Breaking Phenomena Research Articles

Symmetry Breaking: Case Studies with Organic Cage-Racemates.

ConspectusSymmetry is a pervasive phenomenon spanning diverse fields, from art and architecture to mathematics and science. In the scientific realms, symmetry reveals fundamental laws, while symmetry breaking─the collapse of certain symmetry─is the underlying cause of phenomena. Research on symmetry and symmetry breaking consistently provides valuable insights across disciplines, from parity violation in physics to the origin of homochirality in biology. Chemistry is particularly rich in symmetry breaking studies, encompassing areas such as asymmetric synthesis, chiral resolution, chiral structure assembly, and so on. Across different disciplines, a well-defined methodology is fundamental and necessary to analyze the symmetry or symmetry breaking nature behind the phenomenon, enabling researchers to uncover the underlying principles and mechanisms. Basically, three key points underpin symmetry-related research: the scale-dependency of symmetry/symmetry breaking, the driving force behind symmetry breaking phenomena, and the properties arising from symmetry breaking.This Account will focus on the three aforementioned key points elucidated with organic cages as proof-of-concept models, as organic cages exhibit shape-persistent 3D molecular frameworks, well-defined molecular motion, and a high propensity for crystallization.First, we examine racemization processes of organic cages with dynamic molecular motions to illustrate that symmetry and symmetry breaking are time-scale-dependent. Specifically, the racemization, driven by molecular motion, is influenced by hydrogen bonding and the rigidity of the cage framework, which may or may not be observable within the experimental temporal scale. This determines whether the enantiomeric excess system, namely, the symmetry broken system, can be detected experimentally. We also investigate the hierarchical structures self-assembled by racemic organic cages, demonstrating that symmetry and asymmetry manifest differently across spatial scales, from molecular to supramolecular and macroscopic levels. Second, we discuss the driving force behind spontaneous chiral resolution─a classic symmetry-breaking event during crystallization─from a thermodynamic perspective. We suggest that racemic compounds, compared to conglomerates, are more entropy-favored, explaining their greater prevalence in nature. Spontaneous chiral resolution can take place only when a favorable enthalpy compensates for unfavorable entropy. In conglomerates composed of organic cages, strong intermolecular interactions along the screw axes provide the necessary compensation. Finally, we explore the unique properties that emerge from symmetry-broken molecular packing within crystals of cage racemates, such as second-harmonic generation and piezoelectricity. It turns out that the symmetry operation in molecular packing plays a critical role in determining material properties. By comprehensively analyzing symmetry and symmetry-breaking in organic cage racemates, this Account provides insights into symmetry-related phenomena across scientific disciplines. It also paves the way for designing novel materials with tailored properties for applications in optics, electronics, and beyond.

Methodology for Modeling Nonlinear Thermomechanical Response With Wear at High-Speed Interactions: Application to a Pin–Disk Configuration

Abstract An aircraft engine is a complex structure for which some components can come into contact at high speed. Modeling this behavior is very complex as multiple physics must be considered. State-of-the-art methodologies usually account for permanent contact and thermal modeling. In this paper, a new approach is proposed and embeds various phenomena such as nonregular and nonlinear contact mechanics, surface rubbing, wear, and nonlinear heat transfer. A nonlinear version of Moreau–Jean algorithm is employed to compute the transient response of the system and to capture accurately the contact dynamics. Moreover, the full nonlinear coupling between the dynamics and the heating process is taken into account through both a semi-analytical formulation and the finite element (FE) method. At the contact interface, heat flux is generated by dry rubbing and flows into both interacting bodies. The heat flux partition is evaluated thanks to a coefficient that depends on the material properties of the solids in contact. The proposed method also accounts for the adhesive wear between the solids through an energetic approach. This methodology is applied to an academic, yet realistic, disk connected to a rotor shaft that is free to move axially and to rotate around its revolution axis. Gyroscopic effects and variation of the rotation velocity are included leading to a full nonlinear mechanical behavior. The disk undergoes aerodynamic load moving it to contact with a clamped free pin. The rotor shaft and the pin are both modeled as one-dimensional (1D) elastic bodies, while the rotor disk is assumed to be rigid. Through this example, the developed strategy shows its potential to compute the complete transient highly nonlinear response of the breaking phenomenon, in an acceptable time simulation.

Nuclear Structure of Dripline Nuclei Elucidated through Precision Mass Measurements of ^{23}Si, ^{26}P, ^{27,28}S, and ^{31}Ar.

Using the Bρ-defined isochronous mass spectrometry technique, we report the first determination of the ^{23}Si, ^{26}P, ^{27}S, and ^{31}Ar masses and improve the precision of the ^{28}S mass by a factor of 11. Our measurements confirm that these isotopes are bound and fix the location of the proton dripline in P, S, and Ar. We find that the mirror energy differences of the mirror-nuclei pairs ^{26}P-^{26}Na, ^{27}P-^{27}Mg, ^{27}S-^{27}Na, ^{28}S-^{28}Mg, and ^{31}Ar-^{31}Al deviate significantly from the values predicted assuming mirror symmetry. In addition, we observe similar anomalies in the excited states, but not in the ground states, of the mirror-nuclei pairs ^{22}Al-^{22}F and ^{23}Al-^{23}Ne. Using abinitio VS-IMSRG and mean field calculations, we show that such a mirror-symmetry breaking phenomenon can be explained by the extended charge distributions of weakly bound, proton-rich nuclei. When observed, this phenomenon serves as a unique signature that can be valuable for identifying proton-halo candidates.

Engineering circularly polarized luminescence through symmetry manipulation in achiral tetraphenylpyrazine structures

Symmetry breaking, a critical phenomenon in both natural and artificial systems, is pivotal in constructing chiral structures from achiral building units. This study focuses on the achiral molecule 8,8',8'',8'''-((pyrazine-2,3,5,6-tetrayltetrakis(benzene-4,1-iyl))tetrakis (oxy))tetrakis (octan-1-ol) (TPP-C8OH), an aggregation-induced emission (AIE) molecule, to explore its symmetry breaking behavior in supramolecular assembly. By analyzing TPP-C8OH in various solvents‒both non-chiral and chiral‒we find that chiral solvents significantly enhance the molecule's symmetry breaking and chiroptical properties. Specially, alcohol solvents, particularly dodecyl alcohol, facilitate the formation of helical structures with both left-handed (M) and right-handed (P) helices within single twisted nanoribbons. This observation contrasts with previously reported symmetry breaking phenomena in assembly systems. Chiral solvents induce assemblies with distinct helical orientations, resulting in notable circularly polarized luminescence (CPL) and circular dichroism (CD) signals. This study elucidates the impact of solvent choice on symmetry breaking and chiral assembly, offering insights into the design of advanced chiral materials with tailored self-assembly processes.

Spontaneous symmetry breaking in generative diffusion models*

Abstract Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking phenomenon that divides the generative dynamics into two distinct phases: (1) a linear steady-state dynamics around a central fixed-point and, (2) an attractor dynamics directed towards the data manifold. These two ‘phases’ are separated by the change in stability of the central fixed-point, with the resulting window of instability being responsible for the diversity of the generated samples. Using both theoretical and empirical evidence, we show that an accurate simulation of the early dynamics does not significantly contribute to the final generation, since early fluctuations are reverted to the central fixed point. To leverage this insight, we propose a Gaussian late initialization scheme, which significantly improves model performance, achieving up to 3× Fréchet inception distance improvements on fast samplers, while also increasing sample diversity (e.g. racial composition of generated CelebA images). Our work offers a new way to understand the generative dynamics of diffusion models that has the potential to bring about higher performance and less biased fast-samplers.

Spontaneous symmetry breaking and vortices in a tri-core nonlinear fractional waveguide

We introduce a waveguiding system composed of three linearly-coupled fractional waveguides, with a triangular (prismatic) transverse structure. It may be realized as a tri-core nonlinear optical fiber with fractional group-velocity dispersion (GVD), or, possibly, as a system of coupled Gross–Pitaevskii equations for a set of three tunnel-coupled cigar-shaped traps filled by a Bose–Einstein condensate of particles moving by Lévy flights. The analysis is focused on the phenomenon of spontaneous symmetry breaking (SSB) between components of triple solitons, and the formation and stability of vortex modes. In the self-focusing regime, we identify symmetric and asymmetric soliton states, whose structure and stability are determined by the Lévy index of the fractional GVD, the inter-core coupling strength, and the total energy, which determines the system’s nonlinearity. Bifurcation diagrams (of the supercritical type) reveal regions where SSB occurs, identifying the respective symmetric and asymmetric ground-state soliton modes. In agreement with the general principles of the SSB theory, the solitons with broken inter-component symmetry prevail, as stable states, with the increase of the energy in the weakly-coupled system. Three-components vortex solitons (which do not feature SSB) are studied too. Because the fractional GVD breaks the system’s Galilean invariance, we also address mobility of the vortex solitons, by applying a boost to them.

Laboratory study of energy transformation characteristics in breaking wave groups

The spilling-breaking waves that appear in chirped wave packets are studied in a two-dimensional wave channel. These waves are produced by superposing waves with gradually decreasing frequencies. The analysis focuses on the nonlinear characteristics, energy variation, and energy transformation during the evolution and breaking of wave groups. Ensemble empirical mode decomposition is used to analyze the non-breaking and breaking energy variations of the intrinsic mode functions (IMFs). It is found that the third-order IMF component is a source of non-breaking energy dissipation and the second-order IMF, which represents a short wave group with a relatively higher energy content, is a primary source of the energy loss caused by wave breaking. Additionally, the findings reveal that among the three waves preceding the maximum crest, the wave closest to the maximum crest carried most of the energy. When wave breaking occurs, the energy dissipation caused by the wave breaking primarily originates from that wave. After wave breaking, whether it is the first breaker or subsequent breakers, the main energy dissipation occurs in a frequency range higher than the dominant frequency. This energy loss plays a significant role in increasing the energy of free waves. Moreover, a potential link between the number of carrier waves and wave breaking phenomena has been found. As the number of carrier waves increased, both the nonbreaking and breaking energy dissipation rates exhibited an overall increasing trend. The amount of nonbreaking energy dissipation was generally more than twice the breaking energy dissipation rate. For wave groups with more carrier waves, the modulation instability plays a significant role in generating larger waves. Furthermore, an analysis of the dominant frequency variations of the wave group before wave breaking suggests that wave breaking is not a sufficient condition for a frequency downshift in the wave spectra.

Three-dimensional wave breaking

Although a ubiquitous natural phenomenon, the onset and subsequent process of surface wave breaking are not fully understood. Breaking affects how steep waves become and drives air–sea exchanges1. Most seminal and state-of-the-art research on breaking is underpinned by the assumption of two-dimensionality, although ocean waves are three dimensional. We present experimental results that assess how three-dimensionality affects breaking, without putting limits on the direction of travel of the waves. We show that the breaking-onset steepness of the most directionally spread case is double that of its unidirectional counterpart. We identify three breaking regimes. As directional spreading increases, horizontally overturning ‘travelling-wave breaking’ (I), which forms the basis of two-dimensional breaking, is replaced by vertically jetting ‘standing-wave breaking’ (II). In between, ‘travelling-standing-wave breaking’ (III) is characterized by the formation of vertical jets along a fast-moving crest. The mechanisms in each regime determine how breaking limits steepness and affects subsequent air–sea exchanges. Unlike in two dimensions, three-dimensional wave-breaking onset does not limit how steep waves may become, and we produce directionally spread waves 80% steeper than at breaking onset and four times steeper than equivalent two-dimensional waves at their breaking onset. Our observations challenge the validity of state-of-the-art methods used to calculate energy dissipation and to design offshore structures in highly directionally spread seas.

Physics and chemistry from parsimonious representations: image analysis via invariant variational autoencoders

Electron, optical, and scanning probe microscopy methods are generating ever increasing volume of image data containing information on atomic and mesoscale structures and functionalities. This necessitates the development of the machine learning methods for discovery of physical and chemical phenomena from the data, such as manifestations of symmetry breaking phenomena in electron and scanning tunneling microscopy images, or variability of the nanoparticles. Variational autoencoders (VAEs) are emerging as a powerful paradigm for the unsupervised data analysis, allowing to disentangle the factors of variability and discover optimal parsimonious representation. Here, we summarize recent developments in VAEs, covering the basic principles and intuition behind the VAEs. The invariant VAEs are introduced as an approach to accommodate scale and translation invariances present in imaging data and separate known factors of variations from the ones to be discovered. We further describe the opportunities enabled by the control over VAE architecture, including conditional, semi-supervised, and joint VAEs. Several case studies of VAE applications for toy models and experimental datasets in Scanning Transmission Electron Microscopy are discussed, emphasizing the deep connection between VAE and basic physical principles. Python codes and datasets discussed in this article are available at https://github.com/saimani5/VAE-tutorials and can be used by researchers as an application guide when applying these to their own datasets.

Broken symmetries in quasi-2D charged systems via negative dielectric confinement

We report spontaneous symmetry breaking (SSB) phenomena in symmetrically charged binary particle systems under planar nanoconfinement with negative dielectric constants. The SSB is triggered solely via the dielectric confinement effect, without any external fields. The mechanism of SSB is found to be caused by the strong polarization field enhanced by nanoconfinement, giving rise to charge/field oscillations in the transverse directions. Interestingly, dielectric contrast can even determine the degree of SSB in transverse and longitudinal dimensions, forming charge-separated interfacial liquids and clusters on square lattices. Furthermore, we analytically show that the formed lattice constant is determined by the dielectric mismatch and the length scale of confinement, which is validated via molecular dynamics simulations. The novel broken symmetry mechanism may provide new insights into the study of quasi-2D systems and the design of future nanodevices.

Random sequential adsorption with correlated defects : A series expansion approach.

The random sequential adsorption (RSA) problem holds crucial theoretical and practical significance, serving as a pivotal framework for understanding and optimizing particle packing in various scientific and technological applications. Here the problem of the one-dimensional RSA of k-mers onto a substrate with correlated defects controlled by uniform and power-law distributions is theoretically investigated: the coverage fraction is obtained as a function of the density of defects and several scaling laws are examined. The results are compared with extensive Monte Carlo simulations and more traditional methods based on master equations. Emphasis is given in elucidating the scaling behavior of the fluctuations of the coverage fraction. The phenomenon of universality breaking and the issues of conventional Gaussian fluctuations and the Lévy type fluctuations from a simple perspective, relying on the central limit theorem, are also addressed.

Investigation on algorithms for simulating large deformation and impact loads

It is a challenge to simulate the hydrodynamic problems covering the large deformation of the free surface arising in severe circumstances with intense flow. This paper investigates algorithms based on the moving particle semi-implicit method for simulating large deformation and impact loads. The algorithm discretizes the fluid domain into a series of particles, each representing a part of the fluid. The pressure field calculation is implicit, and the velocity field calculation is explicit. Three models, including the gradient model, source term, and free-surface detection, have been improved and compared to determine which improvement is the best to enhance the accuracy and stability. The enhanced pressure gradient guarantees that momentum conservation can be satisfied. Particle density and velocity divergence are incompressible conditions combined in the mixed source term approach. The arc approach is used in the free-surface judging process. The results show that the combination of three models is the most effective in exploring the problems of hydrodynamic pressure and dam break. The issue of liquid sloshing including roll and sway investigates the effect of the initial distance and time step. It is found that the simulation accuracy of impact pressure can be increased as the initial distance and the time step decrease. Finally, the free surface breaking and liquid splashing phenomena are easily observed, and the method can accurately simulate the massive deformation of the free surface. These findings are helpful for hazard assessments of the various fluid mechanics-related problems.

Vortex-shedding and bistability in cylinder-flexible plate assembly in a channel

This study numerically investigates the fluid–structure interaction dynamics of a stationary circular cylinder with an attached flexible splitter plate in a confined fluid domain. We explore how variations in Reynolds number (Re), plate length, offset from the channel centerline, and blockage ratio influence the vortex-shedding and oscillatory behavior of the plates in laminar flow. Results indicate that at low Reynolds numbers (Re = 100), there are no vortex shedding or oscillations, while at higher Reynolds (Re = 200 to 300), the shorter plate exhibits first-mode oscillations and symmetry breaking, whereas the longer plate shows only transient second-mode oscillations at Re = 300 that diminish in amplitude, suggesting that increased plate length reduces vortex-induced forces. Dynamic Mode Decomposition (DMD) analysis confirms consistent primary flow structures across different Reynolds numbers, with initial modes encapsulating the majority of the system’s dynamics. In addition to determining the critical Re for vortex-shedding, vortex-induced oscillations and bistability, the study also examines the critical blockage ratios on the symmetry breaking phenomenon, and also shows that plate stability is influenced by domain asymmetry. These insights enhance understanding of the biomechanics of fish-like robots and inform the design and control of bioinspired flexible structures in fluid flows.

Statistical Mechanics Approaches for Studying Temperature and Rate Effects in Multistable Systems

Systems with a multistable energy landscape are widespread in physics, biophysics, technology, and materials science. They are strongly influenced by thermal fluctuations and external mechanical actions that can be applied at different rates, moving the system from equilibrium to non-equilibrium regimes. In this paper, we focus on a simple system involving a single breaking phenomenon to describe the various theoretical approaches used to study these problems. To begin with, we propose the exact solution at thermodynamic equilibrium based on the calculation of the partition function without approximations. We then introduce the technique of spin variables, which is able to simplify the treatment even for systems with a large number of coordinates. We then analyze the energy balance of the system to better understand its underlying physics. Finally, we introduce a technique based on transition state theory useful for studying the non-equilibrium dynamical regimes of these systems. This method is appropriate for the evaluation of rate effects and hysteresis loops. These approaches are developed for both the Helmholtz ensemble (prescribed extension) and the Gibbs ensemble (applied force) of statistical mechanics. The symmetry and duality of these two ensembles is discussed in depth. While these techniques are used here for a simple system with theoretical purposes, they can be applied to complex systems of interest for several physical, biophysical, and technological applications.

Fully conservative difference schemes for the rotation-two-component Camassa–Holm system with smooth/nonsmooth initial data

This paper derives a semi-discrete conservative difference scheme for the rotation-two-component Camassa–Holm system based on its Hamiltonian invariants. Mass, momentum and energy are preserved for the semi-discrete scheme. Furthermore, a fully discrete finite difference scheme is proposed without destroying any one of the conservative laws. Combining a nonlinear iteration with a threshold strategy, the accuracy of the scheme is guaranteed. Meanwhile, this scheme captures the formation and propagation of solitary wave solutions in long time behavior under smooth/nonsmooth initial data. Remarkably, a new type of asymmetric wave breaking phenomenon is revealed in the case of the nonzero rotational parameter.

Existence and symmetry breaking results for positive solutions of elliptic Hamiltonian systems

Abstract In this paper, we are interested in positive solutions of $$ \begin{align*}\left\{ \begin{array}{@{}ll} -\Delta u = a(x)v^{p-1}, \quad &\text{ in } \Omega,\\ -\Delta v = b(x)u^{q-1}, \quad &\text{ in } \Omega,\\ u,v>0, \quad &\text{ in } \Omega,\\ u=v=0, \quad &\text{ on } \partial\Omega, \end{array} \right. \end{align*} $$ where $\Omega $ is a bounded annular domain (not necessarily an annulus) in ${\mathbb {R}}^N (N \ge 3)$ and $ a(x), b(x)$ are positive continuous functions. We show the existence of a positive solution for a range of supercritical values of p and q when the problem enjoys certain mild symmetry and monotonicity conditions. We shall also address the symmetry breaking phenomena where the system is fully symmetric. Indeed, as a consequence of our results, we shall show that problem (1) has $\Bigl \lfloor \frac {N}{2} \Bigr \rfloor $ (the floor of $\frac {N}{2}$ ) positive non-radial solutions when $ a(x)=b(x)=1$ and $\Omega $ is an annulus with certain assumptions on the radii. In general, for the radial case where the domain is an annulus, we prove the existence of a non-radial solution provided $$ \begin{align*}(p-1)(q-1)> \Big(1+\frac{2N}{\lambda_H}\Big)^2\left(\frac{q}{p}\right),\end{align*} $$ where $\lambda _H$ is the best constant for the Hardy inequality on $\Omega .$ We remark that the best constant $\lambda _H$ for the Hardy inequality is just the characteristic of the domain, and is independent of the choices of p and $q.$ For this reason, the aforementioned inequality plays a major role to prove the existence and multiplicity of non-radial solutions when the problem is fully symmetric. Our proofs use a variational formulation on appropriate convex subsets for which the lack of compactness is recovered for the supercritical problem.

Indications for an alternative breaking of symmetry in fracture-induced electromagnetic emissions recorded prior to the 2023 Mw7.8 and Mw7.5 Turkey Earthquakes

Several evidence has been reported corroborating the view that the MHz band fracture-induced electromagnetic emissions (FEME), also known as fracture-induced electromagnetic radiation (FEMR), which are detected prior to shallow main earthquakes (EQs) of moment magnitude Mw>5.5 with epicenters on land or near coastline, can be studied in analogy to a Z(2) spin system undergoing a second-order phase transition. Specifically, by analyzing MHz FEME/FEMR time series recorded prior to several earthquakes in the past >20 years, information has been extracted about the organization to critical state, the critical state itself, as well as for the step-by-step development of the spontaneous symmetry breaking (SSB) phenomenon. Using the “method of critical fluctuations” (MCF) and a recently proposed method for the wavelet-based detection of scaling behavior in noisy experimental data, we identified for the first time a different way of breaking the symmetry embedded in the MHz FEME/FEMR time series recorded by the hELlenic Seismo-ElectroMagnetics Network (ELSEM-Net) prior to the devastating (Mw=7.8 and Mw=7.5) EQs that occurred in south-east Turkey on 06/02/2023. Particularly, after the achievement of the critical state, indications were found that, although the underlying system started to break the symmetry according to the second-order phase transition mechanism (through SSB), SSB was not completed. Instead, the system seems to have changed symmetry and presented indications that the break of symmetry was finally achieved according to the first-order phase transition mechanism. Specifically, after the incomplete SSB, it was found to present tricritical behavior, followed by indications of triple degeneration of the order parameter fixed-point. This change of behavior observed in the MHz FEME/FEMR is a puzzling phenomenon for several reasons, which are discussed in detail, whereas suggestions are expressed as a first attempt for the possible explanation of the new findings.

Observation of Replica Symmetry Breaking in Standard Mode-Locked Fiber Laser.

We report the first experimental demonstration of the replica symmetry breaking (RSB) phenomenon in a fiber laser system supporting standard mode-locking (SML) regime. Though theoretically predicted, this photonic glassy phase remained experimentally undisclosed so far. We employ an ytterbium-based mode-locked fiber laser with a very rich phase diagram. Two phase transitions are observed separating three different regimes: cw, quasi-mode-locking (QML), and SML. The regimes are intrinsically related to the distinct dynamics of intensity fluctuations in the laser spectra. We set the connection between the RSB glassy phase with frustrated modes and onset of L-shaped intensity distributions in the QML regime, which impact directly the replica overlap measure.

Wave breaking phenomenon in the unidirectional non-local wave model

In this paper, we investigate wave breaking phenomenon in the unidirectional non-local wave model. Making use of the L2-conservation law and fine structure of the model, we show a local-in-space wave breaking condition for the unidirectional non-local wave model.

Selective Encapsulation and Chiral Induction of C60 and C70 Fullerenes by Axially Chiral Porous Aromatic Cages

AbstractChiral induction has been an important topic in chemistry, not only for its relevance in understanding the mysterious phenomenon of spontaneous symmetry breaking in nature but also due to its critical implications in medicine and the chiral industry. The induced chirality of fullerenes by host–guest interactions has been rarely reported, mainly attributed to their chiral resistance from high symmetry and challenges in their accessibility. Herein, we report two new pairs of chiral porous aromatic cages (PAC), R‐PAC‐2, S‐PAC‐2 (with Br substituents) and R‐PAC‐3, S‐PAC‐3 (with CH3 substituents) enantiomers. PAC‐2, rather than PAC‐3, achieves fullerene encapsulation and selective binding of C70 over C60 in fullerene carbon soot. More significantly, the occurrence of chiral induction between R‐PAC‐2, S‐PAC‐2 and fullerenes is confirmed by single‐crystal X‐ray diffraction and the intense CD signal within the absorption region of fullerenes. DFT calculations reveal the contribution of electrostatic effects originating from face‐to‐face arene‐fullerene interactions dominate C70 selectivity and elucidate the substituent effect on fullerene encapsulation. The disturbance from the differential interactions between fullerene and surrounding chiral cages on the intrinsic highly symmetric electronic structure of fullerene could be the primary reason accounting for the induced chirality of fullerene.