Preservation Of Symmetry Research Articles

Emergence of quenched disorder as a dominant control for complex phase diagram of rare-earth nickelates

Competing interactions in complex materials tend to induce multiple quantum phases of comparable energetics close to the ground state stability. This requires novel strategies and tools to segregate such phases with desired control to manipulate the properties relevant for contemporary technologies. Here, we show ‘quenched disorder (QD)’ as a predominant control parameter to realize a broad range of the quantum phases of bulk RNiO3 (R = rare-earth ion) phase diagram in a La x Eu1-x NiO3 compounds by systematic introduction of QD. Using static and terahertz dynamic transport studies on epitaxial thin films, we demonstrate various phases such as Fermi to non-Fermi liquid crossover, bad metallic behavior, quantum criticality, preservation of orbital and charge order symmetry and increased electronic inhomogeneity responsible for Maxwell–Wagner type of dielectric response, etc. The underlying mechanisms are unveiled by the anomalous responses of microscopic quantities such as scattering rate, plasma frequency, spectral weight, effective mass, and disorder. The results and methodology implemented here can be a generic pursuit of disorder based unified control to extract quantum phases submerged in competing energetics in all complex materials.

Symmetry in Seeded Metal Nanocrystal Growth

ConspectusSymmetry underpins the structure and function of the world around us and is also captured in modern nanomaterials, where changing the symmetry of a nanocrystal or the interparticle spacing and orientation of nanocrystal building blocks in a superlattice can give new function. However, the synthesis and assembly of nanocrystals have been limited largely to simple compositions and structures. It remains a grand challenge to achieve nanocrystals with compositional and structural complexity while maintaining the monodispersity required for their use. This Account will illustrate through recent examples that seeded methods enable the synthesis of compositionally and structurally complex multimetallic crystals with defined and predictable symmetries for applications in plasmonics and catalysis. This outcome arises because the barrier for heterogeneous nucleation (i.e., seeded) is lower than that of homogeneous nucleation, where seeds can serve as preferential sites for the growth of complex structures and crystal phases. Our analysis begins by considering metal overgrowth from single-crystalline seeds of different shapes and symmetries, where the kinetics of adatom addition to seeds relative to their diffusion across seeds accounts for the expressed nanocrystal shapes. These results are then compared to overgrowth from seeds with different internal structures (i.e., planar defects), where the relationships between nanocrystal size and volumetric strain energy and surface energy are discussed. A major finding from this analysis is that often the underlying symmetry of seeds can be predictably transferred to the final crystals during overgrowth processes. Consequences of this finding are the predictable syntheses of crystals with different hierarchies akin to snowcrystals as well as nanocrystals with complex compositions (e.g., quaternary nanoparticles). Yet, there are subtle aspects to seeded growth that pave a path toward examples where nanocrystal symmetry has been reduced compared to the original seeds in a controlled manner. As we found, both the concentrations of metal precursors and capping agents can impact whether symmetry is transferred or reduced during overgrowth. Examples from our laboratory will be placed in context to other reported strategies for symmetry breaking. As will be argued, understanding what conditions favor symmetry preservation versus symmetry reduction during seeded crystal growth is central to accessing next-generation crystal forms. The Account concludes by outlining synthetic challenges associated with forming nanoscale heterostructures with precise 3-D placement of different materials within a given nanocrystal as well as facet control within different material domain and interface engineering. We envision meeting these challenges through regioselective and chemoselective seeded syntheses for which a foundation is outlined herein.

Higher-order band topology

A conventional topological insulator (TI) has gapped bulk states but gapless edge states. The emergence of the gapless edge states is dictated by the bulk topological invariant of the insulator and the preservation of relevant symmetries. Over the past four years, a new type of TI has been found, which hosts gapless hinge or corner states, rather than edge states. These unconventional TIs, termed higher-order TIs (HOTIs), are common among crystalline and quasi-crystalline materials. Higher-order band topology expands our previous understanding of topological phases and provides unprecedented lower-dimensional boundary states for devices. Here, we review the principles, theories and experimental realizations of HOTIs for both electrons and classical waves. There is an emphasis on the development of HOTIs in photonic, phononic and circuit systems owing to their special contributions to these fields. From these discussions, we remark on trends and challenges in the field and the impact of higher-order band topology on other scientific disciplines.

The reflection of a blast wave by a very intense explosion.

We demonstrate that the geometric similarity of Taylor’s blast wave persists beyond reflection from an ideal surface. Upon impacting the surface, the spherical symmetry of the blast wave is lost but its cylindrical symmetry endures. As the flow acquires dependence on a second spatial dimension, an analytic solution of the Euler equations becomes elusive. However, the preservation of axisymmetry, geometric similarity and planar symmetry in the presence of a mirror-like surface causes all flow solutions to collapse when scaled by the height of burst (HOB) and the shock arrival time at the surface. The scaled blast volume for any yield, HOB and ambient air density follows a single universal trajectory for all scaled time, both before and after reflection.

Increasing the number of topological nodal lines in semimetals via uniaxial pressure

The application of pressure has been demonstrated to induce intriguing phase transitions in topological nodal-line semimetals. In this work we analyze how uniaxial pressure affects the topological character of BaSn_2, a Dirac nodal-line semimetal in the absence of spin-orbit coupling. Using calculations based on the density functional theory and a model tight-binding Hamiltonian, we find the emergence of a second nodal line for pressures higher than 4 GPa. We examine the topological features of both phases demonstrating that a nontrivial character is present in both of them. Thus, providing evidence of a topological-to-topological phase transition in which the number of topological nodal lines increases. The orbital overlap increase between Ba d_{xz} and d_{yz} orbitals and Sn p_z orbitals and the preservation of crystal symmetries are found to be responsible for the advent of this transition. Furthermore, we pave the way to experimentally test this kind of transition by obtaining a topological relation between the zero-energy modes that arise in each phase when a magnetic field is applied.

Using Modified Equipment in Field Hockey Leads to Positive Transfer of Learning Effect.

Cross-education is the phenomenon in which repeated practice of a unilateral motor task does not only result in performance improvement of the trained limb, but also in the untrained contralateral limb. The aim of this study was to test whether cross-education or positive transfer of learning is also achieved for tasks in which both limbs contribute in different ways by using modified equipment that switches the limbs’ role. To this end, a reverse field hockey stick was used that requires a mirroring of arm and hand use and dominance (i.e., right hand on top of the hockey stick instead of the left hand). Two groups of young skilled female field hockey players participated in a crossover-design, in which participants received four training sessions with a reverse hockey stick followed by four training sessions with a regular hockey stick, or vice versa. In a pre-test, intermediate test (following the first intervention period), a post-test (after the second intervention period) and a retention test, participants’ performance on a field hockey skill test with a regular hockey stick was measured. The results revealed that training with the reversed hockey stick led to significantly increased improvements compared to training with a regular hockey stick. We conclude that modified equipment can be used to exploit positive transfer of learning by switching the limbs’ roles. The findings are discussed by referring to the symmetry preservation principle in dynamic systems theory and have clear practical relevance for field hockey trainers and players seeking to further improve field hockey skills.

The Master Ward Identity for Scalar QED

It is emphasized that for interactions with derivative couplings, the Ward Identity (WI) securing the preservation of a global symmetry should be modified. Scalar QED is taken as an explicit example. More precisely, it is rigorously shown in scalar QED that the naive WI and the improved Ward Identity (‘Master Ward Identity’, MWI) are related to each other by a finite renormalization of the time-ordered product (‘T-product’) for the derivative fields, and we point out that the MWI has advantages over the naive WI—in particular with regard to the proof of the MWI. We show that the MWI can be fulfilled in all orders of perturbation theory by an appropriate renormalization of the T-product, without conflict with other standard renormalization conditions. Relations with other recent formulations of the MWI are established.

Evidence of Potts-Nematic Superfluidity in a Hexagonal sp^{2} Optical Lattice.

As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multiorbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry C_{4} broken down to C_{2}. Here, we report an observation of a three-state (Z_{3}) quantum nematic order, dubbed "Potts-nematicity", in a system of cold atoms loaded in an excited band of a hexagonal optical lattice described by an sp^{2}-orbital hybridized model. This Potts-nematic quantum state spontaneously breaks a three-fold rotation symmetry of the lattice, qualitatively distinct from the Ising nematicity. Our field theory analysis shows that the Potts-nematic order is stabilized by intricate renormalization effects enabled by strong interorbital mixing present in the hexagonal lattice. This discovery paves a way to investigate quantum vestigial orders in multiorbital atomic superfluids.

An Explanation for the Violation of Lepton Universality in Beauty-Quark Decays: The Binary Isotope Mixture of Beauty-Quarks

This paper purposes an explanation for the recent evidence for the violation of lepton universality in beauty-quark decays at CERN’s Large Hadron Collider. A beauty meson (B+) transforms into a strange meson (K+) with the emission of either electron-positron (e+e-) or muon-antimuon (μ+μ-). The ratio (RK) of branching fractions for B+ → K+μ+μ- and B+→ K+e+e- decays is measured to be RK = 0.846 instead of 1 in the violation of lepton universality in the Standard Model. This paper proposes that the violation is derived from the binary isotope mixture of two beauty-quarks, b7 (4979 MeV mass) and b8 (143,258 MeV mass) whose masses are calculated from the periodic table of elementary particles. b7 is the observable B, while b8 is the hidden B to preserve the generation number symmetry between the three lepton family generations and the three quark family generations in the Standard Model. The preservation of the generation number symmetry forbids b8 to decay into K+μ+μ-. In the transition state involving the virtual particles (γ, W± and Z°) before the decay, b7 and b8 emerge to form the binary isotope mixture from B. The rates of emergence as the rates of diffuse in Graham’s law of diffusion are proportional to inverse square root of mass. The rate ratio between b8/b7 is (4979/143,258)1/2 = 0.1864. Since b7 decays into K+, e+e-, and μ+μ-, while b8 decays into K+, e+e-, and forbidden μ+μ-, the calculated ratio (RK) of branching fractions for B+→ K+μ+μ- and B+→ K+e+e- is 0.5/(0.1864 × 0.5+ 0.5) = 0.843 in excellent agreement with the observed 0.846. The agreement between the calculated RK and the observed RK confirms the validity of the periodic table of elementary particles which provides the answers for the dominance of matter over antimatter, dark-matter, and the mass hierarchy of elementary particles.

Isostructural Phase Transition by Point Defect Reorganization in the Binary Type-I Clathrate Ba <sub>7.5</sub>Si <sub>45</sub>

A competition of point defect configurations is inherent to crystalline phases of increased structural complexity. Symmetry preserving phase transitions between them belong to the special class of isostructural transitions. Type-I silicon clathrates are crystalline complex phases whose unit cell containing a fifties of atoms consists of a 3D covalent silicon framework of face-sharing polyhedral cages encapsulating guest cations. At high pressure, an intriguing structural transition is associated to an abrupt volume reduction with no indication for any symmetry breaking. By means of isothermal high-pressure X-ray diffraction performed on single crystal of the simplest representative type-I silicon clathrates, the binary Ba8Si46, we confirm the isostructural character of the transition and identify the associated mechanism. A detailed analysis of the atomic structural parameters across the transition in combination with ab initio studies allow us to pinpoint a microscopic mechanism driven by a defect rearrangement initially present in the structure. An analysis based on the Landau theory allows to give a coherent description of the experimental observations. A discussion on the analogy between this transformation and liquid-liquid transitions is proposed.

Numerical Solution of a Two Dimensional Tumour Growth Model with Moving Boundary

We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls the birth and death rate of the tumour cells. The cell volume fraction, cell velocity--fluid pressure system, and nutrient concentration are the model variables. A coupled system of a hyperbolic conservation law, \cred{a viscous fluid model}, and a parabolic diffusion equation governs the dynamics of the model variables. The tumour boundary moves with the normal velocity of the outermost layer of cells, and this time--dependence is a challenge in designing and implementing a stable and fast numerical scheme. We recast the model into a form where the hyperbolic equation is defined on a fixed extended domain and retrieve the tumour boundary as the interface at which the cell volume fraction decreases below a threshold value. This procedure eliminates the need to track the tumour boundary explicitly and the computationally expensive re--meshing of the time--dependent domains. A numerical scheme based on finite volume methods for the hyperbolic conservation law, Lagrange $\mathbb{P}_2 - \mathbb{P}_1$ Taylor--Hood finite element method for the \cred{viscous} system, and mass--lumped finite element method for the parabolic equations is implemented in two spatial dimensions, and several cases are studied. We demonstrate the versatility of the numerical scheme in catering for irregular and asymmetric initial tumour geometries. We present numerical simulations for both cases and the results are consistent with theoretical and heuristic expectations such as early linear growth rate and preservation of radial symmetry when the boundary conditions are symmetric.

Local orientation-preserving symmetry preserving operations on polyhedra

Unifying approaches by amongst others Archimedes, Kepler, Goldberg, Caspar and Klug, Coxeter, and Conway, and extending on a previous formalization of the concept of local symmetry preserving (lsp) operations, we introduce a formal definition of local operations on plane graphs that preserve orientation-preserving symmetries, but not necessarily orientation-reversing symmetries. This operations include, e.g., the chiral Goldberg and Conway operations as well as all lsp operations. We prove the soundness of our definition as well as introduce an invariant which can be used to systematically construct all such operations. We also show sufficient conditions for an operation to preserve the connectedness of the plane graph to which it is applied.

W-symmetries of backward stochastic differential equations, preservation of simple symmetries and Kozlov’s theory

In this paper, we study the determining equations of W-symmetries for backward stochastic differential equations (BSDEs). We have proved that each simple random symmetry of multi-dimensional BSDE can be preserved under simple deterministic change of coordinates. Finally, we study the use of symmetries in studying BSDEs, and find that symmetries of BSDE can not form Lie algebra.

The dynamics of new motion styles in the time-dependent four-body problem: weaving periodic solutions

In the present investigation, we consider a model originally introduced to obtain new styles of periodic solutions (weaving styles) in the (2, 2)-particle problem. The key feature of these motion styles is the preservation of the axial symmetries of the periodic solutions and the collision free of the bodies. We first derive the equations for the motion of four particles and display how to reduce a dynamical system consisting of twelve differential equations to only three for one body in the new styles of motion, then we prove the existence of collision-free minimizers for the Lagrangian action functional under well chosen class of symmetric loops, to confirm the existence of the weaving periodic solutions for the equal mass four-body problem. Finally, we explore via numerical scheme the dynamics and shapes of the obtained periodic solutions.

Influence of dissipation on extreme oscillations of a forced anharmonic oscillator

Dynamics of a periodically forced anharmonic oscillator with cubic nonlinearity, linear damping, and nonlinear damping, is studied. To begin with, the authors examine the dynamics of an anharmonic oscillator with the preservation of parity symmetry. Due to this symmetric nature, the system has two neutrally stable elliptic equilibrium points in positive and negative potential-wells. Hence, the unforced system can exhibit both single-well and double-well periodic oscillations depending on the initial conditions. Next, the authors include position-dependent damping in the form of nonlinear damping (xẋ) into the system. Then, the parity symmetry of the system is broken instantly and the stability of the two elliptic points is altered to result in stable focus and unstable focus in the positive and negative potential-wells, respectively. Consequently, the system is dual-natured and is either non-dissipative or dissipative, depending on location in the phase space. The total energy of the system is used to explain this dual nature of the system. Furthermore, when one includes a periodic external forcing with suitable parameter values into the nonlinearly damped anharmonic oscillator system and starts to increase the damping strength, the parity symmetry of the system is not broken right away, but it occurs after the damping reaches a threshold value. As a result, the system undergoes a transition from double-well chaotic oscillations to single-well chaos mediated through a type of mixed-mode oscillations called extreme events (EEs) in which the small-amplitude single-well chaotic oscillations are interrupted by rare and recurrent large-amplitude (double-well) chaotic bursts. Furthermore, it is found that the large-amplitude oscillations developed in the system are completely eliminated if one incorporates linear damping into the system. Hence, it is believed that a novel means has been identified for controlling the EEs that occur in forced anharmonic oscillator system with nonlinear damping. The numerically calculated results are in good agreement with the theoretically obtained results on the basis of Melnikov’s function. Further, it is demonstrated that when one includes linear damping into the system, this system has a dissipative nature throughout the entire phase space of the system. This is believed to be the key to the elimination of EEs.

IGA-MPM: The Isogeometric Material Point Method

We propose the use of Isogeometric Analysis (IGA) within the context of the Material Point Method (MPM), and refer to the approach as IGA-MPM. We use the idea of IGA, and its instantiation based on Non-Uniform Rational B-Splines (NURBS), to build higher-order accurate and smooth approximation for MPM. Higher-order smoothness yields a continuous representation of the strain rate, and, as a result, prevents jumps in the stress and other history variables as the material points cross the element boundaries. Furthermore, NURBS can exactly represent all conic sections and the corresponding symmetries in the solution, which may be important in some applications. Several numerical examples of increasing complexity are presented, and show the ability of IGA-MPM to eliminate the well known cell-crossing instability of the conventional MPM. In addition, the examples presented demonstrate improved accuracy, convergence, and symmetry preservation of IGA-MPM compared to the conventional MPM, both for rectilinear and curved geometries.

Pure spin current generation via photogalvanic effect with spatial inversion symmetry

We propose a new idea to generate pure spin current with photogalvanic effect (PGE) by designing devices with spatial inversion symmetry based on two-dimensional spin semiconducting materials. Due to the preservation of spatial inversion symmetry, the electric current generated by the PGE must be zero. However, finite spin-dependent current ${I}_{\ensuremath{\uparrow}/\ensuremath{\downarrow}}$ may still be produced. Once an amount of spin-up electrons flow into the device region from lead $\ensuremath{\alpha}$ and flow out from lead $\ensuremath{\beta}$ under light irradiation, the same amount of spin-down electrons will flow into the device region from lead $\ensuremath{\beta}$ and flow out from lead $\ensuremath{\alpha}$, which results in ${I}_{c}^{\ensuremath{\alpha}/\ensuremath{\beta}}={I}_{\ensuremath{\uparrow}}^{\ensuremath{\alpha}/\ensuremath{\beta}}+{I}_{\ensuremath{\downarrow}}^{\ensuremath{\alpha}/\ensuremath{\beta}}=0$ and ${I}_{s}^{\ensuremath{\alpha}/\ensuremath{\beta}}={I}_{\ensuremath{\uparrow}}^{\ensuremath{\alpha}/\ensuremath{\beta}}\ensuremath{-}{I}_{\ensuremath{\downarrow}}^{\ensuremath{\alpha}/\ensuremath{\beta}}\ensuremath{\ne}0$ simultaneously for each lead and thus finite pure spin current arises. As a concrete example, this idea is demonstrated by calculating the PGE in a photoelectric device constructed with an armchair-edged graphene nanoribbon which is divided into two semi-infinite ribbons. The two semi-infinite ribbons are then periodically and symmetrically patterned with ferromagnetic triangle antidots in the form of ``$▹◃$'' to achieve spatial inversion symmetry of the device. We find that the pure spin current can be robustly generated, neither dependent on the photon energy and polarization/helicity angle, nor dependent on whether it is linearly, circularly, or elliptically polarized.

Soft chemical deintercalation of silver from delafossites AgFeO2, and AgCrO2

Selective deintercalation of Ag+-ion from AgFeO2 and AgCrO2 with the use of dilute aqueous solutions of NH4Cl was achieved successfully. Based on the ICP analysis, the Ag: Fe and Ag: Cr ratios were 0.9:1 and 0.87:1 in the deintercalated sample of AgFeO2 and AgCrO2, respectively. Retention of both structure and the polytypes were noticed after deintercalation together with the reduction in their unit cell c-axis. Raman spectra of deintercalated samples confirmed the preservation of overall symmetry. XPS results confirmed the existence of Fe (III) and Cr (III) in the Ag+-ion deintercalated samples.

Effect of angle-of-attacks on deterministic lateral displacement (DLD) with symmetric airfoil pillars.

Deterministic lateral displacement (DLD) is a microfluidic technique for size fractionation of particles/cells in continuous flow with a great potential for biological and clinical applications. Growing interest of DLD devices in enabling high-throughput operation for practical applications, such as circulating tumor cell (CTC) separation, necessitates employing higher flow rates, leading to operation at moderate to high Reynolds number (Re) regimes. Recently, it has been shown that symmetric airfoil shaped pillars with neutral angle-of-attack (AoA) can be used for high-throughput design of DLD devices due to their mitigation of vortex effects and preservation of flow symmetry under high Re conditions. While high-Re operation with symmetric airfoil shaped pillars has been established, the effect of AoAs on the DLD performance has not been investigated. In this paper, we have characterized the airfoil DLD device with various AoAs. The transport behavior of microparticles has been observed and analyzed with various AoAs in realistic high-Re. Furthermore, we have modeled the flow fields and anisotropy in a representative airfoil pillar array, for both positive and negative AoA configurations. Unlike the conventional DLD device, lateral displacement has been suppressed with +5° and + 15° AoA configurations regardless of particle sizes. On the other hand, stronger lateral displacement has been seen with -5° and - 15° AoAs. This can be attributed to growing flow anisotropy as Re climbs, and significant expansion or compression of streamlines between airfoils with AoAs. The findings in this study can be utilized for the design and optimization of airfoil DLD microfluidic devices with various AoAs.

Inter-Ocular Symmetry of Vascular Density and Retinal Thickness in Unilateral Anisometropic Amblyopia.

BackgroundInter-ocular symmetry of macular vascular anatomy in healthy subjects has been well documented in previous optical coherence tomography angiography (OCTA) studies. In our present study, we have demonstrated that the presence of anisometropic amblyopia in one eye does not alter this unique feature significantly. We investigated whether the presence of unilateral anisometropic amblyopia due to moderate amounts of hyperopia and/or astigmatism would have any significant influence on measurements of retinal thickness (RT) and superficial vessel density (SVD) in adult subjects.Subjects and methodsIn the study group, both eyes of 21 adult subjects with unilateral anisometropic amblyopia were enrolled. Only one eye of an age-matched control group including 33 subjects was randomly selected. RT and SVD were measured in foveal and parafoveal retinal areas and compared in amblyopic eyes, their fellow eyes and in the control group. Inter-ocular symmetry of RT and SVD in amblyopic and fellow eyes were investigated by using correlation analysis.ResultsThere were statistically significant inter-ocular correlations of foveal and parafoveal RT in amblyopic and fellow eyes (P < 0.0001, for both). Foveal and parafoveal RT of the control group were not statistically different from amblyopic eyes (P = 0.072 and P = 0.46, respectively). There was no difference between foveal SVD of amblyopic eyes and control group (P = 0.10) and a significant inter-ocular correlation was found between amblyopic and fellow eyes (P = 0.029).ConclusionFor our adult subjects, none of the investigated OCTA parameters of the amblyopic eyes were found to be statistically different from those of age-matched controls. The preservation of inter-ocular symmetry in the amblyopic and fellow eyes implies that the influence of anisometropic amblyopia in one eye would be relatively small and negligible on routine OCTA examination.