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Colloidal suspensions made of smart core–shell structures are of current interest in many fields. Their properties come from the possibility of varying the core and shell materials for modifying the composite particles' chemical, biological, and optical properties. These particles are formed with a material with a constant refractive index core and a shell with a refractive index decaying until it matches the solvent refractive index. Poly(N-IsoPropyl AcrylaMide) (PNIPAM) is a typical example of materials forming shells. In this report, we present how to apply Mie scattering theory to predict and understand the static light scattering of large nonhomogeneous colloidal particles with spherical symmetry whose size is comparable with or larger than the light wavelength used for developing scattering experiments, where the Rayleigh–Gans–Debye approximation is not valid. Here, the refractive index decay was approximated by a Gaussian RI profile numerically evaluated through a multilayer sphere. We calculated the form factor functions of suspensions of PNIPAM microgels previously reported and core–shell suspensions made of polystyrene/PNIPAM at 20 and 40 °C synthesized by us. In all the cases, our method succeeded in providing the scattering intensity as a function of the angle. The software for using the numerical method is fairly straightforward and is accessible as an open-source code. The results can not only help predict and understand the photonic properties of microgels with large core–shell structures but also for any particle with a refractive index distribution with spherical symmetry, as in the case of microgels with super chaotropic agents, hollow microgels, or microparticles. [ABSTRACT FROM AUTHOR]

Experimental research into the control of particle charge in dusty plasmas conducted at Auburn University indicates that photocurrents generated by exposing dust to intense, near-ultraviolet light can provide a reliable and novel method of independently controlling dust charge without radically altering the background plasma; the experiment also showed that some particles may respond differently to this photo-discharge, with some exhibiting highly periodic responses to the discharge and others exhibiting chaotic behaviour. Since the dust particles in the experiment were a polydisperse sample of different sizes and shapes, particle geometry may play a role in explaining this difference. Simulations of particle discharge and dynamics are used in an attempt to reproduce experimental results and investigate a possible correlation between particle symmetry and dynamic periodicity. [ABSTRACT FROM AUTHOR]

Nonlinear electrophoresis in complex fluids like nematic liquid crystals provides new pathways toward achieving precisely controlled motion and assembly of microscopic objects. The nematic host introduces a paradigm shift in the mechanism of electrophoretic transport by generating unbalanced electro-osmotic flows around the colloidal particle due to symmetry breaking of the medium caused by the induced topological defects. Rationally designed particles, which induce various types of defects and asymmetries, provide new opportunities in this regard. In this Perspective article, we discuss how the asymmetry in the shape and interfacial properties help in piloting the particles using an AC electric field. Finally, we propose some feasible strategies to achieve navigational control using magnetic and photo-responsive particles, guided by orthogonal electric, magnetic fields, and light, respectively. [ABSTRACT FROM AUTHOR]

Unlike a single Carroll particle, a multiparticle Carroll system can move under suitable conditions, as we demonstrate it explicitly for two particles with a momentum-dependent interaction : the center-of-mass remains fixed, however relative motion is possible, confirming previous statements made by Bergshoeff, Casalbuoni, and their collaborators. Analogous results are obtained for electric dipoles with the roles of the center-of-mass and the relative position interchanged. [ABSTRACT FROM AUTHOR]

The study of di-Higgs events, both resonant and non-resonant, plays a crucial role in understanding the fundamental interactions of the Higgs boson. In this work we consider di-Higgs events decaying into four b-quarks and propose to improve the experimental sensitivity by utilizing a novel machine learning algorithm known as Symmetry Preserving Attention Network (Spa-Net) — a neural network structure whose architecture is designed to incorporate the inherent symmetries in particle reconstruction tasks. We demonstrate that the Spa-Net can enhance the experimental reach over baseline methods such as the cut-based and the Dense Neural Network-based analyses. At the Large Hadron Collider, with a 14-TeV center-of-mass energy and an integrated luminosity of 300 fb−1, the Spa-Net allows us to establish 95% C.L. upper limits in resonant production cross-sections that are 10% to 45% stronger than baseline methods. For non-resonant di-Higgs production, Spa-Net enables us to constrain the self-coupling that is 9% more stringent than the baseline method. [ABSTRACT FROM AUTHOR]

While the collective dynamics of spherical active Brownian particles is relatively well understood by now, the much more complex dynamics of nonspherical active particles still raises interesting open questions. Previous work has shown that the dynamics of rod-like or ellipsoidal active particles can differ significantly from that of spherical ones. Here, we obtain the full state diagram of active Brownian ellipsoids in two spatial dimensions without hydrodynamic interactions depending on the Péclet number and packing density via computer simulations. The system is found to exhibit a rich state behavior that includes cluster formation, local polar order, polar flocks, and disordered states. Moreover, we obtain numerical results and an analytical representation for the pair-distribution function of active ellipsoids. This function provides useful quantitative insights into the collective behavior of active particles with lower symmetry and has potential applications in the development of predictive theoretical models. The authors study the collective behavior of ellipsoidal active particles, which is richer and less understood than that of their spherical counterparts. They find a variety of states such as cluster formation, local polar order, polar flocks, and disordered states, and obtain an analytical expression for the pair-distribution function, which allows a quantitative characterization of the system's state. [ABSTRACT FROM AUTHOR]

We analyze topological invariants, in particular Z 2 invariants, which characterize time reversal invariant topological insulators, in the framework of index theory and K-theory. After giving a careful study of the underlying geometry and K-theory, we formalize topological invariants as elements of KR theory. To be precise, the strong topological invariants lie in the higher KR groups of spheres; K R ̃ − j − 1 ( S D + 1 , d ). Here j is a KR-cycle index, as well as an index counting off the Altland-Zirnbauer classification of Time Reversal Symmetry (TRS) and Particle Hole Symmetry (PHS)—as we show. In this setting, the computation of the invariants can be seen as the evaluation of the natural pairing between KR-cycles and KR-classes. This fits with topological and analytical index computations as well as with Poincaré Duality and the Baum–Connes isomorphism for free Abelian groups. We provide an introduction starting from the basic objects of real, complex and quaternionic structures which are the mathematical objects corresponding to TRS and PHS. We furthermore detail the relevant bundles and K-theories (Real and Quaternionic) that lead to the classification as well as the topological setting for the base spaces. [ABSTRACT FROM AUTHOR]

A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries. Two classes of tensor order parameters are associated with polyhedral nematic and bond orientational order. For the latter, a variation of classical bond order parameters (BOPs) is introduced, which takes advantage of the symmetry of constituent particles and/or expected crystalline phases. These symmetrized BOPs can be averaged over an entire system or assigned locally to an individual bond. By combining that with the bond percolation procedure, one is able to identify coherent domains within a self-assembled structure. As a demonstration of the proposed framework, we apply it to a simulated hybrid system that combines isotropic and patchy particles with octahedral symmetry. Not only does the methodology allow one to identify individual crystalline domains but also it detects coherent clusters of a peculiar compact amorphous structure that is not space-filling and lacks any long-range order. [ABSTRACT FROM AUTHOR]

Aviation soot constitutes a significant threat to human well-being, underscoring the critical importance of accurate measurements. The condensation particle counter (CPC) is the primary instrument for quantifying aviation soot, with detection efficiency being a crucial parameter. The properties of small particles and the symmetry of their growth pathways are closely related to the detection efficiency of the CPC. In laboratory environments, sodium chloride is conventionally utilized to calibrate the CPC's detection efficiency. However, aviation soot exhibits distinctive morphological characteristics compared to the calibration particles, leading to detection efficiencies obtained from calibration particles that may not be applicable to aviation soot. To address this issue, a quantitative study was performed to explore the detection efficiency deviations between aviation soot and calibration particles. The experiment initially utilized a differential mobility analyzer to size select the two types of polydisperse particles into monodisperse particles. Subsequently, measurements of the separated particles were performed using the TSI Corporation's aerosol electrometer and a rigorously validated CPC (BH-CPC). These allowed for determining the detection efficiency deviation in the BH-CPC for the two types of particles at different particle sizes. Furthermore, the influence of the operating temperature of the BH-CPC on this detection efficiency deviation was investigated. The experimental results indicate a significant detection efficiency deviation between aviation soot and sodium chloride. In the range of 10–40 nm, the absolute detection efficiency deviation can reach a maximum of 0.15, and the relative deviation can reach a maximum of 0.75. And this detection efficiency deviation can be reduced by establishing a relevant relationship between the detection efficiency of the operating temperature and the calibration temperature. Compared to the saturated segment calibration temperature of 50 °C, the aviation soot detection efficiency is closer to the sodium chloride detection efficiency at the calibration temperature of 50 °C when the saturated segment operates at a temperature of 45 °C. These studies provide crucial theoretical guidance for enhancing the precision of aviation soot emission detection and establish a foundation for future research in monitoring and controlling soot emissions within the aviation sector. [ABSTRACT FROM AUTHOR]

Different ways of representing the group SU(3)$$ SU(3) $$ within a Geometric Algebra approach are explored. As part of this, we consider characteristic multivectors for SU(3)$$ SU(3) $$ and how these are linked with decomposition of generators into commuting bivectors. The setting for this work is within a 6d Euclidean Clifford Algebra. We then go on to consider whether the fundamental forces of particle physics might arise from symmetry considerations in just the 4d geometric algebra of spacetime—the STA. As part of this, a representation of SU(3)$$ SU(3) $$ is found wholly within the STA, involving preservation of a bivector norm. We also show how Octonions can be fully represented within the Spacetime Algebra, which we believe will be useful in making them understandable and accessible to a new community in Physics and Engineering. The two strands of the paper are drawn together in showing how preserving the octonion norm is the same as preserving the timelike part of the Dirac current of a particle. This suggests a new model for the symmetries preserved in particle physics. Following on from work by Günaydin and Gürsey on the link between quarks, and octonions, and by Furey on chains of octonionic multiplications, we show how both of these fit well within our scheme and give some wholly STA versions of the operations involved, which in the cases considered have easily understandable equivalents in terms of 4d geometry. Links with larger groups containing SU(3)$$ SU(3) $$, such as G2$$ {G}_2 $$ and SU(8)$$ SU(8) $$, are also considered. [ABSTRACT FROM AUTHOR]

Self-assembly of isotropically interacting particles into desired crystal structures could allow for creating designed functional materials via simple synthetic means. However, the ability to use isotropic particles to assemble different crystal types remains challenging, especially for generating low-coordinated crystal structures. Here, we demonstrate that isotropic pairwise interparticle interactions can be rationally tuned through the design of DNA shells in a range that allows transition from common, high-coordinated FCC-CuAu and BCC-CsCl lattices, to more exotic symmetries for spherical particles such as the SC-NaCl lattice and to low-coordinated crystal structures (i.e., cubic diamond, open honeycomb). The combination of computational and experimental approaches reveals such a design strategy using DNA-functionalized nanoparticles and successfully demonstrates the realization of BCC-CsCl, SC-NaCl, and a weakly ordered cubic diamond phase. The study reveals the phase behavior of isotropic nanoparticles for DNA-shell tunable interaction, which, due to the ease of synthesis is promising for the practical realization of non-close-packed lattices. [ABSTRACT FROM AUTHOR]

Janus particles, which have an attractive patch on the otherwise repulsive surface, have been commonly employed for anisotropic colloidal assembly. While current methods of particle synthesis allow for control over the patch size, they are generally limited to producing dome-shaped patches with a high symmetry (C∞). Here, we report on the synthesis of Janus particles with patches of various tunable shapes, having reduced symmetries ranging from C2v to C3v and C4v. The Janus particles are synthesized by partial encapsulation of an octahedral metal-organic framework particle (UiO-66) in a polymer matrix. The extent of encapsulation is precisely regulated by a stepwise, asymmetric dewetting process that exposes selected facets of the UiO-66 particle. With depletion interaction, the Janus particles spontaneously assemble into colloidal clusters reflecting the particles' shapes and patch symmetries. We observe the formation of chiral structures, whereby chirality emerges from achiral building blocks. With the ability to encode symmetry and directional bonding information, our strategy could give access to more complex colloidal superstructures through assembly. Janus particles commonly exhibit a high-symmetry patch, constraining the range of possible assemblies. Here, the authors devise a synthetic approach to fine-tune the patch symmetry in Janus particles and showcase the assembly of these particles into chiral colloidal clusters. [ABSTRACT FROM AUTHOR]

Bright beams are commonly represented by sampled data in the numerical algorithms used to simulate their properties. However, in these calculations and the analyses of their outputs, the beam's density is sometimes required and must be calculated from the samples. Axisymmetric beams, which possess a rotational symmetry and are naturally expressed in polar coordinates, pose a particular challenge to density estimators. The area element in polar coordinates shrinks as the radius becomes small, and weighting the samples to account for their reduced frequency may cause unwelcome artifacts. In this work, we derive analytical expressions for two kernel density estimators, which solve these problems in the spatial coordinates and in the transverse phase space. We show how the kernels can be found by averaging the Gaussian kernel in Cartesian coordinates over the polar angle and demonstrate their use on test problems. These results show that particle beam symmetries can be taken advantage of in density estimation while avoiding artifacts. [ABSTRACT FROM AUTHOR]

Two dimensional conformal field theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories. [ABSTRACT FROM AUTHOR]

The problem of calculating the electromagnetic field of a charged test particle moving in the field of a Schwarzschild black hole is considered. In the framework of the non-stationary problem, it is shown that the electromagnetic field produced by the particle moving along the radial geodesic tends to spherical symmetry as the particle approaches the event horizon. [ABSTRACT FROM AUTHOR]

Experimental development of translational DNA nanomotors recently underwent a paradigm shift from bridge-burning monomers to symmetric dimers capable of truly sustainable motion. The focus of direction rectification is changed from carving the external landscape of a single particle to symmetry breaking from within a dimer. The symmetric dimer construction have the potential to facilitate efficient motors as friction, which is inevitable as a single particle moving in a viscous environment, may vanish for paired systems. However, creating high-performing nanomotors remains an open question from a fundamental physics perspective. Here, we present a realistic physical model for dimeric nanomotors that can be exactly solved to yield motor functions from experimentally accessible non-motor elements by mere physical laws—in a surprisingly rich mechanistic variety covering virtually all advanced dimeric DNA nanomotors invented to date plus major biological counterparts to a certain extent. The model exposes a high-performing regime with a sign of superlubricity for efficient motor operation. Reasonably simple for accurate treatments yet mechanistically telling, the present model has potential to evolve into a generic model to guide experimental optimization of DNA nanomotors toward low-dissipation operation. [ABSTRACT FROM AUTHOR]

We show that the ideas related to integrability and symmetry play an important role not only in the string T-duality story but also in its point particle counterpart. Applying those ideas, we find that the T-duality seems to be a more widespread phenomenon in the context of the point particle dynamics than it is in the string one; moreover, it concerns physically very relevant point particle dynamical systems and not just somewhat exotic ones fabricated for the purpose. As a source of T-duality examples, we consider maximally superintegrable spherically symmetric electro-gravitational backgrounds in n dimensions. We then describe in detail four such spherically symmetric dynamical systems which are all mutually interconnected by a web of point particle T-dualities. In particular, the dynamics of a charged particle scattered by a repulsive Coulomb potential in a flat space is T-dual to the dynamics of the Coulomb scattering in the space of constant negative curvature, but it is also T-dual to the (conformal) Calogero–Moser inverse square dynamics both in flat and hyperbolic spaces. Thus knowing just the Hamiltonian dynamics of the scattered particle cannot give us information about the curvature of the space in which the particle moves. [ABSTRACT FROM AUTHOR]

In this work, an analogue to the Pauli spin matrices is presented and investigated. The proposed Hermitian spin matrices exhibit four symmetries for spin-1/n particles. The spin projection operators are derived, and the electrodynamics for hypothetical spin-1/2 fermions are explored using the proposed spin matrices. The fermionic quantum Heisenberg model is constructed using the proposed spin matrices, and comparative studies against simulation results using the Pauli spin matrices are conducted. Further analysis of the key findings as well as discussions on extending the proposed spin matrix framework to describe hypothetical bosonic systems (spin-1 particles) are provided. [ABSTRACT FROM AUTHOR]

Nonlinear fluid simulation of drift wave turbulence in the presence of symmetry breaking particle source is performed for the cylindrical magnetized plasmas. It is demonstrated that the symmetry breaking of the system directly affects the selection rule of structure formations, the streamers disappear, and the zonal flows are enhanced in the case with the symmetry breaking. The symmetry breaking is introduced in the flux-driven simulation by inducing the particle source whose amplitude depends on the azimuthal angle. The symmetry breaking mode is driven stationarily, and the nonlinear process of the drift waves is significantly modified. By scanning the amplitude of the symmetry breaking source, the structure formation processes are systematically investigated. In addition, the nonlinear forces of the turbulence show the relaxation of the density gradient and the drive of the perpendicular/parallel flows in a two-dimensional manner. [ABSTRACT FROM AUTHOR]

The reflection of sunlight off the snow is a major driver of the Earth's climate. This reflection is governed by the shape and arrangement of ice crystals at the micrometer scale, called snow microstructure. However, snow optical models overlook the complexity of this microstructure by using simple shapes, and mainly spheres. The use of these various shapes leads to large uncertainties in climate modeling, which could reach 1.2 K in global air temperature. Here, we accurately simulate light propagation in three-dimensional images of natural snow at the micrometer scale, revealing the optical shape of snow. This optical shape is neither spherical nor close to the other idealized shapes commonly used in models. Instead, it more closely approximates a collection of convex particles without symmetry. Besides providing a more realistic representation of snow in the visible and near-infrared spectral region (400 to 1400 nm), this breakthrough can be directly used in climate models, reducing by 3 the uncertainties in global air temperature related to the optical shape of snow. Micrometre scale simulation of the trajectory of sunlight as it reaches the snowpack shows what snow looks like from the photon's perspective, providing a more universal representation of snow in optical models. [ABSTRACT FROM AUTHOR]

We present the twisted covariant form hierarchies (TCFHs) of warped (massive) IIA AdS backgrounds. As a consequence we demonstrate that all Killing spinor form bilinears satisfy a generalisation of the conformal Killing-Yano equation with respect to the TCFH connections. We also explore some of the properties of TCFHs which include the reduced holonomy of the minimal TCFH connections for generic backgrounds. Furthermore, we investigate the interplay between TCFHs and hidden symmetries of probes propagating on IIA AdS backgrounds. We find that some of the Killing spinor form bilinears of near horizon geometries of a class of IIA intersecting brane configurations are Killing-Yano forms and so generate hidden symmetries for spinning particle probes. [ABSTRACT FROM AUTHOR]

We present the TCFHs of all AdS backgrounds of 11-dimensional supergravity and explore some of the properties of the associated connections. Therefore, we demonstrate that all Killing spinor bilinears satisfy a generalisation of the conformal Killing-Yano equations with respect to the TCFH connection. In addition, we explore the hidden symmetries of spinning particle probes propagating on these backgrounds. We give several examples of hidden symmetries for probes on the maximal supersymmetric AdS backgrounds as well as on some AdS backgrounds that arise as near horizon geometries of intersecting M-branes. [ABSTRACT FROM AUTHOR]

We present the twisted covariant form hierarchies (TCFHs) on the internal spaces of all type IIB warped AdS backgrounds. As a result we demonstrate that the form bilinears on the internal spaces satisfy a generalisation of the conformal Killing-Yano equation. We also explore some of the properties of the TCFHs, like for example the holonomy of the TCFH connections. In addition, we present examples where the form bilinears generate hidden symmetries for particle probes propagating on the internal spaces of some AdS backgrounds. These include the maximally supersymmetric AdS5 solution as well as some of the near horizon geometries of intersecting IIB branes. [ABSTRACT FROM AUTHOR]

Many definitions of moist potential vorticity (PV) have been proposed to extend the dry theory of Ertel PV. None of the moist PV definitions seem to have all of the desirable properties of the dry Ertel PV. For instance, dry PV is not only a globally conserved quantity, but also a material invariant that is conserved along fluid parcel trajectories. Therefore, an open question remains: Is there a moist PV that is a material invariant, if clouds and phase changes of water are present? In prior studies, definitions of moist PV have been proposed based on physical and mathematical intuition. Here, a systematic approach is used. In particular, a particle relabeling symmetry is devised for a moist atmosphere and then Noether's theorem is employed to arrive at the associated conservation laws for a moist PV. A priori, it is not clear whether this systematic approach will be viable, since it relies on variational derivatives in Hamilton's principle, and phase changes introduce singularities that could potentially prevent derivatives at the cloud edge. However, it is shown that the energy and the Lagrangian density are sufficiently smooth to allow variational derivatives, in a moist Boussinesq system with reversible phase transitions between water vapor and liquid cloud water. From the particle relabeling symmetry, a moist Kelvin circulation theorem is found, along with a moist PV conservation law that applies not for each individual parcel but for parcel‐integrated PV, integrated over certain local volumes. [ABSTRACT FROM AUTHOR]

In this review, the modern achievements in studies of the Pauli exclusion principle (PEP) and the properties of the identical particle systems when PEP is not fulfilled are discussed. The validity of conception of the spin in the framework of density functional theory (DFT) approaches is analyzed. The modern state of the recently discovered Fe-based superconductors is discussed in detail. These materials belong to the paramagnetic semimetal family and become superconductors upon doping. Recently, in 2020, room-temperature superconductivity was realized. However, from the following discussion in the SC community, it was not evident that the results of room-temperature superconductivity have been repeated by other laboratories. Thus, the question "is room temperature really achieved?" is still open. In the concluding remarks, we present the explanation of why the PEP limitations on the symmetry of identical particles system exist in nature, and following from it, some important consequences. [ABSTRACT FROM AUTHOR]

The majority of properties of physical systems and molecules are derived from the character and interaction of their constituent atoms. The symmetry of these interactions provides significant insight into the form and quality of resultant properties such as polarizability, dipole moments, and elasticity. In order to better utilise symmetry as a tool within science, here we introduce four novel methods of symmetry analysis as part of the Irregular Particle Symmetry Analysis software (IPSA). The IPSA software package presents a framework for examining continuous symmetry and group theory under a consistent structure, enabling a unique insight into how the geometric symmetry of atomic structures may be examined and quantified. The methods presented within this paper are practical procedures for characterisation and low-cost additions to existing examinations of materials and molecular properties with a wide range of applications, including areas such as electronic structure estimation, calculation simplification, geometry classification, analysis of dynamics, spectrographic interpretation, and property prediction. [ABSTRACT FROM AUTHOR]

The Standard Model (SM) of particle physics is the most general renormalizable theory which is built on a few general principles and fundamental symmetries with the given particle content. However, multiple symmetries are not built into the model and are simply consequences of renormalizabilty, gauge invariance, and particle content of the theory. It is crucial to test the validity of these types of symmetries and related conservation laws experimentally. The CERN LHC provides the highest sensitivity for testing the SM symmetries at high energy scales involving heavy particles such as the top quark. In this article, we are going to review the recent experimental searches of charge–parity and charged-lepton flavor violation in the top quark sector. [ABSTRACT FROM AUTHOR]

In a recent paper Fenni et al. (2021, https://doi.org/10.1029/2020jd034172) compared the code MIDAS, based on the direct solution of the volume‐integral equation combined with advanced cubatures for orientation averaging, to the code DDSCAT, a state‐of‐the‐art implementation of the discrete dipole approximation. This comment highlights methodological issues in this comparison and shows that the quantitative claims of Fenni et al. (2021, https://doi.org/10.1029/2020jd034172), related to superiority of MIDAS over DDSCAT, are based on very specific test cases with respect to particle symmetries or initial orientation, as well as to the selected scattering quantity of interest. Thus, these claims are not expected to hold for other similar particles. Moreover, the detailed discussion of these issues is relevant for all light‐scattering simulation methods, except those allowing analytical orientation averaging. Thus, the comment constructs general guidelines for fair evaluation of orientation‐averaging techniques in a wide range of light‐scattering methods and computer codes. Plain Language Summary: The paper discusses several issues that appear when one is comparing different orientation‐averaging techniques (cubatures) in combination with the same or different light‐scattering simulation methods. Fair evaluation of cubature performance in realistic general scenarios is important both for practitioners (to choose the most efficient combination of the existing codes and cubatures) and for code developers (to set their priorities on the new features with the largest expected benefits). Unfortunately, the performance of the cubatures is complexly interwoven with the internals of the simulation methods and depends on specific test particles and computed scattering quantities. This questions the generality of conclusions in some previous publications. Based on this discussion, the paper ends with general guidelines for fair evaluation of cubatures, allowing future studies to arrive at general conclusions, so that they can be directly used by other researchers. Key Points: Quantitative conclusions of Fenni et al. (2021) are based on very specific test casesOrientation‐averaging techniques should be compared on non‐symmetric particles, and not with a special initial orientationAny comparison of simulated results should consider their uncertainties accounting for all sources of errors [ABSTRACT FROM AUTHOR]

The search for fundamental determinants of bio-molecular chirality is a hot topic in biology, clarifying the meaning of evolution and the enigma of life's origin. The question of origin may be resolved assuming that non-biological and biological entities obey nature's universal laws grounded on space-time symmetry (STS) and space-time relativity (SPR). The fabric of STS is our review's primary subject. This symmetry, encompassing the behavior of elementary particles and galaxy structure, imposes its fundamental laws on all hierarchical levels of the biological world. From the perspective of STS, objects across spatial scales may be classified as chiral or achiral concerning a specific space-related symmetry transformation: mirror reflection. The chiral object is not identical (i.e., not superimposable) to its mirror image. In geometry, distinguish two kinds of chiral objects. The first one does not have any reflective symmetry elements (a point or plane of symmetry) but may have rotational symmetry axes (dissymmetry). The second one does not have any symmetry elements (asymmetry). As the form symmetry deficiency, Chirality is the critical structural feature of natural systems, including sub-atomic particles and living matter. According to the Standard Model (SM) theory and String Theory (StrT), elementary particles associated with the four fundamental forces of nature determine the existence of micro- and galaxy scales of nature. Therefore, the inheritance of molecular symmetry from the symmetry of elementary particles indicates a bi-directional (internal [(micro-scale) and external (galaxy sale)] causal pathway of prevalent bio-chirality. We assume that the laws of the physical world impact the biological matter's appearance through both extremities of spatial dimensions. The extended network of multi-disciplinary experimental evidence supports this hypothesis. However, many experimental results are derived and interpreted based on the narrow-view prerogative and highly specific terminology. The current review promotes a holistic approach to experimental results in two fast-developing, seemingly unrelated, divergent branches of STS and biological chirality. The generalized view on the origin of prevalent bio-molecular chirality is necessary for understanding the link between a diverse range of biological events. The chain of chirality transfer links ribosomal protein synthesis, cell morphology, and neuronal signaling with the laterality of cognitive functions. [ABSTRACT FROM AUTHOR]

We compute the conserved charges associated with the asymptotic symmetries of massless particles by examining their free theory in Minkowski space–time. We give a procedure to systematically deduce the fall off of the massless fields at spatial infinity and show that it has a universal behavior when expressed in tangent space. We do this for generic massless particles. We do not impose gauge fixing conditions, which will allow us to uncover new nonzero charges for the graviton beyond the well-known supertranslation charges. We also compute conserved charges in the dual formulations of certain low-spin particles and argue that this leads to an infinite number of new conserved charges. [ABSTRACT FROM AUTHOR]

Numerical simulation of the process of melting of aluminum nanoparticles is carried out with the use of the methods of molecular dynamics. It is established that the melting of aluminum particles depends on the potential of their interaction and on the type of the particle symmetry. Dependence of the melting temperature of aluminum nanoparticles on the size of the latter is investigated. [ABSTRACT FROM AUTHOR]

Many diseases are caused by viruses of different symmetrical shapes. Rotavirus particles are approximately 75 nm in diameter. They have icosahedral symmetry and particles that possess two concentric protein shells, or capsids. In this research, using a piecewise derivative framework with singular and non-singular kernels, we investigate the evolution of rotavirus with regard to the effect of vaccination. For the considered model, the existence of a solution of the piecewise rotavirus model is investigated via fixed-point results. The Adam–Bashforth numerical method along with the Newton polynomial is implemented to deduce the numerical solution of the considered model. Various versions of the stability of the solution of the piecewise rotavirus model are presented using the Ulam–Hyres concept and nonlinear analysis. We use MATLAB to perform the numerical simulation for a few fractional orders to study the crossover dynamics and evolution and effect of vaccination on rotavirus disease. To check the validity of the proposed approach, we compared our simulated results with real data from various countries. [ABSTRACT FROM AUTHOR]

In this note, we first recall that the sets of all representatives of some special ordinary residue classes become m , n -rings. Second, we introduce a possible p-adic analog of the residue class modulo a p-adic integer. Then, we find the relations which determine when the representatives form a m , n -ring. At very short spacetime scales, such rings could lead to new symmetries of modern particle models. [ABSTRACT FROM AUTHOR]

Small-angle neutron scattering (SANS) is widely used in structural analysis of complex liquid dispersions. An essential feature of SANS experiments for such systems is hydrogen/deuterium isotopic substitution in liquid media, which makes it possible to change the neutron scattering length density of the solvents, thus providing the basis for the contrast variation technique. In some cases, for dispersed particles with near-spherical symmetry, one can observe in the scattering curves specific points at which the scattered intensity is independent of the scattering contrast between dispersed particles and solvent. These points are referred to as 'isoscattering points' and in monodisperse solutions related to the particle size. Here, we report this effect for rather polydisperse (above 40%) magnetic fluids with core-shell particles in a liquid medium (water). It is shown that the effective isoscattering point can be analyzed to some extent for polydisperse systems, which gives additional possibilities for structural characterization of complex solutions via SANS. [ABSTRACT FROM AUTHOR]

We introduce a phase field crystal (PFC) model for particles with n -fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the orientation, and the direction of the orientation, where all these order parameters depend on the position. The functional is constructed such that for particles with axial symmetry (i.e. n = 2) the PFC model for liquid crystals as introduced by Löwen (2010 J. Phys.: Condens. Matter 22 364105) is recovered. We discuss the stability of the functional and explore phases that occur for 1 ⩽ n ⩽ 6. In addition to isotropic, nematic, stripe, and triangular order, we also observe cluster crystals with square, rhombic, honeycomb, and even quasicrystalline symmetry. The n -fold symmetry of the particles corresponds to the one that can be realized for colloids with symmetrically arranged patches. We explain how both, repulsive as well as attractive patches, are described in our model. [ABSTRACT FROM AUTHOR]

I propose using the group SL (4 , ℝ) as a generalization of the Dirac group SL (2 , ℂ) used in quantum mechanics, in an attempt to match the symmetries of the 'internal' spacetime of elementary particles to the symmetries of the 'external' spacetime of general relativity. While my conclusions do not amount to a new model or theory, they do highlight some specific points where there are apparent conflicts between the mathematics and the physics of the standard model, that might repay closer investigation. As evidence that this mathematical approach may have interesting things to say about physics, I propose two mass equations that seem not to have been observed previously. [ABSTRACT FROM AUTHOR]

The invariant imbedding T-matrix (IIM T-matrix) model is regarded as one of the most promising models for calculating the scattering parameters of non-spherical particles. However, the IIM T-matrix model needs to be iterated along the radial direction when calculating the T-matrix, which involves complex calculations such as matrix inversion and multiplication. Therefore, how to improve its computational efficiency is an important problem to be solved. Focused on particles with N-fold symmetric geometry, this paper deduced the symmetry in the calculation process of the IIM T-matrix model, derived the block iteration scheme of the T-matrix, and contracted the IIM T-matrix program for particles with N-fold symmetric geometry. Discrete Dipole Approximation (DDA) and Geometrical Optics Approximation (IGOA) were employed to verify the accuracy of the improved IIM T-matrix model. The results show that the six phase matrix elements (P11, P12/P11, P22/P11, P33/P11, P34/P11 and P44/P11) calculated by our model are in good agreement with other models. The computational efficiency of the improved IIM T-matrix model was further investigated. As demonstrated by the results, the computational efficiency for the particles with N-fold symmetry improved by nearly 70% with the improvement of the symmetry of U matrix and T matrix. In conclusion, the improved model can remarkably reduce the calculation time while maintaining high accuracy. [ABSTRACT FROM AUTHOR]

We present the twisted covariant form hierarchies (TCFH) of type IIA and IIB 10-dimensional supergravities and show that all form bilinears of supersymmetric backgrounds satisfy the conformal Killing-Yano equation with respect to a TCFH connection. We also compute the Killing-Stäckel, Killing-Yano and closed conformal Killing-Yano tensors of all spherically symmetric type II brane backgrounds and demonstrate that the geodesic flow on these solutions is completely integrable by giving all independent charges in involution. We then identify all form bilinears of common sector and D-brane backgrounds which generate hidden symmetries for particle and string probe actions. We also explore the question on whether charges constructed from form bilinears are sufficient to prove the integrability of probes on supersymmetric backgrounds. [ABSTRACT FROM AUTHOR]

Deep learning methods have been increasingly adopted to study jets in particle physics. Since symmetry-preserving behavior has been shown to be an important factor for improving the performance of deep learning in many applications, Lorentz group equivariance — a fundamental spacetime symmetry for elementary particles — has recently been incorporated into a deep learning model for jet tagging. However, the design is computationally costly due to the analytic construction of high-order tensors. In this article, we introduce LorentzNet, a new symmetry-preserving deep learning model for jet tagging. The message passing of LorentzNet relies on an efficient Minkowski dot product attention. Experiments on two representative jet tagging benchmarks show that LorentzNet achieves the best tagging performance and improves significantly over existing state-of-the-art algorithms. The preservation of Lorentz symmetry also greatly improves the efficiency and generalization power of the model, allowing LorentzNet to reach highly competitive performance when trained on only a few thousand jets. [ABSTRACT FROM AUTHOR]

The finite-element method has been employed to calculate the photophoresis force applied to a solid spheroidal aerosol particle, the size of which is much larger than the mean free path of gas molecules. The thermal electromagnetic radiation from the particle surface and the temperature dependences of the density, viscosity, and thermal conductivity of the gaseous medium and the particle material thermal conductivity have been taken into account. The photophoresis force applied to the particle heated by an electromagnetic radiation flux directed along the particle symmetry axis has been numerically calculated. [ABSTRACT FROM AUTHOR]

In this special issue being brought in the centenary year of the birth of Yoichiro Nambu, we exemplify on his discovery of spontaneous symmetry breaking in elementary particle physics, and review precision pion physics in the present era. The notion of spontaneous symmetry breaking in elementary particle physics was introduced by Nambu, and found a realization in the strong interaction sector. It allows one to view the pions as the approximate Nambu–Goldstone bosons of spontaneously broken axial-vector symmetries associated with the (near) masslessness of quarks. Inspired by the phenomenon of superconductivity of condensed matter physics, Nambu found this application in a remarkable tour de force. Nambu's work in collaboration with G. Jona-Lasinio gave a dynamical model where such pions may arise. Pions today play the role of being sensitive probes of the ground state of quantum chromodynamics, the Lagrangian field theory of the strong interactions with (confined) quark and gluon degrees of freedom, and whose ground state spontaneously breaks the approximate chiral symmetry. The presence of non-zero quark masses renders the symmetries approximate, and yet the properties of the low-energy sector can both be described and measured at high precision both in experiment and on the lattice. Notable physical quantities include the neutral pion lifetime and pion scattering lengths. An important role of pions is their contribution to the hadronic radiative corrections to the anomalous magnetic moment of the muon, which is being measured at high precision at Fermilab. We review some of the important aspects of the state of the art. We also say some words about the outstanding contributions of the recently departed Murray Gell-Mann who was a pioneer in the field initiated by Nambu. [ABSTRACT FROM AUTHOR]

We provide a detailed discussion on the electromagnetic modeling and classification of the polarization converting bianisotropic metasurfaces. To do so, we first present a general approach to compute the scattering response of such metasurfaces, which relies on a generalized sheet transition conditions (GSTCs)-based susceptibility model. Then, we review how the fundamental properties of reciprocity, energy conservation, rotation invariance, and matching may be expressed in terms of metasurface susceptibilities and scattering parameters, and show how these properties may affect and limit the polarization effects of metasurfaces. Finally, we connect together the metasurface susceptibility model to the structural symmetries of scattering particles and their associated polarization effects. This work thus provides a detailed understanding of the polarization conversion properties of metasurfaces and may prove to be of particular interest for their practical implementation. [ABSTRACT FROM AUTHOR]

A variety of observations impose upper limits at the nano Gauss level on magnetic fields that are coherent on inter-galactic scales while blazar observations indicate a lower bound ∼10−16 G. Such magnetic fields can play an important astrophysical role, for example at cosmic recombination and during structure formation, and also provide crucial information for particle physics in the early Universe. Magnetic fields with significant energy density could have been produced at the electroweak phase transition. The evolution and survival of magnetic fields produced on sub-horizon scales in the early Universe, however, depends on the magnetic helicity which is related to violation of symmetries in fundamental particle interactions. The generation of magnetic helicity requires new CP violating interactions that can be tested by accelerator experiments via decay channels of the Higgs particle. [ABSTRACT FROM AUTHOR]

Janus particles are widely sought for applications related to colloidal assembly, stabilization of emulsions, and development of active colloids, among others. Here we report a versatile route to the fabrication of well‐controlled Janus particles by simply breaking the symmetry of spherical particles with swelling. When a polystyrene (PS) sphere covered by a rigid shell made of silica or polydopamine is exposed to a good solvent for PS, a gradually increased pressure will be created inside the shell. If the pressure becomes high enough to poke a hole in the shell, the spherical symmetry will break while pushing out the swollen PS through the opening to generate a Janus particle comprised of two distinct components. One of the components is made of PS and its size is controlled by the extent of swelling. The other component is comprised of the rigid shell and remaining PS, with its overall diameter determined by the original PS sphere and the rigid shell. This solution‐based route holds promises for the scalable production of complex Janus particles with a variety of compositions and in large quantities. [ABSTRACT FROM AUTHOR]

The asymmetry between deuterium (D) and tritium (T) turbulent particle fluxes in mixed D–T plasmas is studied with numerical simulations of nonlinear gyrokinetic turbulence in ion temperature gradient-dominated and trapped electron mode-dominated regimes. At 50–50 D–T concentration, the asymmetry, or flow separation, between D and T fluxes is such that the tritium is better confined than the deuterium in both regimes. To supplement the nonlinear simulations, an analytic quasilinear theory of the particle flux symmetry breaking is developed and is valid for general electron dynamics. This theory correctly predicts the numerically computed deviation in the ion density fraction (from 50–50), or ion density gradient (from the electron gradient), required to restore equal deuterium and tritium fluxes. [ABSTRACT FROM AUTHOR]

Janus particles are widely sought for applications related to colloidal assembly, stabilization of emulsions, and development of active colloids, among others. Here we report a versatile route to the fabrication of well‐controlled Janus particles by simply breaking the symmetry of spherical particles with swelling. When a polystyrene (PS) sphere covered by a rigid shell made of silica or polydopamine is exposed to a good solvent for PS, a gradually increased pressure will be created inside the shell. If the pressure becomes high enough to poke a hole in the shell, the spherical symmetry will break while pushing out the swollen PS through the opening to generate a Janus particle comprised of two distinct components. One of the components is made of PS and its size is controlled by the extent of swelling. The other component is comprised of the rigid shell and remaining PS, with its overall diameter determined by the original PS sphere and the rigid shell. This solution‐based route holds promises for the scalable production of complex Janus particles with a variety of compositions and in large quantities. [ABSTRACT FROM AUTHOR]

Baryons B (Q q q ′) for heavy quarks Q = c , b , t , and light quarks q = u , d , s , are considered. Strong interaction coupling-constant sum rules with first-order breaking of SU(3) flavor symmetry are determined for reactions B → B ′ + M where B = B (Q q q ′) , B ′ = B (Q q q ″) and M = M (q ′ q ̄ ″) is a light meson. Specific applications to couplings of J P = 1 2 + charmed and bottom baryons are presented. Also, SU(3) Clebsch–Gordan coefficients for the product of representations 6 ⊗ 8 are explicitly determined. [ABSTRACT FROM AUTHOR]