Galilean Invariance Research Articles

Effect of blade tip cutting angle on energy conversion mechanism of side channel pumps

Typical industrial blade side channel pumps with tip cuts have been used for many years because the blade profile has significant effect on the performance of the pump. To investigate the effect of the tip cutting angle on the energy conversion mechanism of the pump, the original and the industrial blades with different tip cutting angles were studied in detail. A comprehensive analysis revealed that the cutting tip enhances the hydraulic performance of the side channel pump, especially when the angle is equal to 20°. The act of cutting the tip reduces the intersection of exchanged inflow and outflow between the impeller and side channel, especially at the outer radius, and eliminates the secondary flow at the corner. Furthermore, the application of the new Ω vortex identification method characterizes the dynamic vortex structures in three directions: axial, longitudinal, and radial. Based on the Galilean invariance of the vorticity, this paper operates coordinate transformation and uses the dimension reduction method to simplify the complex 3D (3 dimensional) vortex into 2D (2 dimensional) vortex intensity on specific research surfaces. By comparing each type of vortex, it can be established that the total vortex in the tip cutting scheme is more than the original scheme. This is because the cutting tip will produce extra space for vortex formation. Thus, the cutting tip schemes lead to a higher longitudinal vortex and lower axial vortex, thereby increasing the dynamic vortex and decreasing of the unfavorable vortex is the main reason for better performance. While the radial vortex seems equivalent, the tip cutting will increase this kind of vortex in the outlet region but decrease it in the inlet region as above. This work helps to understand the mechanism of energy conversion of side channel pumps and serves as a guide for further research in fluid engineering with strong swirling flows.

Unification of General Relativity and Quantum Mechanics by the Principle of Central System Relativity

This particular article is devoted to a breakthrough which is waiting for 100 years of physics. In this particular article I am unifying two kind of physical structures and law’s governed by them with help of Principle of Central System Relativity obtained by me in my previous article named “Generalization of various kinds of Central Systems exist in Universe and their mathematical representations” [6]. Albert Einstein tried to unify both theories which work on macroscopic and microscopic level (Quantum Mechanics and General Relativity) in his last years as Unified field theory (UFT) but failed. Basically these both theories came from his miraculous year 1905 and 1915 or from his five excellent papers [7] which changed the fundamental understandings of theoretical physics. In this article I had obtained a Universal Principle of Central System Relativity which applied on all type of Geometrical scales exist in Universe. The Principle of Central System Relativity holds in and N-Central Systems predicted by N-Time Inflationary Model of Universe (Obtained by me in my previous paper [6]). This article unified both theories on Macroscopic and Microscopic level (Respectively General Relativity and Quantum Mechanics) into one single theory- “Universal Mechanics”. So, in this particular article I have unified both Macroscopic and Microscopic structures into one single physical structure which is more unique in universal sense and also generalized (theoretically and mathematically) almost all fundamental principles of both physical structures in universal sense and then unified them with help of the Principle of Central System Relativity on each type of bodies (created during each inflation) exists in Universe. On the other hand I also obtained a very elegant principle of relativity defined by me as “Principle of Universal Relativity” which satisfies both Galilean Relativity [22] and Einstein’s Relativity [7] and also includes a very different new term which appears in universal sense or not for observers on same body (like we are on Earth). Key Words: Central

The electric dipole response of even-even 154–164Dy isotopes

The excitation of pygmy dipole resonance (PDR) and giant dipole resonance (GDR) in even–even 154–164Dy isotopes is examined through quasiparticle random-phase approximation (QRPA) with the effective interactions that restore the broken translational and Galilean invariances. In each isotope, an electric response emerges by showing ample distribution at energies below and above 10 MeV. We, therefore, study the transition cross-sections and probabilities, photon strength functions, transition strengths, isospin character, and collectivity of the predicted E1 responses.

Hidden scale invariance in Navier-Stokes intermittency.

We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centres. At a dynamical level, the hidden symmetry projects solutions which differ up to Galilean invariance and global temporal scaling onto the same representative flow. At a statistical level, this projection repairs the scale invariance, which is broken by intermittency in the original formulation. Following previous work by the first author, we here postulate and substantiate with numerics that hidden symmetry statistically holds in the inertial interval of fully developed turbulence. We show that this symmetry accounts for the scale-invariance of a certain class of observables, in particular, the Kolmogorov multipliers. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

Cosmological functional renormalization group, extended Galilean invariance, and approximate solutions to the flow equations

The functional renormalisation group is employed to study the non-linear regime of late-time cosmic structure formation. This framework naturally allows for non-perturbative approximation schemes, usually guided by underlying symmetries or a truncation of the theory space. An extended symmetry that is related to Galilean invariance is studied and corresponding Ward identities are derived. These are used to obtain (formally) closed renormalisation group flow equations for two-point correlation functions in the limit of large wave numbers (small scales). The flow equations are analytically solved in an approximation that is connected to the 'sweeping effect' previously described in the context of fluid turbulence.

Dragging spin–orbit-coupled solitons by a moving optical lattice

It is known that the interplay of the spin–orbit-coupling (SOC) and mean-field self-attraction creates stable two-dimensional (2D) solitons (ground states) in spinor Bose–Einstein condensates. However, SOC destroys the system’s Galilean invariance, therefore moving solitons exist only in a narrow interval of velocities, outside of which the solitons suffer delocalization. We demonstrate that the application of a relatively weak moving optical lattice (OL), with the 2D or quasi-1D structure, makes it possible to greatly expand the velocity interval for stable motion of the solitons. The stability domain in the system’s parameter space is identified by means of numerical methods. In particular, the quasi-1D OL produces a stronger stabilizing effect than its full 2D counterpart. Some features of the domain are explained analytically.

BIBLICAL THESIS ABOUT CREATION “EX NIHILO” AND THE RELATIONAL PARADIGM OF PHYSICS

The biblical story begins with the story of the creation of the world out of nothing. In the context of theological tradition, creation means non-self-being; this is the reason for the constant variability of the universe. Biblical Revelation presupposes the assumption of a special kind of ontology of creation: nothing is self-existent, all being is relative and everything is relative to God. The entire history of natural science, starting with Galileo, shows that its development proceeded along the path of concretizing and expanding the field of applicability of the principle of the relativity of being: from Galilean relativity - to Einstein’s special theory of relativity - and, finally, to quantum mechanics - to the fact that one of the greatest physicists of the XX century academician Vladimir Fock called the principle of relativity to the means of observation. Considering quantum mechanics as the last natural link in this chain of realization of the principle of relativity in physics, we can, from the many alternative interpretations of quantum mechanics existing today, single out those that are organically consistent with the fundamental biblical principle of the relativity of being and consistently explain what is perceived as quantum paradoxes. This will allow you to take the next step towards comprehending the fundamental nature of reality.

Computational Fluid Dynamics Transition Models Validation for Rotors in Unsteady Flow Conditions

Computational fluid dynamics transition models are evaluated for rotors in unsteady axial and in forward flight conditions. The study is carried out using CREATETM-AV Helios. Three transition models are considered: amplification factor transport (AFT), Langtry–Menter (LM), and the LM with a crossflow transition model. The LM model is modified to allow for Galilean invariance. The first rotor configuration is the German Aerospace Center (DLR) rotor tested in the Rotor Test Facility in Göttingen (RTG). It is a four-blade, 2.13-foot-radius rotor in axial flow with pitching blades, operating at Reynolds numbers of and at three quarter radius, for the two test cases studied. The second configuration is the pressure-sensitive-paint rotor. It is a model-scale, 5.58-foot-radius, three-blade rotor operating at a high-advance-ratio, high-thrust forward flight condition and a hover Reynolds number of at three quarter radius. For both rotors, good agreement is found between the computed and the measured transition locations, obtained using the differential infrared thermography technique. The AFT and LM models produced remarkably consistent predictions. The crossflow model predicted an early transition onset compared with the test data.

Data-driven model development for large-eddy simulation of turbulence using gene-expression programing

We apply the gene-expression programing (GEP) method to develop subgrid-scale models for large-eddy simulations (LESs) of turbulence. The GEP model is trained based on Galilean invariants and tensor basis functions, and the training data are from direct numerical simulation (DNS) of incompressible isotropic turbulence. The model trained with GEP has been explicitly tested, showing that the GEP model can not only provide high correlation coefficients in a priori tests but also show great agreement with filtered DNS data when applied to LES. Compared to commonly used models like the dynamic Smagorinsky model and the dynamic mixed model, the GEP model provides significantly improved results on turbulence statistics and flow structures. Based on an analysis of the explicitly given model equation, the enhanced predictions are related to the fact that the GEP model is less dissipative and that it introduces high-order terms closely related to vorticity distribution. Furthermore, the GEP model with the explicit equation is straightforward to be applied in LESs, and its additional computational cost is substantially smaller than that of models trained with artificial neural networks with similar levels of predictive accuracies in a posteriori tests.

Data-driven model for improving wall-modeled large-eddy simulation of supersonic turbulent flows with separation

A machine learning algorithm is presented, serving as a data-driven modeling tool for wall-modeled large eddy simulations (WMLESs). The proposed model is formulated to address the problems of log layer mismatch and inaccurate prediction of skin friction, particularly for supersonic separated and reattached flows. This machine learning algorithm uses random forest regression to map the local mean flow fields to the discrepancies in the skin friction (heat flux) while complying with Galilean invariance as the flow features input is provided using relative velocities. The model is tested on two different supersonic flows, namely, flow over a flat plate and flow around an expansion-compression corner. The performance is evaluated by comparing the skin friction (heat flux) and flow properties with exact values. The ultimate goal is to build a robust and generalizable machine learning model to improve the prediction of WMLES of supersonic flows. To this end, the model is trained by a set of flows containing some essential flow physics to devise a generalizable model. Although the general machine learning model shows some advantages over the baseline WMLES model, it is concluded the data set is far from being representative of the rich flow physics model; therefore, the machine learning model should be trained and tested by a broader set of flows.

Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems.

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an entropic pair—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of entropic mechanics, the study of the relative motions of objects with friction.

New governing equations for fluid dynamics

The difference in the governing equation between inviscid and viscous flows is the introduction of viscous terms. Traditional Navier–Stokes (NS) equations define stress based on Stokes’s assumptions. In NS equations, stress is supposedly proportional to strain, and both strain and stress tensors are symmetric. There are several questions with NS equations, which include the following: 1. Both symmetric shear terms and stretching terms in strain and stress are coordinate-dependent and thus not Galilean invariant. 2. The physical meaning of both diagonal and off-diagonal elements is not clear, which is coordinate-dependent. 3. It is hard to measure strain and stress quantitatively, and viscosity is really measured by vorticity, not by symmetric strain. 4. There is no vorticity tensor in NS equations, which plays an important role in fluid flow, especially for turbulent flow. The newly proposed governing equations for fluid dynamics use the vorticity tensor only, which is anti-symmetric. The advantages include the following: 1. Both shear and stress are anti-symmetric, which are Galilean invariants and independent of coordinate rotation. 2. The physical meaning of off-diagonal elements is clear, which is anti-symmetric shear stress. 3. Viscosity coefficients are obtained by experiments, which use vorticity. 4. The vorticity term can be further decomposed into rigid rotation and anti-symmetric shear, which are important to turbulence research. 5. The computation cost for the viscous term is reduced to half as the diagonal terms are all zero and six elements are reduced to three. Several computational examples are tested, which clearly demonstrate both NS and new governing equations have exactly the same results. As shown below, the new governing equation is identical to NS equations in mathematics, but the new one has lower cost and the several advantages mentioned above, including the possibility to study turbulent flow better. It is recommended to use the new governing equation instead of NS equations. The unique definition and operation of vectors and tensors by matrix and matrix operation are also discussed in this paper.

When scale is surplus

We study a long-recognised but under-appreciated symmetry called dynamical similarity and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton’s principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology.

Galilean transformation in polar coordinates and Doppler effect

First, the derivation of the Galilean transformation in polar coordinates from the Galilean transformation in Cartesian coordinates is presented. Next, it is shown that the Doppler effect formula can be derived very easily from the Galilean transformation in polar coordinates. Indeed, this shows that the Doppler effect is nothing more than Galilean relativity – respectively, that the Doppler effect formula is the Galilean transformation in polar coordinates.

The large scale structure bootstrap: perturbation theory and bias expansion from symmetries

We investigate the role played by symmetries in the perturbative expansion of the large-scale structure. In particular, we establish which of the coefficients of the perturbation theory kernels are dictated by symmetries and which not. Up to third order in perturbations, for the dark matter density contrast (and for the dark matter velocity) only three coefficients are not fixed by symmetries and depend on the particular cosmology. For generic biased tracers, where number/mass and momentum conservation cannot be imposed in general, this number rises to seven in agreement with other bias expansions discussed in the literature. A crucial role in our analysis is provided by extended Galilean invariance, which follows from diffeomorphism invariance in the non-relativistic limit. We identify a full hierarchy of extended Galilean invariance constraints, which fix the analytic structure of the perturbation theory kernels as the sums of an increasing number of external momenta vanish.Our approach is especially relevant for non-standard models that respect the same symmetries as ΛCDM and where perturbation theory at higher orders has not been exhaustively explored, such as dark energy and modified gravity scenarios.In this context, our results can be used to systematically extend the bias expansion to higher orders and set up model independent analyses.

Galilean first-order formulation for the nonrelativistic expansion of general relativity

We reformulate the Palatini action for general relativity (GR) in terms of moving frames that exhibit local Galilean covariance in a large speed of light expansion. For this, we express the action in terms of variables that are adapted to a Galilean subgroup of the $GL(n,\mathbb{R})$ structure group of a general frame bundle. This leads to a novel Palatini-type formulation of GR that provides a natural starting point for a first-order non-relativistic expansion. In doing so, we show how a comparison of Lorentzian and Newton-Cartan metric-compatibility explains the appearance of torsion in the non-relativistic expansion.

Effective theory of nuclear scattering for a WIMP of arbitrary spin

We introduce a systematic approach to characterize the most general non-relativistic WIMP-nucleus interaction allowed by Galilean invariance for a WIMP of arbitrary spin $j_\chi$ in the approximation of one-nucleon currents. Five nucleon currents arise from the nonrelativistic limit of the free nucleon Dirac bilinears. Our procedure consists in (1) organizing the WIMP currents according to the rank of the $2 j_\chi+1$ irreducible operator products of up to $2 j_\chi$ WIMP spin vectors, and (2) coupling each of the WIMP currents to each of the five nucleon currents. The transferred momentum $q$ appears to a power fixed by rotational invariance. For a WIMP of spin $j_\chi$ we find a basis of 4+20$j_\chi$ independent operators that exhaust all the possible operators that drive elastic WIMP-nucleus scattering in the approximation of one-nucleon currents. By comparing our operator basis, which is complete, to the operators already introduced in the literature we show that some of the latter for $j_\chi=1$ were not independent and some were missing. We provide explicit formulas for the squared scattering amplitudes in terms of the nuclear response functions, which are available in the literature for most of the targets used in WIMP direct detection experiments.

Dirac composite fermion theory of general Jain sequences

We reconsider the composite fermion theory of general Jain's sequences with filling factor $\nu=N/(4N\pm1)$. We show that Goldman and Fradkin's proposal of a Dirac composite fermion leads to a violation of the Haldane bound on the coefficient of the static structure factor. To resolve this apparent contradiction, we add to the effective theory a gapped chiral mode (or modes) which already exists in the Fermi liquid state at $\nu=1/4$. We interpret the additional mode as an internal degree of freedom of the composite fermion, related to area-preserving deformations of the elementary droplet built up from electrons and correlation holes. In addition to providing a suitable static structure factor, our model also gives the expected Wen-Zee shift and a Hall conductivity that manifests Galilean invariance. We show that the charge density in the model satisfies the long-wavelength version of the Girvin-MacDonald-Platzman algebra.

Electromagnetic response of composite Dirac fermions in the half-filled Landau level

An effective field theory of composite Dirac fermions was proposed by Son [Phys. Rev. X 5, 031027 (2015)] as a theory of the half-filled Landau level with explicit particle-hole symmetry. We compute the electromagnetic response of this Son-Dirac theory on the level of the random phase approximation (RPA), where we pay particular attention to the effect of an additional composite-fermion dipole term that is needed to restore Galilean invariance. We find that once this dipole correction is taken into account, spurious interband transitions and collective modes that are present in the response of the unmodified theory either cancel or are strongly suppressed. We demonstrate that this gives rise to a consistent theory of the half-filled Landau level valid at all frequencies, at least to leading order in the momentum. In addition, the dipole contribution modifies the Fermi-liquid response at small frequency and momentum, which is a prediction of the Son-Dirac theory within the RPA that distinguishes it from a separate description of the half-filled Landau level by Halperin, Lee, and Read within the RPA.

Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence

Dynamic iterative approximate deconvolution (DIAD) models with Galilean invariance are developed for subgrid-scale (SGS) stress in the large-eddy simulation (LES) of turbulence. The DIAD models recover the unfiltered variables using the filtered variables at neighboring points and iteratively update model coefficients without any a priori knowledge of direct numerical simulation (DNS) data. The a priori analysis indicates that the DIAD models reconstruct the unclosed SGS stress much better than the classical velocity gradient model and approximate deconvolution model with different filter scales ranging from viscous to inertial regions. We also propose a small-scale eddy viscosity (SSEV) model as an artificial dissipation to suppress the numerical instability based on a scale-similarity-based dynamic method without affecting large-scale flow structures. The SSEV model can predict a velocity spectrum very close to that of DNS data, similar to the traditional implicit large-eddy simulation. In the a posteriori testing, the SSEV-enhanced DIAD model is superior to the SSEV model, dynamic Smagorinsky model, and dynamic mixed model, which predicts a variety of statistics and instantaneous spatial structures of turbulence much closer to those of filtered DNS data without significantly increasing the computational cost. The types of explicit filters, local spatial averaging methods, and initial conditions do not significantly affect the accuracy of DIAD models. We further successfully apply DIAD models to the homogeneous shear turbulence. These results illustrate that the current SSEV-enhanced DIAD approach is promising in the development of advanced SGS models in the LES of turbulence.