Numerical analysis of the relation between interactions and structure in a molecular fluid

Coarse graining is a popular technique used in physics to speed up the computer simulation of molecular fluids. An essential part of this technique is a method that solves the inverse problem of determining the interaction potential or its parameters from the given structural data. Due to discrepancies between model and reality, the potential is not unique, such that stability of such method and its convergence to a meaningful solution are issues.rnrnIn this work, we investigate empirically whether coarse graining can be improved by applying the theory of inverse problems from applied mathematics. In particular, we use the singular value analysis to reveal the weak interaction parameters, that have a negligible influence on the structure of the fluid and which cause non-uniqueness of the solution. Further, we apply a regularizing Levenberg-Marquardt method, which is stable against the mentioned discrepancies. Then, we compare it to the existing physical methods - the Iterative Boltzmann Inversion and the Inverse Monte Carlo method, which are fast and well adapted to the problem, but sometimes have convergence problems.rnrnFrom analysis of the Iterative Boltzmann Inversion, we elaborate a meaningful approximation of the structure and use it to derive a modification of the Levenberg-Marquardt method. We engage the latter for reconstruction of the interaction parameters from experimental data for liquid argon and nitrogen. We show that the modified method is stable, convergent and fast. Further, the singular value analysis of the structure and its approximation allows to determine the crucial interaction parameters, that is, to simplify the modeling of interactions. Therefore, our results build a rigorous bridge between the inverse problem from physics and the powerful solution tools from mathematics. rn

Condizioni di equilibrio di una nana bianca

Il seguente lavoro di tesi descrive un modello fisico di nana bianca all'equilibrio partendo da dati empirici tipici per tali stelle. Si schematizza la stella come una sfera di gas He completamente ionizzato di densità uniforme, a temperatura T=const e soggetta ad un potenziale gravitazionale centrale. Il gas si costituisce di una parte degenere relativistica (elettroni) ed una parte classica ideale (gli ioni). Si procede ricavando le relazioni essenziali per determinare le proprietà di un gas di Fermi degenere relativistico, mostrando come, al limite di Boltzmann, descrivano anche il caso classico. La trattazione teorica è progressivamente supportata dalle stime dei parametri caratteristici delle due componenti del gas per verificare le loro condizioni fisiche e stimare l'importanza dei rispettivi contributi all'intero sistema. Si procede quindi all'esposizione dell'equilibrio tra pressione degenere ed attrazione gravitazionale ponendo particolare attenzione alla relazione raggio-massa. Infine si discutono le condizioni entro le quali un sistema fisico con tali caratteristiche può sussistere, con esplicito riferimento al limite di Chandrasekhar.

Dinamica delle galassie a spirale e delle galassie ellittiche

In questa tesi si vuole fornire una descrizione generale delle dinamiche delle galassie ellittiche e a spirale. Nel primo capitolo si danno informazioni generali sulle grandezze che caratterizzano le galassie e come esse vengono classificate. Nel secondo capitolo si espone il concetto di sistema collisionale, si fa notare come le galassie risultino essere sistemi non collisionali e come questo porti delle semplificazioni nella trattazione di questi oggetti e ne spieghi alcune caratteristiche. Si prosegue andando a considerare le equazioni che descrivono il moto (equazione non collisionale di Boltzmann, equazioni di Jeans, teorema del viriale in forma tensoriale) e le informazioni che si possono ricavare. Nel terzo capitolo ci si concentra sulle galassie ellittiche e sulle principali leggi che le descrivono e dalle quali è possibile ottenere stime riguardo distanza e dimensioni. Il quarto e ultimo capitolo è incentrato sulle galassie a spirale e in particolare sulla dinamica del disco, e come si è giunti all'ipotesi dell'esistenza della materia oscura, e sulla dinamica dei bracci.

Simulazione di fluidi in Computer Graphics

Questa tesi si focalizza sullo studio dei modelli fisico-matematici attualmente in uso per la simulazione di fluidi al calcolatore con l’obiettivo di fornire nozioni di base e avanzate sull’utilizzo di tali metodi. La trattazione ha lo scopo di facilitare la comprensione dei principi su cui si fonda la simulazione di fluidi e rappresenta una base per la creazione di un proprio simulatore. E’ possibile studiare le caratteristiche di un fluido in movimento mediante due approcci diversi, l’approccio lagrangiano e l’approccio euleriano. Mentre l’approccio lagrangiano ha lo scopo di conoscere il valore, nel tempo, di una qualsiasi proprietà di ciascuna particella che compone il fluido, l’approccio euleriano, fissato uno o più punti del volume di spazio occupato da quest’ultimo, vuole studiare quello che accade, nel tempo, in quei punti. In particolare, questa tesi approfondisce lo studio delle equazioni di Navier-Stokes, approcciandosi al problema in maniera euleriana. La soluzione numerica del sistema di equazioni differenziali alle derivate parziali derivante dalle equazioni sopracitate, approssima la velocità del fluido, a partire dalla quale è possibile risalire a tutte le grandezze che lo caratterizzano. Attenzione viene riservata anche ad un modello facente parte dell’approccio semi-lagrangiano, il Lattice Boltzmann, considerato una via di mezzo tra i metodi puramente euleriani e quelli lagrangiani, che si basa sulla soluzione dell’equazione di Boltzmann mediante modelli di collisione di particelle. Infine, analogamente al metodo di Lattice Boltzmann, viene trattato il metodo Smoothed Particles Hydrodynamics, tipicamente lagrangiano, secondo il quale solo le proprietà delle particelle comprese dentro il raggio di una funzione kernel, centrata nella particella di interesse, influenzano il valore della particella stessa. Un resoconto pratico della teoria trattata viene dato mediante delle simulazioni realizzate tramite il software Blender 2.76b.

Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications

The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H2SO4(H2O)n where n = 1–6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the Møller–Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO4–·H3O+)(H2O)n−1 clusters are competitive with the neutral (H2SO4)(H2O)n clusters for n ≥ 3 and are more stable than neutral clusters for n ≥ 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H2SO4(H2O)n clusters are favorable in colder regions of the troposphere (T = 216.65–273.15 K) for n = 1–6, but the formation of clusters with n ≥ 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H2SO4–H2O system must contain more than one H2SO4 and are in concert with recent findings(1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere.

Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications

The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H2SO4(H2O)n where n = 1–6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the Møller–Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO4–·H3O+)(H2O)n−1clusters are competitive with the neutral (H2SO4)(H2O)n clusters for n ≥ 3 and are more stable than neutral clusters for n ≥ 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H2SO4(H2O)n clusters are favorable in colder regions of the troposphere (T = 216.65–273.15 K) for n = 1–6, but the formation of clusters with n ≥ 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H2SO4–H2O system must contain more than one H2SO4 and are in concert with recent findings(1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere.

Product Distributions Following Hyperthermal Collisions Between C2H4 And O(3P)

Transient Diode Laser Absorption Spectroscopy (TDLAS) was used to perform vibrational state population studies of the CO2 product from the hyperthermal reaction between C2H4 and O(3P) at room temperature using O3 as the O-atom precursor. Photodissociation of O3 using a frequency quadrupled Q-switch Nd:YAG laser pulse at 266 nm produced O(3P) atoms at high velocities which subsequently reacted with C2H4, producing several primary and secondary products including CO2. The CO2 product was detected using high-resolution TDLAS under five unique sets of reaction conditions. The vibrational distribution of the CO2 product did not follow a Boltzmann distribution at all five sets of conditions. The experiments showed a distribution in which there was a surprisingly high population in the (1000) (symmetric stretching) state compared with the other states probed, all of which contained bend excitation. In general, the CO2 population in the (1000) state was about 15-20% more populated than the Boltzmann distribution predicts. A possible explanation for this result may lie in the mechanism of CO2 evolution from the C2H4 + O(3P) reaction.

Transport model of the human Na+-coupled L-ascorbic acid (vitamin C) transporter SVCT1

Vitamin C (L-ascorbic acid) is an essential micronutrient that serves as an antioxidant and as a cofactor in many enzymatic reactions. Intestinal absorption and renal reabsorption of the vitamin is mediated by the epithelial apical L-ascorbic acid cotransporter SVCT1 (SLC23A1). We explored the molecular mechanisms of SVCT1-mediated L-ascorbic acid transport using radiotracer and voltage-clamp techniques in RNA-injected Xenopus oocytes. L-ascorbic acid transport was saturable (K(0.5) approximately 70 microM), temperature dependent (Q(10) approximately 5), and energized by the Na(+) electrochemical potential gradient. We obtained a Na(+)-L-ascorbic acid coupling ratio of 2:1 from simultaneous measurement of currents and fluxes. L-ascorbic acid and Na(+) saturation kinetics as a function of cosubstrate concentrations revealed a simultaneous transport mechanism in which binding is ordered Na(+), L-ascorbic acid, Na(+). In the absence of L-ascorbic acid, SVCT1 mediated pre-steady-state currents that decayed with time constants 3-15 ms. Transients were described by single Boltzmann distributions. At 100 mM Na(+), maximal charge translocation (Q(max)) was approximately 25 nC, around a midpoint (V(0.5)) at -9 mV, and with apparent valence approximately -1. Q(max) was conserved upon progressive removal of Na(+), whereas V(0.5) shifted to more hyperpolarized potentials. Model simulation predicted that the pre-steady-state current predominantly results from an ion-well effect on binding of the first Na(+) partway within the membrane electric field. We present a transport model for SVCT1 that will provide a framework for investigating the impact of specific mutations and polymorphisms in SLC23A1 and help us better understand the contribution of SVCT1 to vitamin C metabolism in health and disease.

Proteins in silico-modeling and sampling

Proteins are linear chain molecules made out of amino acids. Only when they fold to their native states, they become functional. This dissertation aims to model the solvent (environment) effect and to develop & implement enhanced sampling methods that enable a reliable study of the protein folding problem in silico. We have developed an enhanced solvation model based on the solution to the Poisson-Boltzmann equation in order to describe the solvent effect. Following the quantum mechanical Polarizable Continuum Model (PCM), we decomposed net solvation free energy into three physical terms– Polarization, Dispersion and Cavitation. All the terms were implemented, analyzed and parametrized individually to obtain a high level of accuracy. In order to describe the thermodynamics of proteins, their conformational space needs to be sampled thoroughly. Simulations of proteins are hampered by slow relaxation due to their rugged free-energy landscape, with the barriers between minima being higher than the thermal energy at physiological temperatures. In order to overcome this problem a number of approaches have been proposed of which replica exchange method (REM) is the most popular. In this dissertation we describe a new variant of canonical replica exchange method in the context of molecular dynamic simulation. The advantage of this new method is the easily tunable high acceptance rate for the replica exchange. We call our method Microcanonical Replica Exchange Molecular Dynamic (MREMD). We have described the theoretical frame work, comment on its actual implementation, and its application to Trp-cage mini-protein in implicit solvent. We have been able to correctly predict the folding thermodynamics of this protein using our approach.

A 45nm CMOS DESIGN OF NEUROMORPHIC SYSTEM

Neuromorphic computing has become an emerging field in wide range of applications. Its challenge lies in developing a brain-inspired architecture that can emulate human brain and can work for real time applications. In this report a flexible neural architecture is presented which consists of 128 X 128 SRAM crossbar memory and 128 spiking neurons. For Neuron, digital integrate and fire model is used. All components are designed in 45nm technology node. The core can be configured for certain Neuron parameters, Axon types and synapses states and are fully digitally implemented. Learning for this architecture is done offline. To train this circuit a well-known algorithm Restricted Boltzmann Machine (RBM) is used and linear classifiers are trained at the output of RBM. Finally, circuit was tested for handwritten digit recognition application. Future prospects for this architecture are also discussed.

The Interstellar Neutral He haze in the heliosphere: what can we learn?

Neutral interstellar helium has been observed by the Interstellar Boundary Explorer (IBEX) since 2009, with a signal-to-noise ratio well above 1000. Because of the geometry of the observations, the signal observed from January to March each year is the easiest to identify. However, as we show via simulations, the portion of the signal in the range of intensities from 10(-3) to 10(-2) of the peak value, previously mostly left out from the analysis, may provide important information about the details of the distribution function of interstellar He gas in front of the heliosphere. In particular, these observations may inform us about possible departures of the parent interstellar He population from equilibrium. We compare the expected distribution of the signal for the canonical assumption of a single Maxwell-Boltzmann population with the distributions for a superposition of the Maxwell-Boltzmann primary population and the recently discovered Warm Breeze, and for a single primary population given by a kappa function. We identify the regions on the sky where the differences between those cases are expected to be the most visible against the background. We discuss the diagnostic potential of the fall peak of the interstellar signal, reduced by a factor of 50 due to the Compton-Getting effect but still above the detection limit of IBEX. We point out the strong energy dependence of the fall signal and suggest that searching for this signal in the data could bring an independent assessment of the low-energy measurement threshold of the IBEX-Lo sensor.

Measured Stark widths of several spectral lines of Pb III

The Stark full widths at half of the maximal line intensity (FWHM, ω) have been measured for 25 spectrallines of PbIII (15 measured for the first time) arising from the 5d106s8s, 5d106s7p, 5d106s5f and 5d106s5g electronic configurations, in a lead plasma produced by ablation with a Nd:YAG laser. The optical emission spectroscopy from a laser-induced plasma generated by a 10 640 Å radiation, with an irradiance of 2 × 1010 W cm− 2 on a lead target (99.99% purity) in an atmosphere of argon was analysed in the wavelength interval between 2000 and 7000 Å. The broadening parameters were obtained with the target placed in argon atmosphere at 6 Torr and 400 ns after each laser light pulse, which provides appropriate measurement conditions. A Boltzmann plot was used to obtain the plasma temperature (21,400 K) and published values of the Starkwidths in Pb I, Pb II and PbIII to obtain the electron number density (7 × 1016 cm− 3); with these values, the plasma composition was determined by means of the Saha equation. Local Thermodynamic Equilibrium (LTE) conditions and plasma homogeneity has been checked. Special attention was dedicated to the possible self-absorption of the different transitions. Comparison of the new results with recent available data is also presented.