Profile scaling in decay of nanostructures

The flattening of a crystal cone below its roughening transition is studied by means of a step flow model. Numerical and analytical analyses show that the height profile, h(r,t), obeys the scaling scenario dh/dr = F(r t^{-1/4}). The scaling function is flat at radii r<R(t) \sim t^{1/4}. We find a one parameter family of solutions for the scaling function, and propose a selection criterion for the unique solution the system reaches.Comment: 4 pages, RevTex, 3 eps figure

One-dimensional collision carts computer model and its design ideas for productive experiential learning

We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In the field of designing computer simulations, we discuss briefly three pedagogical considerations such as 1) consistent simulation world view with pen paper representation, 2) data table, scientific graphs and symbolic mathematical representations for ease of data collection and multiple representational visualizations and 3) game for simple concept testing that can further support learning. We also suggest using physical world setup to be augmented complimentary with simulation while highlighting three advantages of real collision carts equipment like tacit 3D experience, random errors in measurement and conceptual significance of conservation of momentum applied to just before and after collision. General feedback from the students has been relatively positive, and we hope teachers will find the simulation useful in their own classes. 2015 Resources added: http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/02-dynamics/46-one-dimension-collision-js-model http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/02-dynamics/195-elastic-collisionComment: 6 pages, 8 figures, 1 table, 1 L. K. Wee, Physics Education 47 (3), 301 (2012); ISSN 0031-912

The Design and Validation of the Quantum Mechanics Conceptual Survey

The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper we describe the design and validation of the survey, a process that included observations of students, a review of previous literature and textbooks and syllabi, faculty and student interviews, and statistical analysis. We also discuss issues in the development of specific questions, which may be useful both for instructors who wish to use the QMCS in their classes and for researchers who wish to conduct further research of student understanding of quantum mechanics. The QMCS has been most thoroughly tested in, and is most appropriate for assessment of (as a posttest only), sophomore-level modern physics courses. We also describe testing with students in junior quantum courses and graduate quantum courses, from which we conclude that the QMCS may be appropriate for assessing junior quantum courses, but is not appropriate for assessing graduate courses. One surprising result of our faculty interviews is a lack of faculty consensus on what topics should be taught in modern physics, which has made designing a test that is valued by a majority of physics faculty more difficult than expected.Comment: Submitted to Physical Review Special Topics: Physics Education Researc

Decay of one dimensional surface modulations

The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the discrete step model into a continuum model for surface dynamics. The model consists of differential equations for the functions alpha(t) and F(x). The solutions of these equations agree with simulation results of the discrete step model. We identify two types of possible scaling solutions. Solutions of the first type have facets at the extremum points, while in solutions of the second type the facets are replaced by cusps. Interactions between steps of opposite signs determine whether a system is of the first or second type. Finally, we relate our model to an actual experiment and find good agreement between a measured AFM snapshot and a solution of our continuum model.Comment: 18 pages, 6 figures in 9 eps file

Resistance and Resistance Fluctuations in Random Resistor Networks Under Biased Percolation

We consider a two-dimensional random resistor network (RRN) in the presence of two competing biased percolations consisting of the breaking and recovering of elementary resistors. These two processes are driven by the joint effects of an electrical bias and of the heat exchange with a thermal bath. The electrical bias is set up by applying a constant voltage or, alternatively, a constant current. Monte Carlo simulations are performed to analyze the network evolution in the full range of bias values. Depending on the bias strength, electrical failure or steady state are achieved. Here we investigate the steady-state of the RRN focusing on the properties of the non-Ohmic regime. In constant voltage conditions, a scaling relation is found between $/_0$ and $V/V_0$, where $$ is the average network resistance, $_0$ the linear regime resistance and $V_0$ the threshold value for the onset of nonlinearity. A similar relation is found in constant current conditions. The relative variance of resistance fluctuations also exhibits a strong nonlinearity whose properties are investigated. The power spectral density of resistance fluctuations presents a Lorentzian spectrum and the amplitude of fluctuations shows a significant non-Gaussian behavior in the pre-breakdown region. These results compare well with electrical breakdown measurements in thin films of composites and of other conducting materials.Comment: 15 figures, 23 page

The profile of a decaying crystalline cone

The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both cases, we describe the decay kinetics in terms of step flow models. Numerical simulations of the models indicate that in the attachment-detachment limited case the system undergoes a step bunching instability if the repulsive interactions between steps are weak. Such an instability does not occur in the diffusion limited case. In stable cases the height profile, h(r,t), is flat at radii r<R(t)\sim t^{1/4}. Outside this flat region the height profile obeys the scaling scenario \partial h/\partial r = {\cal F}(r t^{-1/4}). A scaling ansatz for the time-dependent profile of the cone yields analytical values for the scaling exponents and a differential equation for the scaling function. In the long time limit this equation provides an exact description of the discrete step dynamics. It admits a family of solutions and the mechanism responsible for the selection of a unique scaling function is discussed in detail. Finally we generalize the model and consider permeable steps by allowing direct adatom hops between neighboring terraces. We argue that step permeability does not change the scaling behavior of the system, and its only effect is a renormalization of some of the parameters.Comment: 25 pages, 18 postscript figure

Decay of isolated surface features driven by the Gibbs-Thomson effect in analytic model and simulation

A theory based on the thermodynamic Gibbs-Thomson relation is presented which provides the framework for understanding the time evolution of isolated nanoscale features (i.e., islands and pits) on surfaces. Two limiting cases are predicted, in which either diffusion or interface transfer is the limiting process. These cases correspond to similar regimes considered in previous works addressing the Ostwald ripening of ensembles of features. A third possible limiting case is noted for the special geometry of "stacked" islands. In these limiting cases, isolated features are predicted to decay in size with a power law scaling in time: A is proportional to (t0-t)^n, where A is the area of the feature, t0 is the time at which the feature disappears, and n=2/3 or 1. The constant of proportionality is related to parameters describing both the kinetic and equilibrium properties of the surface. A continuous time Monte Carlo simulation is used to test the application of this theory to generic surfaces with atomic scale features. A new method is described to obtain macroscopic kinetic parameters describing interfaces in such simulations. Simulation and analytic theory are compared directly, using measurements of the simulation to determine the constants of the analytic theory. Agreement between the two is very good over a range of surface parameters, suggesting that the analytic theory properly captures the necessary physics. It is anticipated that the simulation will be useful in modeling complex surface geometries often seen in experiments on physical surfaces, for which application of the analytic model is not straightforward.Comment: RevTeX (with .bbl file), 25 pages, 7 figures from 9 Postscript files embedded using epsf. Submitted to Phys. Rev. B A few minor changes made on 9/24/9

Hole-doping dependence of percolative phase separation in Pr_(0.5-delta)Ca_(0.2+delta)Sr_(0.3)MnO_(3) around half doping

We address the problem of the percolative phase separation in polycrystalline samples of Pr$_{0.5-\delta}$Ca$_{0.2+\delta}$Sr$_{0.3}$MnO$_3$ for $-0.04\leq \delta \leq 0.04$ (hole doping $n$ between 0.46 and 0.54). We perform measurements of X-ray diffraction, dc magnetization, ESR, and electrical resistivity. These samples show at $T_C$ a paramagnetic (PM) to ferromagnetic (FM) transition, however, we found that for $n>0.50$ there is a coexistence of both of these phases below $T_C$. On lowering $T$ below the charge-ordering (CO) temperature $T_{CO}$ all the samples exhibit a coexistence between the FM metallic and CO (antiferromagnetic) phases. In the whole $T$ range the FM phase fraction ($X$) decreases with increasing $n$. Furthermore, we show that only for $n\leq 0.50$ the metallic fraction is above the critical percolation threshold $X_C\simeq 15.5$. As a consequence, these samples show very different magnetoresistance properties. In addition, for $n\leq 0.50$ we observe a percolative metal-insulator transition at $T_{MI}$, and for $T_{MI}<T<T_{CO}$ the insulating-like behavior generated by the enlargement of $X$ with increasing $T$ is well described by the percolation law $\rho ^{-1}=\sigma \sim (X-X_C)^t$, where $t$ is a critical exponent. On the basis of the values obtained for this exponent we discuss different possible percolation mechanisms, and suggest that a more deep understanding of geometric and dimensionality effects is needed in phase separated manganites. We present a complete $T$ vs $n$ phase diagram showing the magnetic and electric properties of the studied compound around half doping.Comment: 9 text pages + 12 figures, submitted to Phys. Rev.