Symmetry Breaking Forces Research Articles

Symmetry-Breaking-Induced Frequency Combs in Graphene Resonators.

Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena-like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we demonstrate a route for generating mechanical frequency combs in graphene resonators undergoing symmetry-breaking forces. We use electrostatic force to break the membrane’s out-of-plane symmetry and tune its resonance frequency toward a one-to-two internal resonance, thus achieving strong coupling between two of its mechanical modes. When increasing the drive level, we observe splitting of the fundamental resonance peak, followed by the emergence of a frequency comb regime. We attribute the observed physics to a nonsymmetric restoring potential and show that the frequency comb regime is mediated by Neimark bifurcation of the periodic solution. These results demonstrate that mechanical frequency combs and chaotic dynamics in 2D material resonators can emerge near internal resonances due to symmetry-breaking.

Toward ab initio charge symmetry breaking in nuclear energy density functionals

We propose a new approach to determine the strength of the charge symmetry breaking (CSB) term in the framework of nuclear density functional theory. It is shown that once ab initio calculations are available including accurate description of isospin symmetry breaking terms in medium and heavy nuclei, the mass difference of mirror nuclei as well as the neutron-skin thickness of doubly-closed-shell nuclei can be used to constrain the strength of the CSB interaction with an uncertainty less than 6%, separately from other isospin symmetry breaking forces. This method opens a new vista of ab initio nuclear energy density functionals.

Ultrafast Relaxation of Symmetry-Breaking Photo-Induced Atomic Forces.

We present a first-principles method for the calculation of the temperature-dependent relaxation of symmetry-breaking atomic driving forces in photoexcited systems. We calculate the phonon-assisted decay of the photoexcited force on the low-symmetry E_{g} mode following absorption of an ultrafast pulse in Bi, Sb, and As. The force decay lifetimes for Bi and Sb are of the order of 10fs and in agreement with recent experiments, demonstrating that electron-phonon scattering is the primary mechanism relaxing the symmetry-breaking forces. Calculations for a range of absorbed photon energies suggest that larger amplitude, symmetry-breaking atomic motion may be induced by choosing a pump photon energy which maximizes the product of the initial E_{g} force and its lifetime. The high-symmetry A_{1g} force undergoes a partial decay to a nonzero constant on similar timescales, which has not yet been measured in experiments. The average imaginary part of the electron self-energy over the photoexcited carrier distribution provides a crude indication of the decay rate of symmetry-breaking forces.

Discovery of a Voltage-Stimulated Heartbeat Effect in Droplets of Liquid Gallium.

Chemomechanical effects are known to initiate fluid oscillations in certain liquid metals; however, they typically produce an irregular motion that is difficult to deactivate or control. Here we show that stimulating liquid gallium with electrochemistry can cause a metal drop to exhibit a heart beating effect by shape shifting at a telltale frequency. Unlike the effects reported in the past for mercury, the symmetry-breaking forces generated by using gallium propel the drop several millimeters with velocities of the order of 1cm per second. We demonstrate pulsating dynamics between 0 and 610 beats per minute for 50-150 μL droplets in a NaOH electrolyte at 34 °C. The underlying mechanism is a self-regulating cycle initiated by fast electrochemical oxidation that adjusts the drop's surface tension and causes a transformation from spherical to pancake form, followed by detachment from the circular electrode. As the beat frequency can be activated and controlled using a dc voltage, the electrochemical mechanism opens the way for fluid-based timers and actuators.

Nuclear Symmetry Energy and the Breaking of the Isospin Symmetry: How Do They Reconcile with Each Other?

We analyze and propose a solution to the apparent inconsistency between our current knowledge of the equation of state of asymmetric nuclear matter, the energy of the isobaric analog state (IAS) in a heavy nucleus such as ^{208}Pb, and the isospin symmetry breaking forces in the nuclear medium. This is achieved by performing state-of-the-art Hartree-Fock plus random phase approximation calculations of the IAS that include all isospin symmetry breaking contributions. To this aim, we propose a new effective interaction that is successful in reproducing the IAS excitation energy without compromising other properties of finite nuclei.

Damping-Induced Self Recovery Phenomenon in Mechanical Systems With an Unactuated Cyclic Variable

Conservation of momentum is often used in controlling underactuated mechanical systems with symmetry. If a symmetry-breaking force is applied to the system, then the momentum is not conserved any longer in general. However, there exist forces linear in velocity such as the damping force that break the symmetry but induce a new conserved quantity in place of the original momentum map. This paper formalizes a new conserved quantity which can be constructed by combining the time integral of a general damping force and the original momentum map associated with the symmetry. From the perspective of stability theories, the new conserved quantity implies the corresponding variable possesses the self recovery phenomenon, i.e., it will be globally attractive to the initial condition of the variable. We discover that what is fundamental in the damping-induced self recovery is not the positivity of the damping coefficient but certain properties of the time integral of the damping force. The self recovery effect and theoretical findings are demonstrated by simulation results using the two-link planar manipulator and the torque-controlled inverted pendulum on a passive cart. The results in this paper will be useful in designing and controlling mechanical systems with underactuation.

FIRST γ-RAY SPECTROSCOPY AND ISOSPIN SYMMETRY STUDY OF THE N = Z - 2 NUCLEUS 44V

Excited states in the Tz = -1 nucleus 44 V have been observed for the first time. The states have been identified through recoil-γ-γ coincidences and comparison with analogue states in the mirror nucleus 44 Sc . Mirror energy differences have been extracted and compared to state-of-the-art fp shell-model calculations which include charge symmetry breaking forces.

Compressional mode softening and Euler buckling patterns in mesoscopic beams

We describe a sequence of Euler buckling instabilities associated with the transverse modes of a mesoscopic beam subjected to compressional strain. As the strain is increased, successively higher normal mode frequencies are driven to zero; each zero signals an instability in the corresponding normal mode that can be realized if all lower instabilities are suppressed by constraints. When expressed in terms of the critical buckling modes, the potential energy functional takes the form of a multimode Ginzburg–Landau system that describes static equilibria in the presence of symmetry breaking forces. This model is used to analyse the complex equilibrium shapes that have been observed experimentally in strained mesoscopic beams. Theoretically predicted critical strain values agree with the appearances of higher order mode structures as the length-to-width aspect ratio increases. The theory also predicts upper bounds on the individual mode amplitudes that are consistent with the data. Based on insights from the theory, we suggest possible origins of the buckling patterns.

What is the biological basis of pattern formation of skin lesions?

Pattern recognition is at the heart of clinical dermatology and dermatopathology. Yet, while every practitioner of the art of dermatological diagnosis recognizes the supreme value of diagnostic cues provided by defined patterns of 'efflorescences', few contemplate on the biological basis of pattern formation in and of skin lesions. Vice versa, developmental and theoretical biologists, who would be best prepared to study skin lesion patterns, are lamentably slow to discover this field as a uniquely instructive testing ground for probing theoretical concepts on pattern generation in the human system. As a result, we have at best scraped the surface of understanding the biological basis of pattern formation of skin lesions, and widely open questions dominate over definitive answer. As a symmetry-breaking force, pattern formation represents one of the most fundamental principles that nature enlists for system organization. Thus, the peculiar and often characteristic arrangements that skin lesions display provide a unique opportunity to reflect upon--and to experimentally dissect--the powerful organizing principles at the crossroads of developmental, skin and theoretical biology, genetics, and clinical dermatology that underlie these--increasingly less enigmatic--phenomena. The current 'Controversies' feature offers a range of different perspectives on how pattern formation of skin lesions can be approached. With this, we hope to encourage more systematic interdisciplinary research efforts geared at unraveling the many unsolved, yet utterly fascinating mysteries of dermatological pattern formation. In short: never a dull pattern!

Westward Propagation of Latitudinal Asymmetry in a Coupled Ocean–Atmosphere Model

Abstract Hemispheric asymmetries of continental geometry have long been speculated to be the cause of the Northern Hemisphere position of the intertropical convergence zone over the central and eastern Pacific. It is unknown, however, how the effects of continental asymmetries are transmitted to and felt by the central Pacific thousands of kilometers away. This paper proposes a transmitter mechanism by investigating the response of a coupled ocean–atmospheric model to a symmetry-breaking force by the American continents. The model treats land forcing implicitly as an eastern boundary condition. In the absence of oceanic feedback, the model response to the eastern boundary forcing is tightly trapped and confined to a small longitudinal extent off the coast, whereas the climate over the interior ocean is symmetric about the equator. Ocean–atmosphere coupling greatly enhances the transmissibility of the effects of the land forcing, establishing large latitudinal asymmetry over a great zonal extent. A westwar...

Effects of valence nucleon orbits and charge symmetry breaking interaction on the Nolen-Schiffer anomally of mirror nuclei

Coulomb energy differences (Nolen-Schiffer anomalies) of mirror nuclei 17O- 17F and 41Ca- 41Sc are studied by using realistic Hartree-Fock and Woods-Saxon single-particle wave functions which are determined precisely through the analysis of the magnetic form factors of electron scattering. These single-particle wave functions are used to evaluate the Coulomb energy differences due to charge symmetry breaking forces, with new coupling constants determined by the analysis of the scattering lengths of pp and nn system which have been successfully applied to the Coulomb energy difference of 3He- 3H. We also evaluated the effects of the charge symmetry breaking forces using Hartree-Fock wave functions. Together with various other contributions, our calculated values of the Coulomb energy differences, which showed deviations of 3–9% from the experimental values in the previous analysis of Nolen and Schiffer, agree with the experimental values within 1% (2%) accuracy for A = 17 (41).

Contribution of charge symmetry breaking forces to energy differences in mirror nuclei

Contributions to energy differences in mirror nuclei and to the scattering length differences a pp − a nn and a nn − a np are evaluated from class III and class IV type charge symmetry breaking (CSB) potentials. We consider ϱ 0-ω mixing π 0-ν mixing, one- and two-pion exchange contributions. Potentials which are consistent with these scattering length differences and with recent CSB p-n elastic scattering data are found to contribute about 150–250 keV to the energy differences in mirror nuclei.

First principles investigation on the validity of the peierls mechanism for the dimerization energy of trans-polyacetylene

Detailed general potential linearized augmented plane-wave calculations indicate that interchain interactions in trans-polyacetylene drastically lower the density of states near the Fermi level in the symmetric (undimerized) state. This is in fact a model-independent result arising solely from interchain coupling and the non-symmorphic symmetry group of the three-dimensional unit cell. Local density total-energy studies indicate that the interchain interactions reduce the strength of the Peierls mechanism so strongly that this mechanism may not provide the majority of the symmetry-breaking force as it is generally believed to do.

Zero-crossing angle in thenpanalyzing power at medium energies and its relation to charge symmetry

The angle at which the analyzing power for free np scattering becomes zero, the zero-crossing angle theta/sub 0/, has been measured simultaneously for the np and np scattering processes at 425, 565, and 665 MeV incident neutron energies. A rather strong energy dependence of the zero-crossing angle is found. Knowledge of this energy dependence is important in designing an experiment which tests for charge symmetry breaking forces by comparing high precision measurements of theta/sub 0/(np) and theta/sub 0/(np).

Coulomb displacement energies of the T = 1, J = 0 states of A = 42 nuclei

Coulomb displacement energies of the T = 1, J = 0 + and 6 1 + states of A = 42 nuclei are analyzed with previously known charge dependent forces and effects, and with the available HartreeFock single-particle wave functions. From the study of the Coulomb displacement energies of the 6 1 + states, it is found that the present knowledge on the charge dependence, including a phenomenological charge symmetry breaking force previously introduced so as to help explain the Nolen-Schiffer anomaly, gives a sufficient and consistent explanation for both single-particle and twoparticle systems. From the study of the 0 + states, we found that the Coulomb displacement energies of the second 0 2 + states can be explained with a compensation between the smaller Coulomb energies of the second lowest two-particle state and larger ones of the deformed 4p-2h state.

Mass Splitting and the Quark Theory. I

We calculate the masses of the decuplet and the octet baryons by using a spin- and $\mathrm{SU}(3)$-spin-dependent quark-quark force. We compare it with the required quark-antiquark force used in a previous paper in order to explain the mass splitting of the $P$ and the $V$ nonet mesons. The result is consistent with the assumption that these two forces are related to each other by charge conjugation. We further observe that the ratio of radial integrals for quark-quark and quark-antiquark symmetry-breaking forces is the same as that for the symmetric forces, if quarks are very heavy.