Preservation Of Symmetry Research Articles

A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation

A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for solving two-dimensional hydrodynamic problems in cell-centered updated Lagrangian formulation. This method is the Lagrangian limit of the unsplit rDG-ALE formulation, and is obtained by assuming the equality of the grid velocity to the fluid velocity only at cell boundaries. The conservative variables and the Taylor basis defined on the time-dependent moving mesh, provide the piece-wise polynomial expansion in the updated Lagrangian formulation. A multi-directional nodal Riemann solver is implemented for computing the grid velocity at the vertices and the numerical flux at the cell boundaries. A characteristic limiting procedure is extended from the primitive variable version to the conservative variable version, and its performance is compared with the limiter on physical variables. A number of benchmark test cases are conducted to assess the accuracy, robustness, and non-oscillatory property of the DG(P0), DG(P1) and rDG(P1P2) methods. The numerical experiments demonstrate that the developed rDG method is able to attain the designed order of accuracy and the characteristic limiting procedure outperforms the limiter on physical variables in terms of the monotonicity and symmetry preservation for shock problems.

Symmetry, symmetry breaking, and pion parton distributions

Pion valence, glue and sea distributions are calculated using a continuum approach to the two valence-body bound-state problem. Since the framework is symmetry preserving, physical features of the distributions are properly expressed. The analysis reveals that the emergent phenomenon of dynamical chiral symmetry breaking causes a hardening of the valence-quark distribution function, ${q}^\pi(x)$. Nevertheless, this distribution exhibits the $x\simeq 1$ behaviour predicted by quantum chromodynamics (QCD). At the scale $\zeta_2:=2\,$GeV, the following momentum fractions are predicted: $\langle x_{\rm valence} \rangle = 0.48(3)$, $\langle x_{\rm glue} \rangle = 0.41(2)$, $\langle x_{\rm sea} \rangle = 0.11(2)$. Evolving to $\zeta=5.2\,$GeV, the result for ${q}^\pi(x)$ agrees with that computed using lattice QCD. These outcomes should both spur improved analyses of existing experiments and stimulate efforts to obtain new data on the pion distribution functions using available and envisioned facilities.

Construction of invariant compact finite-difference schemes.

In this paper we propose a method, which is based on equivariant moving frames, for development of high-order accurate invariant compact finite-difference schemes that preserve Lie symmetries of underlying partial differential equations. In this method, variable transformations that are obtained from the extended symmetry groups of partial differential equations (PDEs) are used to transform independent and dependent variables and derivative terms of compact finite-difference schemes (constructed for these PDEs) such that the resulting schemes are invariant under the chosen symmetry groups. The unknown symmetry parameters that arise from the application of these transformations are determined through selection of convenient moving frames. In some cases, owing to selection of convenient moving frames, numerical representation of invariant (or symmetry-preserving) compact numerical schemes is found to be notably simpler than that of standard, noninvariant compact numerical schemes. Further, the accuracy of these invariant compact schemes can be arbitrarily set to a desired order by considering suitable compact finite-difference algorithms. Application of the proposed method is demonstrated through construction of invariant compact finite-difference schemes for some common linear and nonlinear PDEs (including the linear advection-diffusion equation in one or two dimensions, the inviscid Burgers' equation in one dimension, viscous Burgers' equation in one or two dimensions, spherical Burgers' equation in one dimension, and shallow water equations in two dimensions). Results obtained from our numerical simulations indicate that invariant compact finite-difference schemes not only inherit selected symmetry properties of underlying PDEs, but are also comparably more accurate than the standard, noninvariant base numerical schemes considered here.

Machine Learning design of Volume of Fluid schemes for compressible flows

Our aim is to establish the feasibility of Machine-Learning-designed Volume of Fluid algorithms for compressible flows. We detail the incremental steps of the construction of a new family of Volume of Fluid-Machine Learning (VOF-ML) schemes adapted to bi-material compressible Euler calculations on Cartesian grids. An additivity principle is formulated for the Machine Learning datasets. We explain a key feature of this approach which is how to adapt the compressible solver to the preservation of natural symmetries. The VOF-ML schemes show good accuracy for advection of a variety of interfaces, including regular interfaces (straight lines and arcs of circle), Lipschitz interfaces (corners) and non Lipschitz triple point (the Trifolium test problem). Basic comparisons with a SLIC/Downwind scheme are presented together with elementary bi-material calculations with shocks.

Adaptive mesh refinement in the fast lane

This paper presents an approach for constructing an adaptive mesh refinement (AMR) scheme, targeting next-generation computing hardware. The key to the design is the particular combination of aspects of cell-based AMR and patch-based AMR. We examine the feasibility of this new method with respect to correctness, preservation of circular symmetry, ease of programming and performance impacts on runtime and memory usage. This method exploration is done in CLAMR, a cell-based AMR mini-app that already runs on GPUs and other next-generation hardware platforms. The composability of the application is improved by decoupling the physics code and mesh code. Each level of the mesh is made independent through the use of phantom cells. The net result is a clear pathway to getting the full application on the GPU while also minimizing development requirements to convert a regular grid application to AMR.

Aging transition in the absence of inactive oscillators

The role of counter-rotating oscillators in an ensemble of coexisting co- and counter-rotating oscillators is examined by increasing the proportion of the latter. The phenomenon of aging transition was identified at a critical value of the ratio of the counter-rotating oscillators, which was otherwise realized only by increasing the number of inactive oscillators to a large extent. The effect of the mean-field feedback strength in the symmetry preserving coupling is also explored. The parameter space of aging transition was increased abruptly even for a feeble decrease in the feedback strength, and, subsequently, aging transition was observed at a critical value of the feedback strength surprisingly without any counter-rotating oscillators. Further, the study was extended to symmetry breaking coupling using conjugate variables, and it was observed that the symmetry breaking coupling can facilitate the onset of aging transition even in the absence of counter-rotating oscillators and for the unit value of the feedback strength. In general, the parameter space of aging transition was found to increase by increasing the frequency of oscillators and by increasing the proportion of the counter-rotating oscillators in both symmetry preserving and symmetry breaking couplings. Further, the transition from oscillatory to aging occurs via a Hopf bifurcation, while the transition from aging to oscillation death state emerges via the pitchfork bifurcation. Analytical expressions for the critical ratio of the counter-rotating oscillators are deduced to find the stable boundaries of the aging transition.

Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories

We study the interplay between spontaneously breaking global continuous and discrete antilinear symmetries in a newly proposed general class of non-Hermitian quantum field theories containing a mixture of complex and real scalar fields. We analyse the model for different types of global symmetry preserving and breaking vacua. In addition, the models are symmetric under various types of discrete antilinear symmetries composed out of nonstandard simultaneous charge conjugations, time-reversals and parity transformations; CPT. While the global symmetry governs the existence of massless Goldstone bosons, the discrete one controls the precise expression of the Goldstone bosons in terms of the original fields in the model and its physical regimes. We show that even when the CPT-symmetries are broken on the level of the action expanded around different types of vacua, the mass spectra might still be real when the symmetry is preserved at the tree approximation and the breaking only occurs at higher order. We discuss the parameter space of some of the models in the proposed class and identify physical regimes in which massless Goldstone bosons emerge when the vacuum spontaneously breaks the global symmetry or equivalently when the corresponding Noether currents are conserved. The physical regions are bounded by exceptional points in different ways. There exist special points in parameter space for which massless bosons may occur already before breaking the global symmetry. However, when the global symmetry is broken at these points they can no longer be distinguished from genuine Goldstone bosons.

A symmetry preserving scheme for three-dimensional Lagrangian radiation hydrodynamic simulations of ICF capsule implosion

A symmetry preserving scheme for three-dimensional (3D) Lagrangian radiation hydrodynamic simulations of an inertial confinement fusion (ICF) capsule implosion is presented. Violation of spherical symmetry exists in conventional scheme in 3D Cartesian coordinate system. Following the idea of Caramana et al. (E.J. Caramana, et al., A Compatible, Energy and Symmetry Preserving Lagrangian Hydrodynamics Algorithm in Three-Dimensional Cartesian Geometry, Journal of Computational Physics, 157 (2000) 89–119), a symmetry preserving scheme in 3D Cartesian coordinate system is extended to Lagrangian radiation hydrodynamics. This scheme is specially designed for spherical (radial) grids. Appropriate calculations of auxiliary points in the discretization of Lagrangian hydrodynamic equations are given. Small modification is applied to the flux-related Jacobian matrix in the diffusion scheme. The modified diffusion scheme can guarantee the symmetrical flux. The symmetry preserving properties of the developed scheme for Lagrangian radiation hydrodynamics are proved in theory. The developed symmetry preserving scheme is applied to the 3D simulations of an ICF capsule implosion. Numerical results show that the symmetry preserving scheme for Lagrangian radiation hydrodynamics helps to remove unphysical instability in the 3D simulations of ICF capsule implosion.

Learning from the density to correct total energy and forces in first principle simulations.

We propose a new molecular simulation framework that combines the transferability, robustness, and chemical flexibility of an ab initio method with the accuracy and efficiency of a machine learning model. The key to achieve this mix is to use a standard density functional theory (DFT) simulation as a preprocessor for the atomic and molecular information, obtaining a good quality electronic density. General, symmetry preserving, atom-centered electronic descriptors are then built from this density to train a neural network to correct the baseline DFT energies and forces. These electronic descriptors encode much more information than local atomic environments, allowing a simple neural network to reach the accuracy required for the problem of study at a negligible additional cost. The balance between accuracy and efficiency is determined by the baseline simulation. This is shown in results where high level quantum chemical accuracy is obtained for simulations of liquid water at standard DFT cost or where high level DFT-accuracy is achieved in simulations with a low-level baseline DFT calculation at a significantly reduced cost.

Investigations of the superconducting ground state of Zr3Ir : Introducing a new noncentrosymmetric superconductor

Superconductivity in materials whose crystal structure lacks inversion symmetry is a prime candidate for unconventional superconductivity. A new noncentrosymmetric compound Zr$_{3}$Ir crystallizes in a tetragonal $ \alpha $-V$_{3} $S structure. The magnetization, specific heat and muon spin rotation confirm s-wave superconductivity, having a transition temperature T$_{c}$ = 2.3 K. Muon spin relaxation confirms the preservation of time reversal symmetry in the superconducting ground state.

Symmetry broken and symmetry preserving multi-soliton solutions for nonlocal complex short pulse equation

Abstract In this article we consider a general system of complex short pulse equation (CSPE) that under certain nonlocal symmetry reduction yields a reverse space-time nonlocal complex short pulse equation (NL-CSPE). We apply matrix Darboux transformation to the associated Lax pair and construct multi-soliton solutions. K-soliton solution is expressed in terms of quasideterminant formula which enable us to compute explicit expressions of symmetry broken and symmetry preserving one- and two-soliton solutions for NL-CSPE. In addition to these solutions, we also obtain one-bright and interaction of two-bright solitons for classical CSPE. All these investigations end up with the conclusion that both symmetry preserving and broken solutions exist for NL-CSPE.

Numerical Simulation Using Finite-Difference Schemes with Continuous Symmetries for Processes of Gas Flow in Porous Media

This article presents the applications of continuous symmetry groups to the computational fluid dynamics simulation of gas flow in porous media. The family of equations for one-phase flow in porous media, such as equations of gas flow with the Klinkenberg effect, is considered. This consideration has been made in terms of difference scheme constructions with the preservation of continuous symmetries, which are presented in original parabolic differential equations. A new method of numerical solution generation using continuous symmetry groups has been developed for the equation of gas flow in porous media. Four classes of invariant difference schemes have been found by using known group classifications of parabolic differential equations with partial derivatives. Invariance of necessary conditions for stability has been shown for the difference schemes from the presented classes. Comparison with the classical approach for seeking numerical solutions for a particular case from the presented classes has shown that the calculation speed is greater by several orders than for the classical approach. Analysis of the accuracy for the presented method of numerical solution generation on the basis of continuous symmetries shows that the accuracy of generated numerical solutions depends on the accuracy of initial solutions for generations.

Cranial Bone Flap Fixation: Comparison of Titanium-Based Device (Skull Fix) and PEEK-Based Device (Cranial Loop): Technical Report

AbstractBackground: Reconstruction of the cranial bone flap after craniocerebral surgery is crucial for preservation of skull symmetry, maintenance of aesthetics, brain protection, as well avoiding complications like floating or sunken skull flaps. A host of techniques and materials for fixation of the cranial flaps have emerged over the past several decades.Aim of Study: The aim of this study was to compare the clinical outcomes of bone flap fixation using peek-based (cranial loop) versus titanium-based (skull fix) fixation systems.Patients and Methods: Between July 2013 and December 2016 a series of 54 patients undergoing either an emergency or an elective craniotomy for different intracranial lesions in which the original bone flaps were refixed using cranial loop in 27 patients and skull fix in 27 patients. Clinical and radio-logical outcomes and complication rates were compared between these 2 groups.Results: Satisfactory results were achieved in both fixation systems. Epidural collection occurred in 4 patients 3 in skull fix and one in cranial loop, subdural collection in 4 patients 2 in cranial loop and one in skull fix treated conservatively. One case with cranial loop experienced a bone flap dislocation which was revised and refixed. Subcutaneous effusion occurred in two patients one in skull fix and one in cranial loop. One patient in skull fix developed a mild postoperative wound infection. Post-operative imaging showed satisfactory ana-tomical and morphological position of the flap in all patients.Conclusion: Skull fix and cranial loop are reasonable alternatives to present craniotomy fixation methods. They are easy to use, fast, safe, reliable with very acceptable cosmetic results. The main advantage of the cranial loop might ultimately lie in the absence of artifacts on post-operative CT or MR imaging.

Quantum BRST charge in gauge theories in curved space-time

Renormalized gauge-invariant observables in gauge theories form an algebra which is obtained as the cohomology of the derivation QL,−, with QL as the renormalized interacting quantum BRST charge. For a large class of gauge theories in Lorentzian globally hyperbolic space-times, we derive an identity in renormalized perturbation theory which expresses the commutator [QL, −] in terms of a new nilpotent quantum BRST (Becchi, Rouet, Stora, Tyutin) differential and a new quantum anti-bracket which differ from their classical counterparts by certain quantum corrections. This identity enables us to prove different manifestations of gauge symmetry preservation at the quantum level in a model-independent fashion.

Degenerate soliton solutions and their dynamics in the nonlocal Manakov system: I symmetry preserving and symmetry breaking solutions

In this paper, we construct degenerate soliton solutions (which preserve $\cal{PT}$-symmetry/break $\cal{PT}$-symmetry) to the nonlocal Manakov system through a nonstandard bilinear procedure. Here by degenerate we mean the solitons that are present in both the modes which propagate with same velocity. The degenerate nonlocal soliton solution is constructed after briefly indicating the form of nondegenerate one-soliton solution. To derive these soliton solutions, we simultaneously solve the nonlocal Manakov equation and a pair of coupled equations that arise from the zero curvature condition. The later consideration yields general soliton solution which agrees with the solutions that are already reported in the literature under certain specific parametric choice. We also discuss the salient features associated with the obtained degenerate soliton solutions.

Doubly charmed Ξcc molecular states from meson-baryon interaction

Stimulated by the new experimental LHCb findings associated with the $\Omega_c$ states, some of which we have described in a previous work as being dynamically generated through meson-baryon interaction, we have extended this approach to make predictions for new $\Xi_{cc}$ molecular states in the $C=2$, $S=0$ and $I=1/2$ sector. These states manifest themselves as poles in the solution of the Bethe-Salpeter equation in coupled channels. The kernels of this equation were obtained using the Lagrangians coming from the hidden local gauge symmetry, where the interactions are dominated by the exchange of light vector mesons. The extension of this approach to the heavy sector stems from the realization that the dominant interaction corresponds to having the heavy quarks as spectators, which implies the preservation of the heavy quark symmetry. As a result, we get several states: two states from the pseudoscalar meson-baryon interaction with $J^P=1/2^-$, and masses around $4080$ and $4090$ MeV, and one at $4150$ MeV for $J^P=3/2^-$. Furthermore, from the vector meson-baryon interaction we get three states degenerate with $J^P=1/2^-$ and $3/2^-$ from $4220$ MeV to $4330$ MeV, and two more states around $4280$ MeV and $4410$ MeV, degenerate with $J^P=1/2^-,\, 3/2^-$ and $5/2^-$.

On symmetry preserving and symmetry broken bright, dark and antidark soliton solutions of nonlocal nonlinear Schrödinger equation

We construct symmetry preserving and symmetry broken N-bright, dark and antidark soliton solutions of a nonlocal nonlinear Schrödinger equation. To obtain these solutions, we use appropriate eigenfunctions in Darboux transformation (DT) method. We present explicit one and two bright soliton solutions and show that they exhibit stable structures only when we combine the field and parity transformed complex conjugate field. Further, we derive two dark/antidark soliton solution with the help of DT method. Unlike the bright soliton case, dark/antidark soliton solution exhibits stable structure for the field and the parity transformed conjugate field separately. In the dark/antidark soliton solution case we observe a contrasting behaviour between the envelope of the field and parity transformed complex conjugate envelope of the field. For a particular parametric choice, we get dark (antidark) soliton for the field while the parity transformed complex conjugate field exhibits antidark (dark) soliton. Due to this surprising result, both the field and PT transformed complex conjugate field exhibit sixteen different combinations of collision scenario. We classify the parametric regions of dark and antidark solitons in both the field and parity transformed complex conjugate field by carrying out relevant asymptotic analysis. Further we present 2N-dark/antidark soliton solution formula and demonstrate that this solution may have 22N×22N combinations of collisions.

Krylov integrators for Hamiltonian systems

We consider Arnoldi-like processes to obtain symplectic subspaces for Hamiltonian systems. Large dimensional systems are locally approximated by ones living in low dimensional subspaces, and we especially consider Krylov subspaces and some of their extensions. These subspaces can be utilized in two ways: by solving numerically local small dimensional systems and then mapping back to the large dimension, or by using them for the approximation of necessary functions in exponential integrators applied to large dimensional systems. In the former case one can expect an excellent energy preservation and in the latter this is so for linear systems. We consider second order exponential integrators which solve linear systems exactly and for which these two approaches are in a certain sense equivalent. We also consider the time symmetry preservation properties of the integrators. In numerical experiments these methods combined with symplectic subspaces show promising behavior also when applied to nonlinear Hamiltonian problems.

Pull-through inferiorly based island pedicle flap for a conchal bowl defect

A 39-year-old woman underwent Mohs micrographic surgery for basal cell carcinoma in the conchal bowl (Fig 1), saving cartilage and perichondrium. Adequate reconstruction of this area requires preservation of shape, supportive function, and symmetry. Commonly used reconstructive options include second-intention healing, composite grafts, and skin flaps.

Universal conductance fluctuations and direct observation of crossover of symmetry classes in topological insulators

A key feature of topological insulators (TI) is symplectic symmetry of the Hamiltonian which changes to unitary when time reversal symmetry is lifted and the topological phase transition occurs. However, such a crossover has never been explicitly observed, by directly probing the symmetry class of the Hamiltonian. In this report, we have probed the symmetry class of topological insulators by measuring the mesoscopic conductance fluctuations in the TI Bi$_{1.6}$Sb$_{0:4}$Te$_2$Se, which shows an exact factor of two reduction on application of a magnetic field due to crossover from symplectic to unitary symmetry classes. The reduction provides an unambiguous proof that the fluctuations arise from the universal conductance fluctuations (UCF), due to quantum interference and persists from T = 22 mK to 4.2 K. We have also compared the phase breaking length (l$_\phi$) extracted from both magneto-conductivity and UCF which agree well within a factor of two in the entire temperature and gate voltage range. Our experiment confirms UCF as the major source of fluctuations in mesoscopic disordered topological insulators, and the intrinsic preservation of time reversal symmetry in these systems.