d-Path Laplacians and Quantum Transport on Graphs

We generalize the Schrödinger equation on graphs to include long-range interactions (LRI) by means of the Mellin-transformed d-path Laplacian operators. We find analytical expressions for the transition and return probabilities of a quantum particle at the nodes of a ring graph. We show that the average return probability in ring graphs decays as a power law with time when LRI is present. In contrast, we prove analytically that the transition and return probabilities on a complete and start graphs oscillate around a constant value. This allowed us to infer that in a barbell graph-a graph consisting of two cliques separated by a path-the quantum particle get trapped and oscillates across the nodes of the path without visiting the nodes of the cliques. We then compare the use of the Mellin-transformed d-path Laplacian operators versus the use of fractional powers of the combinatorial Laplacian to account for LRI. Apart from some important differences observed at the limit of the strongest LRI, the d-path Laplacian operators produces the emergence of new phenomena related to the location of the wave packet in graphs with barriers, which are not observed neither for the Schrödinger equation without LRI nor for the one using fractional powers of the Laplacian

Assessment of disparate strategies for octane prediction

Includes bibliographical references.Octane quality is a key factor in determining the profitability in a modern refinery. The final commercial product is defined by the combined blend of various gasoline component streams which are produced from different units within the refinery. The accurate prediction of the octane numbers of these blends enables the economic optimization of the production process. Currently, empirical octane models are used exclusively for this purpose. Octane is a measure of the spontaneous autoignition propensity of a fuel-air mixture and it is quantified using a specific engine-based test method. This research project was founded on the premise that an improved octane prediction model could be harvested from building blocks that included a fundamental understanding of autoignition, appropriate choices of autoignition models and an engine model. This objective was pursued in this work by investigating detailed and reduced kinetic mechanisms for the oxidation of selected fuel molecules using various modeling techniques. Empirical octane models and semi-chemical models of autoignition were also investigated. All of these methodologies were assessed as possible strategies towards octane prediction. In this study it was observed that both detailed and highly reduced kinetic models could describe the oxidation behaviour of pure fuel components and predict their subsequent ignition delays

Characterizing the functional dynamics of the Leak Potassium channel h-TRAAK through Molecular Dynamics Simulations under physiological conditions

Two Pore domain K+ channels (K2P) are a specific family of channels whose functionality is finely tuned by a rich ensemble of chemical and physical stimuli. The ionic currents produced by these proteins are usually referred as ‘’leak’’ or ‘’background’’ potassium currents because they stabilize the resting potential of membranes to highly negative values close to the K+ equilibrium potential. In particular, the human TRAAK channel (Twik Related Arachidonic Acid K+ channel) is influenced by chemicals (anesthetics or drugs), and physical agents (pH, temperature, membrane stretching or bending). Although the firsts experimental findings date back to early ‘00 a full comprehension of the gating mechanism and ion transport is still missing. Among the most influential theories on gating, we mention the two states hypothesis suggested by MacKinnon thanks to the crystal structure availability. The existence of an atomistic model paved the way to furthers investigations, as well by using theoretical approaches. In this context, exploiting in silico techniques belonging to computational biophysics, we provided a comprehensive characterization of the channel behaviour. Advanced simulating conditions were used, with the purpose of mimicking as close as possible the real protein behaviour, and some of those key-biases playing a modulation role of channel activity. By using Molecular Dynamics simulations, several protocols were applied to simulate hTRAAK in presence of different conditions: i) membrane stretching, ii) ions concentration gradients, iii) applied electrostatic potential. These strategies were chosen to gain new insights into the putative conductive state of the channel, promoting the translocation of K+ ions through it

Theoretical Investigation of Static and Dynamic Properties of Zeolite ZSM-5 Based Amorphous Material

Results of molecular dynamics simulations on structural, vibrational and relaxational properties of zeolite ZSM-5 based amorphous solids are presented. The effects of extent of amorphization, measured by an energetic criterion, on properties like distribution of coordination numbers, internal surface area, ring statistics and effective pore size are studied. Ring statistics indicates that upon amorphization not only rings with larger size break down to give rings with smaller size, but that for intermediate degree of amorphization also larger rings are generated. The vibrational density of states was determined for different extents of amorphization. The vibrational modes are analyzed by projecting them on those of the SiO4 and Si-O-Si subunits and individual frequency-dependent contributions of stretching, bending and rotation are discussed. Analysis of low-frequency spectrum show that for higher crystallinity the intensity of the boson peak decreases upon amorphization, whereas the opposite behavior is observed for forms with lower crystallinity. These effects are explained in the framework of Maxwell counting of floppy modes. The modes associated with the boson peak for these materials are found to be mainly optic in nature. Relaxations were studied for temperatures below the critical temperature. At low temperatures the relaxations comprise mainly one-dimensional chains of atoms. The dimensionality of the relaxing centers increases with the temperature due to side branching. The possibility of having reversible jumps decreases with increasing temperature due to a strong drop in the potential energy during aging. There exist very prominent peaks in the van Hove correlation functions as a manifestation of the hopping processes. The dynamics of the oxygen atoms is found to be more heterogeneous than those of the silicon atoms. Ab initio many-body calculations on the strain energy ofW-silica, taken as a model system for edge-sharing tetrahedral SiO2-systems with respect to corner-sharing ones as in a-quartz was performed. Correlation contributions are found to play an important role to determine the stability of edge-sharing units. Our calculation reveal that edge-sharing SiO4 tetrahedra in (partially) amorphous silicate systems are possible at a modest energetic expense

The Structure and Properties of Weakly Bound Clusters

In this thesis, two novel methods are introduced to advance the study of gas phase clusters. The structure similarity method is a computational technique that is able to quantify the structure difference for a pair of isomers, with a structure interpolation technique capable of finding intermediates in-between the isomer pair. A new experimental method, which couples differential mobility spectrometry with ultraviolet photodissociation spectroscopy (DMS-UVPD), is also developed and tested. Three test cases are discussed herein. These test cases showcase new theoretical techniques for mapping and visualizing potential energy surface (PES) and finding transition state (TS) structures, as well as experimental techniques of measuring UVPD spectra of DMS-MS isolated ion populations. Introduce of structure similarity, a technique developed for unsupervised machine learning (ML), enables effective domain of mapping PESs, which may subsequently be used to interpret experimental observations for systems of high geometric complexity. The experimental DMS-UVPD technique is shown capable of isolating ion species such that UVPD spectra may be recorded for characterization of analytes of interest. For the test cases described herein, these new methods provide meaningful (sometimes anti-intuitive) directions for future work. For the structure similarity method, its PES mapping capability is tested in Chapter 3 with a collection of protonated serine dimer cations, [Ser2 + H]+ to rationalize its infrared multiphoton dissociation (IRMPD) spectrum. Eventually, the spectral carrier is assigned to a non-global minimum (GM) isomer based on the partitioning information of the PES and spectral similarity. In Chapter 4, the accompanying structural interpolation method is employed to find TSs that can rationalize a regioselective alkylation reaction between a barbituric acid derivative and an alkyl-tricarbastannatrane complex. By combining the interpolation method together with chemical intuition, a total of 3 reaction channels are found, and the regioselectivity of the alkylation is identified as a kinetic effect. In Chapter 5, an acylhydrazone (AY) derivative, a photoswitch candidate, is examined using the DMS-UVPD technique. Experimentally, the protonated [AY + H]+ cation is injected into the instrument for DMS separation and laser interrogation, while theoretically, a number of neutral and protonated isomers are sampled. Eventually, separation of the ion population is observed and attributed to some ion-solvent cluster. Four isomers are found from theoretical calculation that may account for the UVPD spectr