interface for two-phase flow analysis. There is a need for a simpler method to predict rollover in these applications. In this work, a novel solution to address this problem is proposed in the form of the Zero Moment Point (ZMP) of a dynamic liquid region. Computational experiments of a partially filled, two-dimensional liquid vessel were carried out using the Volume of Fluid (VOF) method in a finite volume based open-source computational fluid dynamics solver. The movement of the air–liquid interface was tracked, while the Center of Mass and the resulting Zero Moment Point were determined from the numerical simulations at each time step. The computational model was validated by comparing the wall pressure and movement of the liquid-free surface to experimentally obtained values. It was concluded that for a dynamic liquid domain, the Zero Moment Point can be instrumental in determining the stability of partially filled containers subjected to sloshing.

scholarly journals ACCELERATION AND DECELERATION IN THE CURVATURE-INDUCED PHANTOM MODEL OF THE LATE AND FUTURE UNIVERSE: COSMIC COLLAPSE AND ITS QUANTUM ESCAPE

2009 ◽  
Vol 18 (05) ◽  
pp. 865-887
Author(s):  
S. K. SRIVASTAVA ◽  
J. DUTTA
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Early Universe ◽  
High Energy ◽  
High Energy Density ◽  
Energy Models ◽  
Acceleration And Deceleration ◽  
The Universe

In this paper, the cosmology of the late and future universe is obtained from f(R) gravity with nonlinear curvature terms R2 and R3 (R is the Ricci scalar curvature). It is different from f(R) dark energy models where nonlinear curvature terms are taken as a gravitational alternative to dark energy. In the present model, neither linear nor nonlinear curvature terms are taken as dark energy. Rather, dark energy terms are induced by curvature terms and appear in the Friedmann equation derived from f(R) gravitational equations. This approach has an advantage over f(R) dark energy models in three ways: (i) results are consistent with WMAP observations, (ii) dark matter is produced from the gravitational sector and (iii) the universe expands as ~ t2/3 during dominance of the curvature-induced dark matter, which is consistent with the standard cosmology. Curvature-induced dark energy mimics phantom and causes late acceleration. It is found that transition from matter-driven deceleration to acceleration takes place at the redshift 0.36 at time 0.59 t0 (t0 is the present age of the universe). Different phases of this model, including acceleration and deceleration during the phantom phase, are investigated. It is found that expansion of the universe will stop at the age of 3.87 t0 + 694.4 kyr. After this epoch, the universe will contract and collapse by the time of 336.87 t0 + 694.4 kyr. Further, it is shown that cosmic collapse obtained from classical mechanics can be avoided by making quantum gravity corrections relevant near the collapse time due to extremely high energy density and large curvature analogous to the state of the very early universe. Interestingly, the cosmological constant is also induced here; it is extremely small in the classical domain but becomes very high in the quantum domain. This result explains the largeness of the cosmological constant in the early universe due to quantum gravity effects during this era and its very low value in the present universe due to negligible quantum effect in the late universe.

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