scholarly journals Multi-state Condensation in Berlin–Kac Spherical Models

2019 ◽  
Vol 373 (1) ◽  
pp. 389-433 ◽  
Author(s):  
Jani Lukkarinen
Keyword(s):  
Energy Function ◽  
Degrees Of Freedom ◽  
Free Field ◽  
Independent Random Variables ◽  
Periodic Lattice ◽  
Rectangular Lattice ◽  
Global Minima ◽  
Normal Fluid ◽  
Finite Moment ◽  
Lattice Size

AbstractWe consider the Berlin–Kac spherical model for supercritical densities under a periodic lattice energy function which has finitely many non-degenerate global minima. Energy functions arising from nearest neighbour interactions on a rectangular lattice have a unique minimum, and in that case the supercritical fraction of the total mass condenses to the ground state of the energy function. We prove that for any sufficiently large lattice size this also happens in the case of multiple global minima, although the precise distribution of the supercritical mass and the structure of the condensate mass fluctuations may depend on the lattice size. However, in all of these cases, one can identify a bounded number of degrees of freedom forming the condensate in such a way that their fluctuations are independent from the rest of the fluid. More precisely, the original Berlin–Kac measure may be replaced by a factorized supercritical measure where the condensate and normal fluid degrees of freedom become independent random variables, and the normal fluid part converges to the critical Gaussian free field. The proof is based on a construction of a suitable coupling between the two measures, proving that their Wasserstein distance is small enough for the error in any finite moment of the field to vanish as the lattice size is increased to infinity.

Bat Noseleaves as an Inspiration for Smart Emission Baffle Structures

2013 ◽  
Author(s):  
Anupam K. Gupta ◽  
Yanqing Fu ◽  
Dane Webster ◽  
Rolf Müller
Keyword(s):  
Computer Animation ◽  
Degrees Of Freedom ◽  
Free Field ◽  
Shape Features ◽  
Test Bed ◽  
Physical Test ◽  
Current Form ◽  
Local Shape ◽  
Old World ◽  
Horseshoe Bats

Baffle shapes are commonly used in engineered devices to interface sound sources with the free field. Examples are acoustic horns seen in megaphones and horn-loaded loudspeakers. Typical for these devices are simple, static shapes that serve primarily an impedance-matching function. Diffracting baffles linked to a sound source are also common in the biosonar system of bats. In particular in bat groups that emit their ultrasonic pulses nasally, the nostrils are always surrounded by some baffle shape. This is the case across several large and diverse bat families such as horseshoe bats (Rhinolophidae), Old World leaf-nosed bats (Hipposideridae), and New World leaf-nosed bats (Phyllostomidae). However, biosonar baffles differ from their technical counterparts in two important ways: They typically have a much greater geometrical complexity and they are capable of non-rigid shape changes over time. Although simple horn shapes can be found in the noseleaves of many bat species, they are rarely as plain and regular as in megaphones and other technical applications of acoustical horns. Instead, the baffles are broken up into several parts that are frequently augmented with intricate local shape features such as ridges, furrows, and spikes. Furthermore, we have observed that in species belonging to the horseshoe bats and the related Old World leaf-nosed bats these local shape features are often not static, but can undergo displacements as well as non-rigid deformations. At least some of these dynamic effects are not passive byproducts of e.g., sound production or exhalation, but due to specific muscular actuation that can be controlled by the animals. To study these intricate, dynamic baffles as inspirations for smart structures, we have recreated the degrees of freedoms that Old World leaf-nosed bats have in deforming their noseleaves in a digital model using computer animation techniques. In its current form, our model has 6 degrees of freedom that can be used to test interactions between different motions using actuation patterns that occur in life as well as patterns that have not been observed, but could aid understanding. Because of the high-dimensional parameter space spanned by the different degrees of freedom, a high-performance computing platform has been used to characterize the acoustic behavior across a larger number of deformed no seleaf shapes. A physical test bed is currently under construction for implementing baffle motions that have been found to result in interesting changes of the acoustic device characteristics and could hence be of use to engineering applications.

scholarly journals Coherent Phonon Disruption and Lock-In During a Photoinduced Charge-Density-Wave Phase Transition

2021 ◽  
Author(s):  
Spencer A. Reisbick ◽  
Yichao Zhang ◽  
Jialiang Chen ◽  
Paige Engen ◽  
David Flannigan
Keyword(s):  
Charge Density ◽  
Charge Density Wave ◽  
Degrees Of Freedom ◽  
Structural Phase ◽  
Density Wave ◽  
Optical Excitation ◽  
Partial Coherence ◽  
Periodic Lattice ◽  
Coherent Phonon ◽  
Quantum Materials

Ultrafast manipulation of phases and phase domains in quantum materials is a key approach to unraveling and harnessing interwoven effects of charge and lattice degrees of freedom. In the intensely-studied charge-density-wave (CDW) material, 1<i>T</i>-TaS<sub>2</sub>, phonon coupling to periodic lattice distortions (PLDs) and atomically-incoherent picosecond structural phase transitions suggest transitional periods could exist for delayed onset of mode coherence. Here we find evidence for such a connection between displacively-excited coherent acoustic phonons and PLDs using 4D ultrafast electron microscopy. Following femtosecond optical excitation of an ultrathin crystal, a propagating hybridized mode is imaged emerging from linear defects within a 1-μm region. Partial coherence and low amplitudes during onset of the incommensurate phase convert to higher-amplitude, increasingly-coherent oscillations as phase-growth stabilizes. The hybrid mode consists of large out-of-plane distortions coupled to basal-plane bond oscillations propagating at anomalously high velocities. The strongly-correlated behaviors observed here represent a potential means to control phase behaviors in quantum materials using defect-engineered coherent-phonon seeding.

scholarly journals Atom-Field Interaction: From Vacuum Fluctuations to Quantum Radiation and Quantum Dissipation or Radiation Reaction

Physics ◽  
2019 ◽  
Vol 1 (3) ◽  
pp. 430-444 ◽  
Author(s):  
Jen-Tsung Hsiang ◽  
B. L. Hu
Keyword(s):  
Degrees Of Freedom ◽  
Mutual Influence ◽  
Equations Of Motion ◽  
Free Field ◽  
Radiation Reaction ◽  
Linear Response Theory ◽  
Quantum Field ◽  
Quantum Dissipation ◽  
Vacuum Fluctuations ◽  
Quantum Radiation

In this paper, we dwell on three issues: (1) revisit the relation between vacuum fluctuations and radiation reaction in atom-field interactions, an old issue that began in the 1970s and settled in the 1990s with its resolution recorded in monographs; (2) the fluctuation–dissipation relation (FDR) of the system, pointing out the differences between the conventional form in linear response theory (LRT) assuming ultra-weak coupling between the system and the bath, and the FDR in an equilibrated final state, relaxed from the nonequilibrium evolution of an open quantum system; (3) quantum radiation from an atom interacting with a quantum field: We begin with vacuum fluctuations in the field acting on the internal degrees of freedom (idf) of an atom, adding to its dynamics a stochastic component which engenders quantum radiation whose backreaction causes quantum dissipation in the idf of the atom. We show explicitly how different terms representing these processes appear in the equations of motion. Then, using the example of a stationary atom, we show how the absence of radiation in this simple cases is a result of complex cancellations, at a far away observation point, of the interference between emitted radiation from the atom and the local fluctuations in the free field. In so doing we point out in Issue 1 that the entity which enters into the duality relation with vacuum fluctuations is not radiation reaction, which can exist as a classical entity, but quantum dissipation. Finally, regarding issue 2, we point out for systems with many atoms, the co-existence of a set of correlation-propagation relations (CPRs) describing how the correlations between the atoms are related to the propagation of their (retarded non-Markovian) mutual influence manifesting in the quantum field. The CPR is absolutely crucial in keeping the balance of energy flows between the constituents of the system, and between the system and its environment. Without the consideration of this additional relation in tether with the FDR, dynamical self-consistency cannot be sustained. A combination of these two sets of relations forms a generalized matrix FDR relation that captures the physical essence of the interaction between an atom and a quantum field at arbitrary coupling strength.

scholarly journals Gumbel and Fréchet convergence of the maxima of independent random walks

2020 ◽  
Vol 52 (1) ◽  
pp. 213-236 ◽  
Author(s):  
Thomas Mikosch ◽  
Jorge Yslas
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Point Process ◽  
Asymptotic Theory ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Independent Random Variables ◽  
Finite Moment ◽  
Process Convergence ◽  
Precise Large Deviation

AbstractWe consider point process convergence for sequences of independent and identically distributed random walks. The objective is to derive asymptotic theory for the largest extremes of these random walks. We show convergence of the maximum random walk to the Gumbel or the Fréchet distributions. The proofs depend heavily on precise large deviation results for sums of independent random variables with a finite moment generating function or with a subexponential distribution.

SELF-TUNING FIELDS AND RESONANT CORRELATIONS IN 2d-GRAVITY

1991 ◽  
Vol 06 (07) ◽  
pp. 635-644 ◽  
Author(s):  
A.M. POLYAKOV
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
2D Gravity ◽  
Free Field ◽  
Minimal Models ◽  
Self Tuning

We show that minimal models coupled to quantum gravity have special type of resonant correlations defined by the free field representations and are explicitly computable. The key phenomena in these models are shown to be discontinuity of the number of degrees of freedom at exceptional values of momenta and incomplete decoupling of the spurious states.

Advances in Structural Studies of Materials Using Scattering Probes

MRS Bulletin ◽  
2010 ◽  
Vol 35 (7) ◽  
pp. 520-530 ◽  
Author(s):  
Ashfia Huq ◽  
Richard Welberry ◽  
Emil Bozin
Keyword(s):  
Powder Diffraction ◽  
Diffuse Scattering ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Structural Defects ◽  
Theoretical Interpretation ◽  
Periodic Lattice ◽  
Related Phenomenon ◽  
Characterization Of Materials

AbstractX-ray and neutron diffraction have been two key techniques for structural characterization of materials since their inception. If single crystals of the materials of interest cannot be synthesized, one has to resort to powder diffraction. This results in the loss of three-dimensional orientation information of the crystal, and one has to contend with the one-dimensional information that is inherent to powder diffraction, making it harder to analyze the data. The structural study of contemporary materials and their remarkable properties is a challenging problem, particularly when properties of interest result from interplay of multiple degrees of freedom. Very often these are associated with structural defects or relate to different length scales in a material. The signature of the defect-related phenomenon is visible as diffuse scattering in the diffraction pattern, and the signals associated with diffuse scattering are orders of magnitude smaller than Bragg scattering. Given these limitations, it is crucial to have high-resolution and high-intensity data along with the ability to carry out theoretical interpretation that goes beyond periodic lattice formalism of crystallography. Great advances have been achieved due to the advent of synchrotron and neutron sources, along with the availability of high-speed computational algorithms allowing materials scientists to work with a very small amount of sample (both single crystal and powder) and analyze vast amounts of data to unravel detailed structural descriptions that were not previously possible. This article presents some of these great advances in using scattering probes for materials characterization.

scholarly journals Coherent Phonon Disruption and Lock-In During a Photoinduced Charge-Density-Wave Phase Transition

2021 ◽  
Author(s):  
Spencer A. Reisbick ◽  
Yichao Zhang ◽  
Jialiang Chen ◽  
Paige Engen ◽  
David Flannigan
Keyword(s):  
Charge Density ◽  
Charge Density Wave ◽  
Degrees Of Freedom ◽  
Transition Period ◽  
Density Wave ◽  
Domain Growth ◽  
Periodic Lattice ◽  
Coherent Phonon ◽  
Linear Defects ◽  
Quantum Materials

Ultrafast manipulation of phases and phase domains in quantum materials is a key approach to unraveling and harnessing interwoven effects of charge and lattice degrees of freedom. In the intensely-studied charge-density-wave (CDW) material, 1<i>T</i>-TaS<sub>2</sub>, static Rayleigh-phonon coupling to periodic lattice distortions (PLDs), as well as incommensurate (IC) domain growth and coarsening over the first 100 ps following femtosecond photoexcitation, suggests ultrafast, displacively-excited coherent acoustic phonons (CAPs) may strongly couple to PLDs. Here we find evidence for such coupling using 4D ultrafast electron microscopy (UEM). For ultrathin room-temperature crystals, photoinduced Bragg-peak dynamics spanning the first 75 ps are characterized by partial CAP coherence and localized low-amplitude <i>c</i>-axis dilations. These relatively weak, partially-coherent dynamics then give way to higher-amplitude, increasingly-coherent oscillations, the transition period of which is well-matched to timescales of photoinduced IC domain growth and stabilization from the nearly-commensurate (NC) phase. Diffraction experiments are correlated with nanoscale UEM imaging, where it is found that phonon wave trains emerge from nanoscale linear defects 100 ps after photoexcitation. The CAPs consist of coupled longitudinal and transverse character and propagate at an anomalously-high 4.6 nm/ps along wave vectors independent from NC-phase PLDs, instead being dictated by static defect orientation. Such behaviors illustrate a potential means to control phases in quantum materials using defect-engineered coherent-phonon seeding.<br>

Dynamic Continuum Models of Large Platelike Lattice Structures

1991 ◽  
Author(s):  
Usik Lee
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Continuum Models ◽  
Periodic Lattice ◽  
Lattice Structures ◽  
Straightforward Method ◽  
Energy Equivalence ◽  
Mass Matrices ◽  
Equivalent Continuum ◽  
The Continuum

Abstract A rational and straightforward method is introduced for developing continuum models of large platelike periodic lattice structures based on energy equivalence. The procedure for developing continuum plate models involves the use of existing well-defined finite element matrices for the easy calculation of strain and kinetic energies of a repeating cell, from which the reduced stiffness and mass matrices are obtained in terms of continuum degrees-of-freedom defined in this paper. The equivalent continuum plate properties are obtained from the direct comparison of the reduced matrices for continuum plate with those for lattice plate. Free vibration analyses for the continuum and lattice plates are conducted to evaluate the continuum method proposed in this paper. Numerical results show that the present continuum method gives very reliable structural and dynamic properties compared to other well-recognized methods.

A Simplified Strain Energy Function to Represent the Mechanical Behavior of the Annulus Fibrosus

2009 ◽  
Author(s):  
Jose J. García ◽  
Christian Puttlitz
Keyword(s):  
Finite Element ◽  
Mechanical Behavior ◽  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Degrees Of Freedom ◽  
Strain Energy Function ◽  
Efficient Simulation ◽  
Matrix Interactions ◽  
Complex Functions

Models to represent the mechanical behavior of the annulus fibrosus are important tools to understand the biomechanics of the spine. Many hyperelastic constitutive equations have been proposed to simulate the mechanical behavior of the annulus that incorporate the anisotropic nature of the tissue. Recent approaches [1,2] have included terms into the energy function which take into account fiber-fiber and fiber-matrix interactions, leading to complex functions that cannot be readily implemented into commercial finite element codes for an efficient simulation of nonlinear realistic models of the spine (which are generally composed of 100,000+ degrees of freedom). An effort is undertaken here to test the capability of a relatively simple strain energy function [3] for the description of the annulus fibrosus. This function has already been shown to successfully represent the mechanical behavior of the arterial tissue and can be readily implemented into existing finite element codes.

On the Stability of Linear Discrete Dynamic Systems

1970 ◽  
Vol 37 (2) ◽  
pp. 271-275 ◽  
Author(s):  
J. A. Walker
Keyword(s):  
Dynamic Systems ◽  
Energy Method ◽  
Energy Function ◽  
Degrees Of Freedom ◽  
Symmetric Matrix ◽  
Discrete Dynamic ◽  
Stability Theorems ◽  
Discrete Dynamic Systems ◽  
The Stability ◽  
General Method

A technique is presented for studying the stability of equilibria of linear discrete dynamic systems involving general types of forces: elastic, nonconservative, dissipative, and gyroscopic. The techniqe is a generalization of the energy method, based upon a restricted version of the general method of Liapunov, and often allows stability to be determined in terms of unspecified parameters. For systems of n degrees of freedom, stability theorems are given which require the existence of an n × n symmetric matrix G having certain properties. Several examples are given to illustrate the method of construction of this matrix and the type of information which it may be expected to yield. In general the method and its results are quite similar to the energy method, but apply even when the energy function does not exist.

Sign in / Sign up

Export Citation Format

Share Document