Dynamical Symmetry Research Articles

Assessment of deep plane facelift combined with fascia lata graft for the static treatment of facial palsy: A preliminary report

Addressing facial palsy (FP) presents intricate challenges in achieving natural expressions.While free functional muscle transfers (FFMT) offer effective smile restoration, age impacts their efficacy.The optimal FFMT age range of 5-55 is limited by physical fitness, which extends beyond age boundaries. Unilateral FP demands vary; younger patients require dynamic solutions like FFMT, whereas older individuals prioritize public appearance due to baseline distortion. The aim of this study is to describe and to assess a new static technique combining deep plane facelift and fascia lata graft (FLG) for FP treatment. We conducted a prospective pilot study enrolling unilateral FP patients aged >55 and declining FFMT. Exclusions encompassed prior FP surgery, recent injections, uncontrolled diabetes cognitive deficits and Patients unable to quit smoking.To evaluate this technique, the Glasgow Benefit Inventory (GBI), along with two objective scales: the Face and Neck-Lift Objective Photo-Numerical Assessment Scale and the eFACE scale, were used. Interrater reliability and Intrarater reliability were assessed. Fifteen patients (mean age: 60.9 years) underwent the procedure. Both static and dynamic symmetry significantly improved (p<0.05), including check volume and position, oral commissure, and jawline. Notably, eye closure enhancement was observed. GBI scores also significantly increased (p<0.05). Interrater reliability and Intrarater reliability were minimal (p=0.12 and p=0.13).This combined approach offers a static FP treatment option, especially for the elderly or FFMT-ineligible patients. The relatively brief procedure yields immediate and satisfactory results, suggesting its potential value in FP management. Further comprehensive studies are encouraged to validate the technique's long-term efficacy and applicability across larger populations.

Conservation and breaking of pseudospin symmetry

Pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the lower component of the Dirac spinor. Here, we investigate the conservation and breaking of PSS in the single-nucleon resonant states, as an example, using Green's function method that provides a novel way to precisely describe not only the resonant energies and widths but also the spacial density distributions for both narrow and wide resonances. The PSS conservation and breaking are perfectly displayed in the evolution of resonant parameters and density distributions with the potential depth: In the PSS limit, i.e., when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign, PSS is exactly conserved with strictly the same energy and width between the PS partners as well as identical density distributions of the lower components. As the potential depth increases, the PSS is broken gradually with energy and width splittings and a phase shift in the density distributions.

Unveiling Dynamical Symmetries in 2D Chaotic Iterative Maps with Ordinal-Patterns-Based Complexity Quantifiers

Effectively identifying and characterizing the various dynamics present in complex and chaotic systems is fundamental for chaos control, chaos classification, and behavior-transition forecasting, among others. It is a complicated task that becomes increasingly difficult as systems involve more dimensions and parameters. Here, we extend methods inspired in ordinal patterns to analyze 2D iterative maps to unveil underlying approximate symmetries of their dynamics. We distinguish different families of chaos within the systems, find similarities among chaotic maps, identify approximate temporal and dynamical symmetries, and anticipate sharp transitions in dynamics. We show how this methodology displays the evolution of the spatial correlations in a dynamical system as the control parameter varies. We prove the power of these techniques, which involve simple quantifiers as well as combinations of them, in extracting relevant information from the complex dynamics of 2D systems, where other techniques are less informative or more computationally demanding.

Finding nonlocal Lie symmetries algorithmically

Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and nonlocal symmetries) admitted by a rational 2ODE if it presents a Liouvillian first integral. The procedure is based on an idea arising from the formal equivalence between the total derivative operator and the vector field associated with the 2ODE over its solutions (Cartan vector field). Basically, from the formal representation of a Lie symmetry it is possible to extract information that allows to use this symmetry practically (in the 2ODE integration process) even in cases where the formal operation cannot be performed, i.e., in cases where the symmetry is nonlocal. Furthermore, when the 2ODE in question depends on parameters, the procedure allows an analysis that determines the regions of the parameter space in which the integrable cases are located. We finish by applying the method to the 2ODE that represents a forced modified Duffing–Van der Pol oscillator (which presents chaos for arbitrary values of the parameters) and determining a region of the parameter space that leads to integrable cases, some not previously known.

Book Review: Dynamic Design: Jay Hambidge, Mary Crovatt Hambidge, and the Founding of the Hambidge Center for Creative Arts and Sciences

Book Review: Dynamic Design: Jay Hambidge, Mary Crovatt Hambidge, and the Founding of the Hambidge Center for Creative Arts and Sciences

Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model

The dynamical scaling and ageing in the relaxational dynamics of the quenched directed spherical model is analysed. The exact two-time correlation and response functions display new regimes of ballistic or anisotropic ballistic scaling, at larger distances than probed in the usual regime of diffusive scaling. The role of long-ranged initial correlations on the existence of these scaling regimes is clarified. Their dynamical symmetries are described in terms of extensions of the Schrödinger algebra appropriate to non-equilibrium dynamics in that the anisotropic ballistic scaling regime can be interpreted in terms of meta-Schrödinger invariance while the regime of isotropic ballistic scaling is meta-conformally invariant.

Active Ising Models of flocking: a field-theoretic approach

Using an approach based on Doi-Peliti field theory, we study several different Active Ising Models (AIMs), in each of which collective motion (flocking) of self-propelled particles arises from the spontaneous breaking of a discrete symmetry. We test the predictive power of our field theories by deriving the hydrodynamic equations for the different microscopic choices of aligning processes that define our various models. At deterministic level, the resulting equations largely confirm known results, but our approach has the advantage of allowing systematic generalization to include noise terms. Study of the resulting hydrodynamics allows us to confirm that the various AIMs share the same phenomenology of a first-order transition from isotropic to flocked states whenever the self-propulsion speed is nonzero, with an important exception for the case where particles align only pairwise locally. Remarkably, this variant fails entirely to give flocking—an outcome that was foreseen in previous work, but is confirmed here and explained in terms of the scalings of various terms in the hydrodynamic limit. Finally, we discuss our AIMs in the limit of zero self-propulsion where the ordering transition is continuous. In this limit, each model is still out of equilibrium because the dynamical rules continue to break detailed balance, yet it has been argued that an equilibrium universality class (Model C) prevails. We study field-theoretically the connection between our AIMs and Model C, arguing that these particular models (though not AIMs in general) lie outside the Model C class. We link this to the fact that in our AIMs without self-propulsion, detailed balance is not merely still broken, but replaced by a different dynamical symmetry in which the dynamics of the particle density is independent of the spin state.Graphical .

Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

Holographic quantum scars

We discuss a construction of quantum many-body scars in the context of holography. We consider two-dimensional conformal field theories and use their dynamical symmetries, naturally realized through the Virasoro algebra, to construct scarred states. By studying their Loschmidt amplitude, we evaluate the states’ periodic properties. A geometrical interpretation allows us to compute the expectation value of the stress tensor and entanglement entropy of these scarred states. We show that their holographic dual is related by a diffeomorphism to empty AdS, even for energies above the black hole threshold. We also demonstrate that expectation values in the scarred states are generally non-thermal and that their entanglement entropy grows with the energy as \log(E)log(E) in contrast to \sqrt{E}E for the typical (bulk) states. Furthermore, we identify fixed points on the CFT plane associated with divergent or vanishing entanglement entropy in the limit where the scarred states have infinite energy.

Description of energy levels and decay properties in 158Gd nucleus

In this paper, IBM-1 and IBM-2 with a SU(3) limit are used to describe the 158Gd isotope. The calculations of energy levels in the ground state, beta-, and gamma-bands are made up, which account for 15 energy levels. However, we found that the energy states of the same spin of the beta- and vibrational bands become degenerate states. In breaking the SU(3) dynamical symmetry by introducing a value of pairing interaction, the degeneracy is lifted and the energy levels are brought up to the same order as the experimental ones.

The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking

We present a comprehensive non-perturbative study of the phase structure of the asymptotically safe Standard Model. The physics scales included range from the asymptotically safe trans-Planckian regime in the ultraviolet, the intermediate high-energy regime with electroweak symmetry breaking to strongly correlated QCD in the infrared. All flows are computed with a self-consistent functional renormalisation group approach, using a vertex expansion in the fluctuation fields. In particular, this approach takes care of all physical threshold effects and the respective decoupling of ultraviolet degrees of freedom. Standard Model and gravity couplings and masses are fixed by their experimental low energy values. Importantly, we accommodate for the difference between the top pole mass and its Euclidean analogue. Both, the correct mass determination and the threshold effects have a significant impact on the qualitative properties, and in particular on the stability properties of the specific ultraviolet-infrared trajectory with experimental Standard Model physics in the infrared. We show that in the present rather advanced approximation the matter part of the asymptotically safe Standard Model has the same number of relevant parameters as the Standard Model, and is asymptotically free. This result is based on the novel UV fixed point found in the present work: the fixed point Higgs potential is flat but has two relevant directions. These results and their analysis are accompanied by a thorough discussion of the systematic error of the present truncation, also important for systematic improvements.

Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate

Dynamical chiral symmetry breaking (DχSB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator has been evident since the seminal work of Nambu and Jona-Lasinio has been recast in terms of QCD. It not only highlights one of the most important aspects of DχSB, the dynamical generation of constituent quark masses, but also makes plausible that DχSB is a robustly occurring phenomenon in QCD. The latter impression, however, changes when higher n-point functions are taken into account. In particular, the quark–gluon vertex, i.e., the most elementary n-point function describing the full, non-perturbative quark–gluon interaction, plays a dichotomous role: It is subject to DχSB as signalled by its scalar and tensor components but it is also a driver of DχSB due to the infrared enhancement of most of its components. Herein, the relevant self-consistent mechanism is elucidated. It is pointed out that recently obtained results imply that, at least in the covariant gauge, DχSB in QCD is located close to the critical point and is thus a delicate effect. In addition, requiring a precise determination of QCD’s three-point functions, DχSB is established, in particular in view of earlier studies, by an intricate interplay of the self-consistently determined magnitude and momentum dependence of various tensorial components of the gluon–gluon and the quark–gluon interactions.

Nuclear Shape-Phase Transition From Spherical U(5) to Deformed gamma-Unstable O(6) Dynamical Symmetries of Interacting Boson Model Applied to Ru, Pd, and Xe Isotopic Chains

The shape transition from spherical vibrator U(5) to gamma-unstable deformed rotor O(6) in even-even Ru, Pd, and Xe isotopic chains are studied in framework of sd interacting boson model (IBM1) using the coherent state formalism to obtain the potential energy surfaces (PES’s). The location of critical points in the transition are identified by analysis the PES’s in terms of the deformation parameter beta and by using the catastrophe theory in terms of the two essential parameters (r_1, r_2). By using the most general IBM1 Hamiltonian in Casimir form with neglecting the U(5) and SU(3) quadratic Casimir operators and introducing only one control parameter the PES leads to the same energy surface as the Q-consistent IBM Hamiltonian at gamma =0. For the studied isotopic chains, the chi ^2-test is used to perform the fitting between the experimental and the corresponding calculated IBM for some selected energy levels and electric quadrupole transition probabilities B(E2) values using a simulated search program. A good agreement is produced for both energies and B(E2) transition rates. The present model calculations suggest that ^{100}Ru, ^{102}Pd and ^{130}Xe nuclei are good candidates for the E(5) critical point symmetry.

The Dynamics of Small Satellites with the Three-Axial Gravitational Damper

The questions of the dynamics of the angular motion of nanosatellites with gravitational dampers are considered. The damper is a solid body rotating in a spherical cavity with a viscous liquid filling and creating internal friction with the dissipation of the kinetic energy of the angular motion. Unlike classical models of similar viscous dampers using the M.A. Lavrentiev with spherical dynamic symmetry of the body-damper, in this work the body-damper has a central triaxial ellipsoid of inertia, which increases the efficiency of interaction with an external gravitational field. This makes it possible to use almost any autonomous nanosatellite assembly as such an internal body-damper, placing it in a sealed spherical shell inside a spherical cavity with a viscous liquid in the center of mass of the main body-satellite body. The presence of a three-axis inertia tensor of the damper body changes and complicates the mathematical model of the angular motion in comparison with the classical one, which can be considered as a certain generalization and development of research in this direction.

Towards an Evidence-Based Classification System for Para Dressage: Associations between Impairment and Performance Measures.

This study follows a previously defined framework to investigate the impact of impairment on performance in Para dressage athletes. Twenty-one elite Para dressage athletes (grades I to V) and eleven non-disabled dressage athletes (competing at Prix St. Georges or Grand Prix) participated. Data were collected in two phases: performing a two minute custom dressage test on a riding simulator while kinematic data were synchronously collected using inertial measurement units (2000 Hz) and optical motion capture (100 Hz), and clinically assessed using a battery of impairment assessment tools administered by qualified therapists. Impairment and performance measures were compared between Para and non-disabled athletes. Significant differences between athlete groups were found for all impairment measures and two performance measures: simulator trunk harmonics (p = 0.027) and athlete trunk dynamic symmetry (p < 0.001). Impairment assessments of sitting function and muscle tone could predict 19 to 35% of the impact of impairment on performance in Para athletes but not in non-disabled athletes. These findings provide the basis for a robust, scientific evidence base, which can be used to aid in the refinement of the current classification system for Para dressage, to ensure that it is in line with the International Paralympic Committee's mandate for evidence-based systems of classification.

Dynamical symmetries of the anisotropic oscillator

It is well known that the Hamiltonian of an n-dimensional isotropic oscillator admits an SU(n) symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle. We introduce a novel set of canonical transformations that map an n-dimensional anisotropic oscillator to the corresponding isotropic problem. Consequently, the anisotropic oscillator is found to possess the same number of conserved quantities as the isotropic oscillator, making it maximally superintegrable too. The first integrals are explicitly calculated in the case of a two-dimensional anisotropic oscillator and remarkably, they admit closed-form expressions.

Solvable model for discrete time crystal enforced by nonsymmorphic dynamical symmetry

Solvable model for discrete time crystal enforced by nonsymmorphic dynamical symmetry

REALIZATION OF THE LAWS OF DYNAMIC SYMMETRY IN THE DESIGN OF THE ENVIRONMENT BY MEANS OF COMPUTER THREE-DIMENSIONAL MODELING

The purpose of the study is to determine the possibilities of applying the laws of dynamic symmetry in the design of the environment through computer three-dimensional modeling.&#x0D; Methodology. The study used methods of historical and logical analysis of the problem of the role of dynamic symmetry in nature, art, and design; methods of comparison, comparison, and generalization. According to the transdisciplinary approach, dynamic symmetry is considered as a phenomenon of nature, a concept of geometry, and a principle of forming in design. &#x0D; Results. The concepts of "dynamic symmetry" and "phyllotaxis" in the research of D. Hambidge have been analyzed, and the peculiarities of using the above categories to analyze the proportions of art and design objects have been revealed. It has been established that modern methods of computer modeling make it possible to use the laws of dynamic symmetry in environmental design. On the examples of design developments of interior elements (lighting fixtures, spiral staircases), the methods of combining the patterns of change in the shape and size of model elements, orientation in space, and on the plane have been shown. &#x0D; The scientific novelty of the research is in the implementation of approaches to the laws of dynamic symmetry in the design of the environment through computer three-dimensional modeling. &#x0D; Practical significance. The results of the study can be used in the study of the disciplines "3D modeling in environmental design", "Fundamentals of computer design", "Environmental design", "Design of furniture and equipment".

Control Landscape of Measurement-Assisted Transition Probability for a Three-Level Quantum System with Dynamical Symmetry

Quantum systems with dynamical symmetries have conserved quantities that are preserved under coherent control. Therefore, such systems cannot be completely controlled by means of only coherent control. In particular, for such systems, the maximum transition probability between some pairs of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximum attainable transition probability. The simplest example of such a situation occurs in a three-level quantum system with dynamical symmetry, for which the maximum probability of transition between the ground and intermediate states using only coherent control is 1/2, whereas it is about 0.687 using coherent control assisted by incoherent control implemented through the non-selective measurement of the ground state, as was previously analytically computed. In this work, we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). The measurement-driven control used in this work is different from both quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points or second-order traps. For comparison, we study the transition probability between the ground and highest excited states, as well as the case when both these transition probabilities are assisted by incoherent control implemented through the measurement of the intermediate state.

Tunable voltage polarity-dependent resistive switching characteristics by interface energy barrier modulation in ceria-based bilayer memristors for neuromorphic computing

Synaptic characteristics with tunable dependence on the voltage polarity are demonstrated in ceria (CeO2) and Gd-doped ceria (GDC) bilayer memristors with respect to their stacking orders. Both Pt/GDC/CeO2/Pt and Pt/CeO2/GDC/Pt memristors with different oxide stacking orders exhibit analog, linear, and symmetric synaptic weights for potentiation and depression, paired-pulse facilitation, and short- and long-term plasticity (STP and LTP, respectively). Potentiation and depression behaviors are highly linear and symmetric thanks to the stacking of more oxygen-deficient GDC layer with CeO2, which facilitates the redistribution of oxygen vacancies for analog resistance change. These memristors have opposite dependence of synaptic weight updates on the polarity of potentiation and depression voltages for the stacking order of CeO2 and GDC, which are consistently interpreted by voltage-driven energy barrier modulation at the interface between CeO2 and GDC or with Pt electrodes via oxygen vacancy redistribution. Recognition simulation with modified handwritten digits patterns using a two-layer perceptron neural network exhibits accuracy of approximately 88% with achieved dynamic range, linearity, symmetry, and precision states. These synaptic characteristics are also demonstrated in a 32 × 32 crossbar array of GDC-top memristors. This verifies the potential of bilayer memristors for application in artificial synapse networks in neuromorphic computing systems.