Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with $\mathscr{K}(t)\simeq t^{\alpha-1}$ for $0<\alpha<2$. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.Comment: 7 pages, 5 figure

Concurrent investigation of global motion and form processing in amblyopia: an equivalent noise approach

PURPOSE: Directly comparing the motion and form processing in neurologic disorders has remained difficult due to the limitations in the experimental stimulus. In the current study, motion and form processing in amblyopia was characterized using random dot stimuli in different noise levels to parse out the effect of local and global processing on motion and form perception. METHODS: A total of 17 amblyopes (8 anisometropic and 9 strabismic), and 12 visually normal subjects monocularly estimated the global direction of motion and global orientation in random dot kinematograms (RDK) and Glass patterns (Glass), whose directions/orientations were drawn from normal distributions with a range of means and variances that served as external noise. Direction/orientation discrimination thresholds were measured without noise first then variance threshold was measured at the multiples of the direction/orientation threshold. The direction/orientation and variance thresholds were modelled to estimate internal noise and sampling efficiency parameters. RESULTS: Overall, the thresholds for Glass were higher than RDK for all subjects. The thresholds for both Glass and RDK were higher in the strabismic eyes compared with the fellow and normal eyes. On the other hand, the thresholds for anisometropic amblyopic eyes were similar to the normal eyes. The worse performance of strabismic amblyopes was best explained by relatively low sampling efficiency compared with other groups (P < 0.05). CONCLUSIONS: A deficit in global motion and form perception was only evident in strabismic amblyopia. Contrary to the dorsal stream deficiency hypothesis assumed in other developmental disorders, deficits were present in both motion (dorsal) and form (ventral) processing

Zero range model of traffic flow

A multi--cluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is directly mapped to the mathematically well-studied zero-range process. Knowledge of the asymptotic behaviour of the transition rates for large clusters allows us to apply an established criterion for phase separation in one-dimensional driven systems. The distribution over cluster sizes in our zero-range model is given by a one--step master equation in one dimension. It provides an approximate mean--field dynamics, which, however, leads to the exact stationary state. Based on this equation, we have calculated the critical density at which phase separation takes place. We have shown that within a certain range of densities above the critical value a metastable homogeneous state exists before coarsening sets in. Within this approach we have estimated the critical cluster size and the mean nucleation time for a condensate in a large system. The metastablity in the zero-range process is reflected in a metastable branch of the fundamental flux--density diagram of traffic flow. Our work thus provides a possible analytical description of traffic jam formation as well as important insight into condensation in the zero-range process.Comment: 10 pages, 13 figures, small changes are made according to finally accepted version for publication in Phys. Rev.

Cd3As2 is Centrosymmetric

This is a revised version of a manuscript that was originally posted here in February of 2014. It has been accepted at the journal Inorganic Chemistry after reviews that included those of two crystallographers who made sure all the t's were crossed and the i's were dotted. The old work (from 1968) that said that Cd3As2 was noncentrosymmetric was mistaken, with the authors of that study making a type of error that in the 1980s became infamous in crystallography. As a result of the increased scrutiny of the issue of centrosymmetricity of the 1980's, there are now much better analysis tools to resolve the issue fully, and its important to understand that not just our crystals are centrosymmetric, even the old guy's crystals were centrosymmetric (and by implication everyone's are). There is no shame in having made that error back in the day and those authors would not find the current centrosymmetric result controversial; their paper is excellent in all other aspects. This manuscript describes how the structure is determined, explains the structure schematically, calculates the electronic structure based on the correct centrosymmetric crystal structure, and gives the structural details that should be used for future analysis and modeling.Comment: Accepted by ACS Inorganic Chemistr

Synthesis of Recursive ADT Transformations from Reusable Templates

Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often requires nontrivial effort from the user, which impedes the usability of the synthesizer. We present a solution to this problem in the context of recursive transformations on algebraic data-types. Our approach relies on polymorphic synthesis constructs: a small but powerful extension to the language of syntactic templates, which makes it possible to define a program space in a concise and highly reusable manner, while at the same time retains the scalability benefits of conventional templates. This approach enables end-users to reuse predefined templates from a library for a wide variety of problems with little effort. The paper also describes a novel optimization that further improves the performance and scalability of the system. We evaluated the approach on a set of benchmarks that most notably includes desugaring functions for lambda calculus, which force the synthesizer to discover Church encodings for pairs and boolean operations

Fragility curves for non-ductile reinforced concrete frames that exhibit different component response mechanisms

Around the world, a large percentage of buildings in regions of high seismicity are older, non-ductile reinforced concrete. To assess the risk posed by these buildings, fragility functions are required to define the likelihood that these buildings will sustain damage and collapse under earthquake loading. This paper presents the initial phase of a research effort to develop fragility functions for non-ductile concrete frames using numerical simulation; the research presented in this paper focuses on development of the numerical model and application of the model to develop fragility functions for a prototype non-ductile concrete frame. To enable numerical simulation of concrete frame buildings, response models for beam–column joints and columns are developed to provide (1) appropriate simulation of component response and, thereby, reliable assessment of risk and (2) computational efficiency and robustness. These new models are developed using existing experimental data, build on response models proposed by others, and employ component and material models available in the OpenSees analysis platform (http://opensees.berkeley.edu). A new beam–column joint model combines a new expression for joint strength and newly developed cyclic response parameters; a new column response model includes a new shear-strength model and newly developed cyclic response parameters. Numerical models of a prototype non-ductile concrete frame are developed that include simulation of one or more of the following characteristics: (1) rigid beam–column joint, (2) nonlinear joint shear response, (3) nonlinear joint shear and bond–slip response, and (4) column shear failure. Dynamic analyses are performed using these frame models and a suite of ground motions; analysis results are used to develop fragility curves. Fragility curves quantify the vulnerability of the frame and provide understanding of the impact of different component failure mechanisms on frame vulnerability.This research was supported by the National Science Foundation under NSF Grant # 1000700.This is the accepted manuscript of a paper published in Engineering Structures (J-S Jeon, LN Lowes, R DesRoches, I Brilakis, Engineering Structures 2015, 85, 127–143

Shear viscosity in ϕ4\phi^4 theory from an extended ladder resummation

We study shear viscosity in weakly coupled hot $\phi^4$ theory using the CTP formalism . We show that the viscosity can be obtained as the integral of a three-point function. Non-perturbative corrections to the bare one-loop result can be obtained by solving a decoupled Schwinger-Dyson type integral equation for this vertex. This integral equation represents the resummation of an infinite series of ladder diagrams which contribute to the leading order result. It can be shown that this integral equation has exactly the same form as the Boltzmann equation. We show that the integral equation for the viscosity can be reexpressed by writing the vertex as a combination of polarization tensors. An expression for this polarization tensor can be obtained by solving another Schwinger-Dyson type integral equation. This procedure results in an expression for the viscosity that represents a non-perturbative resummation of contributions to the viscosity which includes certain non-ladder graphs, as well as the usual ladders. We discuss the motivation for this resummation. We show that these resummations can also be obtained by writing the viscosity as an integral equation involving a single four-point function. Finally, we show that when the viscosity is expressed in terms of a four-point function, it is possible to further extend the set of graphs included in the resummation by treating vertex and propagator corrections self-consistently. We discuss the significance of such a self-consistent resummation and show that the integral equation contains cancellations between vertex and propagator corrections.Comment: Revtex 40 pages with 29 figures, version to appear in Phys. Rev.

InGaN nano-ring structures for high-efficiency light emitting diodes

A technique based on the Fresnel diffraction effect for the fabrication of nano-scale site-controlled ring structures in InGaN/GaN multi-quantum well structures has been demonstrated. The ring structures have an internal diameter of 500 nm and a wall width of 300 nm. A 1 cm-1 Raman shift has been measured, signifying substantial strain relaxation from the fabricated structure. The 9 nm blueshift observed in the cathodoluminescence spectra can be attributed to band filling and/or screening of the piezoelectric field. A light emitting diode based on this geometry has been demonstrated

Automated Damage Index Estimation of Reinforced Concrete Columns for Post-Earthquake Evaluations

In emergency scenarios, immediate reconnaissance efforts are necessary. These efforts often take months to complete in full. While underway, building occupants are unable to return to their homes/businesses, and thus, the impact on the society of the disaster-stricken region is increased. In order to mitigate the impact, researchers have focused on creating a more efficient means of assessing the condition of buildings in the post-disaster state. In this paper, a machine vision-based methodology for real-time post-earthquake safety assessment is presented. A novel method of retrieving spalled properties on reinforced concrete (RC) columns in RC frame buildings using image data is presented. In this method, the spalled region is detected using a local entropy-based approach. Following this, the depth properties are retrieved using contextual information pertaining to the amount and type of reinforcement which is exposed. The method is validated using a dataset of damaged RC column images.This material is based in part upon work supported by the National Science Foundation under Grant Numbers CMMI-1034845 and CMMI-0738417.This is the accepted manuscript. The final version is available from ASCE at http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.000120