Scaling Symmetry Research Articles

Negative flows and non-autonomous reductions of the Volterra lattice

We study reductions of the Volterra lattice corresponding to stationary equations for the additional, noncommutative subalgebra of symmetries. It is shown that, in the case of general position, such a reduction is equivalent to the stationary equation for a sum of the scaling symmetry and the negative flows, and is written as $(m+1)$-component difference equations of the Painlev\'e type generalizing the dP$_1$ and dP$_{34}$ equations. For these reductions, we present the isomonodromic Lax pairs and derive the B\"acklund transformations which form the $\mathbb{Z}^m$ lattice.

Validation of symmetry-induced high moment velocity and temperature scaling laws in a turbulent channel flow.

The symmetry-based turbulence theory has been used to derive new scaling laws for the streamwise velocity and temperature moments of arbitrary order. For this, it has been applied to an incompressible turbulent channel flow driven by a pressure gradient with a passive scalar equationcoupled in. To derive the scaling laws, symmetries of the classical Navier-Stokes and the thermal energy equationshave been used together with statistical symmetries, i.e., the statistical scaling and translation symmetries of the multipoint moment equations. Specifically, the multipoint moments are built on the instantaneous velocity and temperature fields other than in the classical approach, where moments are based on the fluctuations of these fields. With this instantaneous approach, a linear system of multipoint correlation equationshas been obtained, which greatly simplifies the symmetry analysis. The scaling laws have been derived in the limit of zero viscosity and heat conduction, i.e., Re_{τ}→∞ and Pr>1, and they apply in the center of the channel, i.e., they represent a generalization of the deficit law, thus extending the work of Oberlack etal. [Phys. Rev. Lett. 128, 024502 (2022)0031-900710.1103/PhysRevLett.128.024502]. The scaling laws are all power laws, with the exponent of the high moments all depending exclusively on those of the first and second moments. To validate the new scaling laws, the data from a large number of direct numerical simulations (DNS) for different Reynolds and Prandtl numbers have been used. The results show a very high accuracy of the scaling laws to represent the DNS data. The statistical scaling symmetry of the multipoint moment equations, which characterizes intermittency, has been the key to the new results since it generates a constant in the exponent of the final scaling law. Most important, since this constant is independent of the order of the moments, it clearly indicates anomalous scaling.

BMS-invariant free fermion models

We used the Cartan formalism to construct fermionic models that are compatible with Galilean or Carrollian symmetry and rigid scaling symmetry. The free Carrollian fermion model exhibits conformal Carrollian symmetry which is isomorphic to the asymptotic symmetries for flat spacetime in three dimensions, namely the BMS3 symmetry. We performed canonical quantization to this free Bondi-van der Burg-Metzner-Sachs (BMS) fermion model, discussed both the highest weight vacuum and the induced vacuum, calculated the correlation functions and the torus partition function. Finally, we constructed N=2 supersymmetric theories by combining the free fermion model and the free scalar model []. Published by the American Physical Society 2024

Theoretical analysis of radiation effects in laminar flow over a von-Kármán body of revolution

An analysis presents the impact of thermal radiation on the laminar boundary layer established due to the motion of a von-Kármán surface. The reason for choosing such a shape is its appearance in many aeronautical vehicles, especially the F-16 fighter jet nose cone. However, the transverse curvature effects are also observable in many other shapes of bodies of revolution. But considering such a practical body of revolution provides a chance to quantify the transport phenomena happening on sophisticated aerospace vehicles. As a result, a correct understanding of the momentum and the thermal process in actual situations can be achieved. Power-law form of wall temperature is assumed to cover a variety of non-isothermal wall conditions. The typical body contour of a von-Kármán surface does not allow the scaling symmetry in the longitudinal direction; thus making the flow of non-similar in nature. An efficient numerical scheme (Keller–Box) with the second order accuracy is used for the solution purposes. The results are found to be satisfactory regarding the previous published work for moving cylinder cases. This ensures the validity of the tabulated data for the von-Kármán surface case. Through numerous tables and graphs, the impacts of thermal radiation parameter, wall temperature exponent, and transverse curvature parameter have been highlighted and thoroughly analyzed. Once the radiation parameter is increased, it is noticed that the rate of heat transfer increases and the thermal thickness of the boundary layer grows, whereas the reverse behavior is seen when the wall temperature exponent is increased. Furthermore, it has been found that increasing the surface transverse curvature increases the thermal thickness of the boundary layer and the rate of heat transfer. To the considered body shape, the reported data are expected to serve as a good source for the development of approximate methods concerning complex flow geometries involving transverse curvature effects.

Emergent scalar symmetry in discrete dynamical systems

Discrete quadratic dynamical systems are frequently used to define models of reality. To understand these recursive systems is to know the behavior of their complex orbits. The Mandelbrot Set plays an important role in this: the behavior of the orbits of its points can be extrapolated to all quadratic polynomials. In calculating the map of periods for the orbits of the points belonging to the Mandelbrot Set by means of discrete (and finite) encoding, some singular points called symmetrical points appear on the map. Such points configure, in a surprisingly harmonic and regular manner, the values of the rest of points in the map of periods. Thus, knowing these points and their properties is extremely helpful to better understand the behavior of quadratic and discrete dynamical systems. Important properties of such points are described in this article. We emphasize the emergent scalar symmetry property, which appears as a consequence of the finiteness of discrete values with which we are inevitably limited to represent the continuum. Thanks to this property, the images created around these points are not altered when removing or selecting one of their several pixel rows and columns. The image can be sampled in its vicinity, at any scale, without losing information regarding the vicinity. We propose a justification on why the map of periods is highly hypersensitive to small changes in the parameters defining the calculation mode of the map.

Non-minimally coupled scalar field and scaling symmetry in a cosmological background

We study Noether symmetries of a class of non-minimally coupled scalar field in a background spatially flat Friedmann-Robertson-Walker (FRW) spacetime. We explore the model symmetries and its conserved currents and charges. Especially, the scaling symmetry, its possible break down and outcomes of such a symmetry breaking are treated in details. A suitable potential of the non-minimally coupled scalar field is adopted which is necessary to get a symmetric Lagrangian of the system including gravity, scalar field and ordinary matter density. We use the obtained charge and the adopted potential in the equations of motions to see the role of the non-minimal coupling (NMC) on the cosmic expansion. We study evolution of the scalar field in the phase space of the model and explore the stability of the obtained critical point. In this manner we derive a relation that relates the cosmological constant and gravitational constant via a unique identity which reflects the scaling symmetry breaking in the space (a, φ).

$\mu-e$ conversion in a model of electroweak scale right-handed neutrino mass

We perform a detailed analysis of the \(\mu-e\) conversion within an extended version of the standard model (SM) with mirror symmetry and low energy of the electroweak scale of the type I seesaw neutrino mass generation. After a brief introduction to the model, we derive the \(\mu-e\) conversing ratio at one-loop approximation, in which the running inside are W gauge boson or singly charged scalars accompanying with neutrinos, and neutral scalars with new leptons. We focus, mainly, on predictions of observable possibilities and constraints set on relevant couplings from the \(\mu-e\) conversion in nuclei.

Local scale symmetry in non-riemannian geometry based gravitational theories and the role of the noether current

Local scale symmetry in non-riemannian geometry based gravitational theories and the role of the noether current

CanStoc: A Hybrid Stochastic–GCM System for Monthly, Seasonal and Interannual Predictions

Beyond their deterministic predictability limits of ≈10 days and 6 months, the atmosphere and ocean become effectively stochastic. This has led to the development of stochastic models specifically for this macroweather regime. A particularly promising approach is based on the Fractional Energy Balance Equation (FEBE), an update of the classical Budyko–Sellers energy balance approach. The FEBE has scaling symmetries that imply long memories, and these are exploited in the Stochastic Seasonal and Interannual Prediction System (StocSIPS). Whereas classical long-range forecast systems are initial value problems based on spatial information, StocSIPS is a past value problem based on (long) series at each pixel. We show how to combine StocSIPS with a classical coupled GCM system (CanSIPS) into a hybrid system (CanStoc), the skill of which is better than either. We show that for one-month lead times, CanStoc’s skill is particularly enhanced over either CanSIPS or StocSIPS, whereas for 2–3-month lead times, CanSIPS provides little extra skill. As expected, the CanStoc skill is higher over ocean than over land with some seasonal dependence. From the classical point of view, CanStoc could be regarded as a post-processing technique. From the stochastic point of view, CanStoc could be regarded as a way of harnessing extra skill at the submonthly scales in which StocSIPS is not expected to apply.

Scaling symmetries and canonoid transformations in Hamiltonian systems

In this paper, we investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case, we pay special attention to non-standard (non-canonical) symmetries, in particular scaling symmetries and canonoid transformations, as they provide new interesting tools for the qualitative study of these systems. Our main results are the characterizations of these non-standard symmetries and the analysis of their relation with conserved (or dissipated) quantities.

Standard Model in conformal geometry: Local vs gauged scale invariance

We discuss comparatively local versus gauged Weyl symmetry beyond Standard Model (SM) and Einstein gravity and their geometric interpretation. The SM and Einstein gravity admit a natural embedding in Weyl integrable geometry which is a special limit of Weyl conformal (non-metric) geometry. The theory has a local Weyl scale symmetry but no associated gauge boson. Unlike previous models with such symmetry, this embedding is truly minimal i.e. with no additional fields beyond SM and underlying geometry. This theory is compared to a similar minimal embedding of SM and Einstein gravity in Weyl conformal geometry (SMW) which has a full gauged scale invariance, with an associated Weyl gauge boson. At large field values, both theories give realistic, Starobinsky–Higgs like inflation. The broken phase of the current model is the decoupling limit of the massive Weyl gauge boson of the broken phase of SMW, while the local scale symmetry of the current model is part of the larger gauged scale symmetry of SMW. Hence, the current theory has a gauge embedding in SMW. Unlike in the SMW, we note that in models with local scale symmetry the associated current is trivial, which is a concern for the physical meaning of this symmetry. Therefore, the SMW is a more fundamental UV completion of SM in a full gauge theory of scale invariance that generates Einstein gravity in the (spontaneously) broken phase, as an effective theory.

Cosmic expansion and Noether Gauge symmetries in [formula omitted] gravity

The present work explores different evolutionary phases of isotropically homogeneous and flat cosmos filled with dust fluid in non-minimally coupled gravity. We consider different models of this gravity to discuss the presence of symmetry generators together with conserved integrals using Noether Gauge symmetry scheme. In most of the cases, we obtain temporal and scaling symmetries that yield conservation of energy and linear momentum, respectively. In the absence of contracted Ricci and energy–momentum tensors, we obtain maximum symmetries but none of them correspond to any standard symmetry or conservation law. We formulate exact solutions and construct graphical analysis of standard cosmological parameters. We observe realistic nature of new models via squared speed of sound, viability conditions suggested by Dolgov-Kawasaki instability and state-finder parameters. We investigate the behavior of fractional densities and check the compatibility with Planck 2018 observational data. The new models are stable and viable preserving compatibility with ΛCDM and Chaplygin gas models. It is concluded that most of the solutions favor accelerated cosmic expansion.

Multi-Wavelength Coherent-Perfect-Absorption−Laser Points and Half-Wave Phase Shift in Parity-Time-Reciprocal Scaling Symmetry Structure

Two slabs of dielectrics with different values of refractive index are synthesized to form a composite structure and the whole system satisfies parity-time-reciprocal scaling symmetry. Four coherent-perfect-absorber-laser points are induced by modulating the incident wavelength of lightwaves and the loss/gain factor of materials. The locations of coherent-perfect-absorber-laser points in parameter space, which manifests the multi-wavelengths of coherent-perfect-absorber-lasers could be regulated by the incidence angle. Especially, a value of π phase shift in the transmitted/reflected light wave has been observed as well. This research has potential applications in multi-wavelength absorbers/lasers and half-wave phase shifters.

Modelling coupled electro-mechanical phenomena in elastic dielectrics using local conformal symmetry

The local scaling symmetry of the Lagrange density is exploited to investigate the myriad electro-mechanical coupling effects observed in the elastic dielectrics. In contrast to most known flexoelectricity theories, this approach has also explicated on the geometric underpinnings of the induced polarization and electric potential. Due to the inhomogeneous scaling of the metric, the invariance of the Lagrange density will be lost. To restore the gauge invariance of the Lagrange density, we introduce the notion of minimal replacement, viz., define a gauge covariant operator in place of the ordinary partial derivative. Minimal replacement introduces gauge compensating one form field. We relate the exact part of the gauge compensating one form field with electric potential. However, the gauge compensating one form field's anti-exact part is correlated with the electric polarization vector. We constructed different components of the gauge invariant energy density using the geometric objects like scale invariant gauge curvature. We appropriately contracted the skew symmetric gauge curvature tensor with the metric to construct the scale invariant energy associated with the gauge field. Finally, we derive the governing coupled equations employing Hamilton's principle. In order to assess how the theory performs, we carry out a few numerical simulations and validation. Model prediction of the pressurized flexoelectric disk with a central hole shows good agreement with the analytical solution. We also investigated flexoelectric cantilever beam subjected to a point load and different earthing conditions. Explorations of this kind of coupling may have notable implications in many industrial and laboratory applications.

Operando Electron Microscopy of Catalysts: The Missing Cornerstone in Heterogeneous Catalysis Research?

Heterogeneous catalysis in thermal gas-phase and electrochemical liquid-phase chemical conversion plays an important role in our modern energy landscape. However, many of the structural features that drive efficient chemical energy conversion are still unknown. These features are, in general, highly distinct on the local scale and lack translational symmetry, and thus, they are difficult to capture without the required spatial and temporal resolution. Correlating these structures to their function will, conversely, allow us to disentangle irrelevant and relevant features, explore the entanglement of different local structures, and provide us with the necessary understanding to tailor novel catalyst systems with improved productivity. This critical review provides a summary of the still immature field of operando electron microscopy for thermal gas-phase and electrochemical liquid-phase reactions. It focuses on the complexity of investigating catalytic reactions and catalysts, progress in the field, and analysis. The forthcoming advances are discussed in view of correlative techniques, artificial intelligence in analysis, and novel reactor designs.

Isotropic exact solutions via Noether symmetries in f(R, T, R μ ν T μ ν ) gravity

In this paper, we study cosmic evolutionary stages in the background of modified theory admitting non-minimal coupling between Ricci scalar, trace of the energy-momentum tensor, contracted Ricci and energy-momentum tensors. For dust distribution, we consider isotropic, homogeneous and flat cosmic model to determine symmetry generators, conserved integrals and exact solutions using Noether symmetry scheme. We find maximum symmetries for non-minimally interacting Ricci scalar and trace of the energy-momentum tensor but none of them correspond to any standard symmetry. For rest of the models, we obtain scaling symmetry with conserved linear momentum. The graphical analysis of standard cosmological parameters, squared speed of sound, viability conditions suggested by Dolgov-Kawasaki instability and state-finder parameters identify realistic nature of new models compatible with Chaplygin gas model, quintessence and phantom regions. The fractional densities relative to ordinary matter and dark energy are found to be consistent with Planck 2018 observational data. It is concluded that the constructed non-minimally coupled models successfully explore cosmic accelerated expansion.

Scaling symmetries, contact reduction and Poincaré’s dream

We state conditions under which a symplectic Hamiltonian system admitting a certain type of symmetry (a scaling symmetry) may be reduced to a type of contact Hamiltonian system, on a space of one less dimension. We observe that such contact reductions underly the well-known McGehee blow-up process from classical mechanics. As a consequence of this broader perspective, we associate a type of variational Herglotz principle associated to these classical blow-ups. Moreover, we consider some more flexible situations for certain Hamiltonian systems depending on parameters, to which the contact reduction may be applied to yield contact Hamiltonian systems along with their Herglotz variational counterparts as the underlying systems of the associated scale-invariant dynamics. From a philosophical perspective, one obtains an equivalent description for the same physical phenomenon, but with fewer inputs needed, thus realizing Poincaré’s dream of a scale-invariant description of the Universe.

Dynamically vanishing Dirac neutrino mass from quantum scale symmetry

We present a mechanism which drives Dirac neutrino masses to tiny values along the Renormalization Group flow, starting from an asymptotically safe ultraviolet completion of the third generation of the Standard Model including quantum gravity. At the same time, the mechanism produces a mass-splitting between the neutrino and the quark sector and also generates the mass splitting between top and bottom quark. The mechanism hinges on the hypercharges of the fermions and produces a tiny neutrino Yukawa coupling, because the right-handed neutrino is sterile and does not carry hypercharge.

Dark stars and gravitational waves: Topical review

Motivated by recent observations of compact binary gravitational wave events reported by LIGO/Virgo/KAGRA, we review the basics of dark and hybrid stars11In this review “hybrid stars” means “dark-matter admixed stars”, though this term usually refers to compact stars that compose of both hadronic and quark matter. and examine their probabilities as mimickers for black holes and neutron stars. This review aims to survey this exciting topic and offer the necessary tools for the research study at the introductory level. Although called a review, some results are newly derived, such as the equations of state for specific dark star models and the scaling symmetry for the Tidal Love number.

Scale anomaly in a Lorentz and CPT-violating quantum electrodynamics

We compute the classical and the quantum breaking of the dilatation current in the minimal Lorentz and CPT-violating quantum electrodynamics. At the classical level, scale symmetry is broken by the general mass term and the Chern-Simons–like term. At the quantum level, it is broken by all expected observable fermion operators in the massless limit.