Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics

We use renormalization group to calculate the reunion and survival exponents of a set of random walkers interacting with a long range $1/r^2$ and a short range interaction. These exponents are used to study the binding-unbinding transition of polymers and the behavior of several quantum problems.Comment: Revtex 3.1, 9 pages (two-column format), 3 figures. Published version (PRE 63, 051103 (2001)). Reference corrections incorporated (PRE 64, 059902 (2001) (E

A shifting method for dynamic system Model Order Reduction

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.Includes bibliographical references (p. 83-86).Model Order Reduction (MOR) is becoming increasingly important in computational applications. At the same time, the need for more comprehensive models of systems is generating problems with increasing numbers of outputs and inputs. Classical methods, which were developed for Single-Input Single-Output (SISO) systems, generate reduced models that are too computationally inefficient for large Multiple-Input Multiple-Output (MIMO) systems. Although many approaches exclusively designed for MIMO systems have emerged during the past decade, they cannot satisfy the overall needs for maintaining the characteristics of systems. This research investigates the reasons for the poor performances of the proposed approaches, using specific examples. Inspired by these existing methods, this research develops a novel way to extract information from MIMO systems, by means of system transfer functions. The approach, called Shifting method, iteratively extracts time-constant shifts from the system and splits the transfer function into several simple systems referred to as contour terms that outline the system structure, and a reducible system referred to as remainder system that complement the Contour Terms. This algorithm produces a remainder system that existing approaches can reduce more effectively. This approach works particularly well for systems with either tightly clustered or well separated modes, and all the operations are O(n). The choice of shifts is based on an optimization process, with Chebyshev Polynomial roots as initial guesses. This paper concludes with a demonstration of the procedure as well as related error and stability analysis.by Xu, Song.S.M

Numerical Investigation of turbulent coupling boundary layer of air-water interaction flow

Thesis (S.M. in Mechanical Engineering and S.M. in Ocean Engineering)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 159-164).Air-water interaction flow between two parallel flat plates, known as Couette flow, is simulated by direct numerical simulation. The two flowing fluids are coupled through continuity of velocity and shear stress condition across the interface. Pseudo-spectral method is used in each flow subdomain with Fourier expansion in streamwise and spanwise directions and finite difference in vertical direction. Statistically quasi-steady flow properties, such as mean velocity profiles, turbulent intensities, Reynolds stress and turbulent kinetic energy (TKE) budget terms show significant differences between air-water interface turbulence near the water side (IntT-w) and wall-bounded turbulence(WT) while there are some similarities between IntT-w and free surface turbulence (FST). Due to the velocity fluctuation at the interface, water side near interface turbulence flow (IntT-w) is characterized with a thinner viscous sub-layer and decreased intercept parameter B in log-law layer, strengthened Reynolds stress and eddy viscosity, together with a stronger production term, decreasing-then-increasing dissipation term and negative turbulent diffusion term in TKE budget.(cont.) Abundant physical phenomena exist on the water side turbulent flow with four major types of three-dimensional vortex structures identified near the interface by variable-interval spacing averaging (VISA) techniques. Each type of vortex structures is found to play an essential role in the turbulent energy balance and passive scalar transport.by Song Liu.S.M.in Mechanical Engineering and S.M.in Ocean Engineerin

Atomic-scale perspective on the origin of attractive step interactions on Si(113)

Recent experiments have shown that steps on Si(113) surfaces self-organize into bunches due to a competition between long-range repulsive and short-range attractive interactions. Using empirical and tight-binding interatomic potentials, we investigate the physical origin of the short-range attraction, and report the formation and interaction energies of steps. We find that the short-range attraction between steps is due to the annihilation of force monopoles at their edges as they combine to form bunches. Our results for the strengths of the attractive interactions are consistent with the values determined from experimental studies on kinetics of faceting.Comment: 4 pages, 3 figures, to appear in Phys. Rev B, Rapid Communication

Improving the efficiency of an automated manufacturing system through a tri-part approach

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 71-72).This research investigates a complex automated manufacturing system at three levels to improve its efficiency. In the system there are parallel loops of stations connected by a single closed conveyor. In each loop there are a series of identical stations, each with multiple storage slots and with capability to process several jobs simultaneously. At the system level we undertake capacity planning and explore Work-in-Process (WIP) control. We build an Excel model to calculate the implied load of each station, applying the model to sensitivity analyses of the system capacity. In addition, we identify a concave relationship between output and WIP based on actual factory data from our industrial partner. We surprisingly observe a reduction in output when WIP is high. Therefore, we suggest adopting a CONWIP policy in the system in order to increase and smooth the output. At the loop level we study the assignment policy. The complexity of this study is highlighted by non-trivial travel time between stations. We build a simulation model in Matlab to compare different assignment policies. The objective is to find the assignment policy that balances the station load, decreases the flow time for jobs, and reduces the rejection or blockage rate for the system. At the station level we investigate the holding time between simultaneous processes. We model this as a semi-Markov process, building a simulation model in Matlab to confirm the analytical results. We discover a tradeoff between flow time and production rate with different holding times, and propose new holding rules to further improve station performance. The conclusions from this research are useful for our industrial partner in its efforts to improve the operation of the system and to increase its capacity. Moreover, the methodologies and insights of this work can be beneficial to further research on related industry practice.by Chen Song.S.M

A system theoretic approach to design safety into medical device

Thesis (S.M. in Engineering and Management)--Massachusetts Institute of Technology, Engineering Systems Division, System Design and Management Program, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 65-66).The goal of this thesis is to investigate and demonstrate the application of a systems approach to medical device safety in China. Professor Leveson has developed an accident modeling framework called STAMP (Systems Theoretic Accident Modeling and Processes.) Traditional accident models typically focus on component failure; in contrast, STAMP includes interactions between components as well as social, economic, and legal factors. In this thesis, the accident of the artificial heart at a level II hospital in China was used as a test case to study whether Causal Analysis based on STAMP (CAST) is used to outline the interactions between the different medical device system components, identify the safety control structure in place, and understand how this control structure failed to prevent artificial heart accident in a Chinese hospital. The analysis suggested that further changes might be necessary to protect the Chinese public and so, based on the results of the CAST, a new set of systemic recommendations was proposed.by Qingyang Song.S.M.in Engineering and Managemen

Ab initio study of electron transport in lead telluride

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 91-97).Last few years have witnessed significant enhancement of thermoelectric figure of merit of lead telluride (PbTe) via nanostructures. Despite the experimental progress, current understanding of the electron transport in PbTe is based on either band structure simulated using first-principles in combination with constant relaxation time approximation or empirical models, both requiring adjustable parameters obtained by fitting experimental data. This thesis aims to compute thermoelectric properties of PbTe all from first-principles. We start by discussing the formalism based on Boltzmann transport equation to calculate the electron transport properties in PbTe using first principles and identify the importance to calculate electron-phonon interaction accurately. We then discuss the challenges in studying electron-phonon interaction in semiconductors using first-principles and introduce electron-phonon Wannier interpolation which allows us to calculate the strength of electron-phonon coupling on a very fine mesh. In polar materials like PbTe, the Fröhlich interaction due to long-range dipole field of longitudinal optical phonons contributes to the electron-phonon coupling as well. As the long-range nature of the dipole field makes the standard Wannier interpolation fail, we have discussed the detailed procedures for correction. Next, we study the screening effect of free carriers on electron transport by modulating the polar scattering. These considerations enabled us to report parameter-free first-principles calculation of electron and phonon transport in PbTe, including mode-by-mode electron-phonon scattering, leading to detailed information on electron mean free paths and the cumulative contributions by electrons and phonons with different mean free paths to thermoelectric transport properties in PbTe. Such information will help to rationalize the use and optimization of nanostructures to achieve high thermoelectric figure of merit.by Qichen Song.S.M

Entropic Interactions in Suspensions of Semi-Flexible Rods: Short-Range Effects of Flexibility

We compute the entropic interactions between two colloidal spheres immersed in a dilute suspension of semi-flexible rods. Our model treats the semi-flexible rod as a bent rod at fixed angle, set by the rod contour and persistence lengths. The entropic forces arising from this additional rotational degree of freedom are captured quantitatively by the model, and account for observations at short range in a recent experiment. Global fits to the interaction potential data suggest the persistence length of fd-virus is about two to three times smaller than the commonly used value of $2.2 \mu {m}$.Comment: 4 pages, 5 figures, submitted to PRE rapid communication

Analysis of the intraspinal calcium dynamics and its implications on the plasticity of spiking neurons

The influx of calcium ions into the dendritic spines through the N-metyl-D-aspartate (NMDA) channels is believed to be the primary trigger for various forms of synaptic plasticity. In this paper, the authors calculate analytically the mean values of the calcium transients elicited by a spiking neuron undergoing a simple model of ionic currents and back-propagating action potentials. The relative variability of these transients, due to the stochastic nature of synaptic transmission, is further considered using a simple Markov model of NMDA receptos. One finds that both the mean value and the variability depend on the timing between pre- and postsynaptic action-potentials. These results could have implications on the expected form of synaptic-plasticity curve and can form a basis for a unified theory of spike time-dependent, and rate based plasticity.Comment: 14 pages, 10 figures. A few changes in section IV and addition of a new figur