Physics Commons^™

Why The Crackling Deformations Of Single Crystals, Metallic Glasses, Rock, Granular Materials, And The Earth’S Crust Are So Surprisingly Similar, Karin A. Dahmen, Jonathan T. Uhl, Wendelin J. Wright

Faculty Journal Articles

Recent experiments show that the deformation properties of a wide range of solid materials are surprisingly similar. When slowly pushed, they deform via intermittent slips, similar to earthquakes. The statistics of these slips agree across vastly different structures and scales. A simple analytical model explains why this is the case. The model also predicts which statistical quantities are independent of the microscopic details (i.e., they are "universal"), and which ones are not. The model provides physical intuition for the deformation mechanism and new ways to organize experimental data. It also shows how to transfer results from one scale to another. …

Quantum Quench And Scaling Of Entanglement Entropy, Pawel Caputa, Sumit R. Das, Masahiro Nozaki, Akio Tomiya

Physics and Astronomy Faculty Publications

Global quantum quench with a finite quench rate which crosses critical points is known to lead to universal scaling of correlation functions as functions of the quench rate. In this work, we explore scaling properties of the entanglement entropy of a subsystem in a harmonic chain during a mass quench which asymptotes to finite constant values at early and late times and for which the dynamics is exactly solvable. When the initial state is the ground state, we find that for large enough subsystem sizes the entanglement entropy becomes independent of size. This is consistent with Kibble–Zurek scaling for slow …

Wrinkling In Buckling And A Thin Sheet, Narayanan Menon

Patterns Around Us

Module 1: Euler Buckling

Learning Objectives:

• What is an instability? A sudden change in behaviour in response to a small change in conditions.

• Instabilities usually involve a change in symmetry from a more symmetric situation to a less symmetric one

• The mechanism for an instability usually involves two competing forces (one force stabilizing the symmetric state, and the other one destabilizing it), with one suddenly winning the contest

• These competing forces in thin objects are often the forces of compression (destabilizing force - favors buckling or wrinkling) and of bending (stabilizing force).

Understanding by data collapse, the power of using …

Decorrelation Of Samples In Quantum Monte Carlo Calculations And Scaling Of Autocorrelation Time In Li And H₂O Clusters, D. Nissenbaum, B. Barbiellini, A. Bansil

Bernardo Barbiellini

We have investigated decorrelation of samples in Quantum Monte Carlo (QMC) ground-state energy calculations for large Li and H₂O nanoclusters. Binning data as a way of eliminating statistical correlations, as is the common practice, is found to become increasingly impractical as the system size grows. We demonstrate nevertheless that it is possible to perform accurate energy calculations—without decorrelating samples—by exploiting the scaling of the integrated autocorrelation time τ as a function of the number of electrons in the system.

Scaling Behavior Of The Exchange-Bias Training Effect, Christian Binek, Srinivas Polisetty, Sarbeswar Sahoo

Christian Binek

The dependence of the exchange-bias training effect on temperature and ferromagnetic film thickness is studied in detail and scaling behavior of the data is presented. Thickness-dependent exchange bias and its training are measured using the magneto-optical Kerr effect. A focused laser beam is scanned across a Co wedge probing local hysteresis loops of the Co film which is pinned by an antiferromagnetic CoO layer of uniform thickness. A phenomenological theory is best fitted to the exchange-bias training data resembling the evolution of the exchange-bias field on subsequently cycled hysteresis loops. Best fits are done for various temperatures and Co thicknesses. …

Renormalization-Group Approach To The Critical-Behavior Of The Forest-Fire Model, V Loreto, L Pietronero, A Vespignani, S Zapperi

Alessandro Vespignani

We introduce a renormalization scheme for the one- and two-dimensional forest-fire model in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field associated with a repulsive fixed point. This model is therefore critical in the usual sense because the control parameter has to be tuned to its critical value in order to get criticality. It turns out that this is not just the condition for a time scale separation. The critical exponents are computed analytically and we obtain nu = 1.0, tau = 1.0 and nu …

Decorrelation Of Samples In Quantum Monte Carlo Calculations And Scaling Of Autocorrelation Time In Li And H₂O Clusters, D. Nissenbaum, B. Barbiellini, A. Bansil

Arun Bansil

We have investigated decorrelation of samples in Quantum Monte Carlo (QMC) ground-state energy calculations for large Li and H₂O nanoclusters. Binning data as a way of eliminating statistical correlations, as is the common practice, is found to become increasingly impractical as the system size grows. We demonstrate nevertheless that it is possible to perform accurate energy calculations—without decorrelating samples—by exploiting the scaling of the integrated autocorrelation time τ as a function of the number of electrons in the system.

Density And Temperature Scaling Of Disorder-Induced Heating In Ultracold Plasmas, Scott D. Bergeson, A. Denning, M. Lyon, F. Robicheaux

Faculty Publications

We report measurements and simulations of disorder-induced heating in ultracold neutral plasmas. Fluorescence from plasma ions is excited using a detuned probe laser beam while the plasma relaxes from its initially disordered nonequilibrium state. This method probes the wings of the ion velocity distribution. The simulations yield information on time-evolving plasma parameters that are difficult to measure directly and make it possible to connect the fluorescence signal to the rms velocity distribution. The disorder-induced heating signal can be used to estimate the electron and ion temperatures ~100 ns after the plasma is created. This is particularly interesting for plasmas in …

Cluster Solver For Dynamical Mean-Field Theory With Linear Scaling In Inverse Temperature, Ehsan Khatami, C. Lee, Z. Bai, R. Scalettar, M. Jarrell

Faculty Publications

Dynamical mean-field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians and, in combination with electronic structure theory, constitute powerful methods to treat strongly correlated materials. The key advantage to the technique is that, unlike competing real-space methods, the sign problem is well controlled in the Hirsch-Fye (HF) quantum Monte Carlo used as an exact cluster solver. However, an important computational bottleneck remains; the HF method scales as the cube of the inverse temperature, β. This often makes simulations at low temperatures extremely challenging. We present here a method based on determinant …

Scaling Behavior Of The Exchange-Bias Training Effect, Christian Binek, Srinivas Polisetty, Sarbeswar Sahoo

Christian Binek Publications

The dependence of the exchange-bias training effect on temperature and ferromagnetic film thickness is studied in detail and scaling behavior of the data is presented. Thickness-dependent exchange bias and its training are measured using the magneto-optical Kerr effect. A focused laser beam is scanned across a Co wedge probing local hysteresis loops of the Co film which is pinned by an antiferromagnetic CoO layer of uniform thickness. A phenomenological theory is best fitted to the exchange-bias training data resembling the evolution of the exchange-bias field on subsequently cycled hysteresis loops. Best fits are done for various temperatures and Co thicknesses. …

Exact Enumeration And Scaling For Fragmentation Of Percolation Clusters, Boyd F. Edwards, M. F. Gyure, M. V. Ferer

All Physics Faculty Publications

The fragmentation properties of percolation clusters yield information about their structure. Monte Carlo simulations and exact cluster enumeration for a square bond lattice and exact calculations for the Bethe lattice are used to study the fragmentation probability a_s(p) of clusters of mass s at an occupation probability p and the likelihood b_s′s(p) that fragmentation of an s cluster will result in a daughter cluster of mass s′. Evidence is presented to support the scaling laws a_s(p_c)∼s and b_s′s(p_c)=s^-φg(s′/s), with φ=2-σ given by the standard cluster-number scaling …

Rate Equation And Scaling For Fragmentation With Mass Loss, Boyd F. Edwards, M. Cai, H. Han

All Physics Faculty Publications

A linear rate equation describes fragmentation with continuous and discrete mass loss typified by consumption of porous reactive solids and two-phase heterogeneous solids. For a mass-dependent fragmentation rate x^α and a continuous-mass-loss rate εx^γ,σ=γ-α-1<0 yields a>‘‘recession regime’’ where small particles lose mass continuously without breaking, σ>0 yields a ‘‘fragmentation regime’’ where all particles break, and σ=0 yields scaling for α>0. Shattering for α<0 and>σ≥0 is runaway fragmentation producing an infinte number of particles in a finite time, Exact and asymptotic solutions, exponent relations, and connections with static percolation are found.

Scaling Approach To Spin-Glass Phenomena, S. E. Barnes, A. P. Malozemoff, B. Barbara

Physics Articles and Papers

The scaling model of spin-glass phenomena is extended to consider both longitudinal and transverse order parameters q₁ and q_t. The lowest-order coupling in the free energy goes as q_l²q_t². The field (h) dependence of the reduced temperature t for transverse freezing is found to be t∼h^4/δ where δ is the conventional nonlinear susceptibility field exponent (χ∼h^2/δ). While the transverse correlation length diverges at t=0, the longitudinal correlation length remains finite.