This report describes a project performed at Linnaeus University with the task of solving the Schrodinger equation for electrons in homonuclear diatomic molecules, using the finite element method in Python. The Schrodinger equation is solved for the hydrogen atom, nitrogen atom, hydrogen molecule and nitrogen molecule using a finite element method. The results of the hydrogen atom showed a high accuracy compared to the analytical solution, given that the domain had high enough resolution. The solutions of the hydrogen molecule, nitrogen atom and nitrogen molecule showed reasonable accuracy although the resolution appeared sufficient. This foundation of Python code can be further built upon to explore more molecules and more properties, such as total energies and vibrational energies.

In this project we simulate explosions of nano water droplets using molecular dynamics. The water droplets are put under the exposure of a high-energy X-ray laser, which induces a quick Coulomb explosion. The explosion patterns, reporting the resulting position of the atoms, are then analyzed in different ways. Methods to deduce the initial shape of an ellipsoidal water droplet based on its explosion pattern are developed.

We constructed a standalone optical trapping system that was steerable in three dimensions and allowed for sufficient imaging of one цm particles with a CCD camera. The motion of the trapped particles was monitored by both a position sensitive detector as well with the CCD camera. The trap stiffness was evaluated by the power spectrum method and the equipartition theorem. For calibration of the stiffness of the trap, we found that the power spectrum method with data assessed by the PSD was most straightforward and accurate. The equipartition method was compromised by noise, low resolution and the bandwidth of the detector. With a HeNe laser run at 10 mW output power the trap strength of our system reached ~2 pN/um. The results also showed a decrease in the trap stiffness and particle's position variance when the size of trapped particles increased.

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Assessing the mixing of two liquids is a critical task in the biotechnical industry. At Cytiva, affinity chromatography columns depend on a well-mixed aqueous salt solution to release the target from the affinity resin. A mixer is often incorporated into the flow path to ensure effective mixing of the liquids.These mixers generate complex three-dimensional flowfields, and existing measurement techniques frequently average the flow depth, thereby losing essential spatial information. This project introduces and implements a novel method for assessing mixing in four dimensions, requiring simultaneous imaging of the flow from multiple view points. The flowfield is reconstructed from the image data using a least squares tomographic reconstruction technique. Additionally, a methodwas developed to reconstruct the same flowfield numerous times using different underlying section meshes. These results are then interpolated on a common grid and averaged. The findings demonstrate that this method accurately resolves the flowfield qualitatively and quantitatively. The averaging method enables lower downsampling factors and higher overall accuracy. However, challenges such as achieving uniform pipe illumination and enhancing data acquisition rates remain. Addressing these issues is essential for fully resolving three-dimensional flowfields over time. Future work will improve lighting and data acquisition to enhance the method’s applicability for higher Reynolds number applications.

Doctor of Philosophy / Department of Physics / Vinod Kumarappan / In general, molecules in the gas phase are free to rotate, and measurements made on such samples are averaged over a randomly oriented distribution of molecules. Any orientation dependent information is lost in such measurements. The goal of the work presented here is to a) mitigate or completely do away with orientational averaging, and b) make fully resolved orientation dependent measurements. In pursuance of similar goals, over the past 50 years chemists and physicists have developed techniques to align molecules, or to measure their orientation and tag other quantities of interest with the orientation. We focus on laser induced alignment of asymmetric top molecules. The first major contribution of our work is the development of an effective method to align all molecular axes under field-free conditions. The method employs a sequence of nonresonant, impulsive laser pulses with varied ellipticities. The efficacy of the method is first demonstrated by solution of the time dependent Schr\"{o}dinger equation for iodobenzene, and then experimentally implemented to three dimensionally align 3,5 difluoroiodobenzene. Measurement from molecules aligned in this manner greatly reduces orientational averaging. The technique was developed via a thorough understanding and extensive computations of the dynamics of rotationally excited asymmetric top molecules. The second, and perhaps more important, contribution of our work is the development of a new measurement technique to extract the complete orientation dependence of a variety of molecular processes initiated by ultrashort laser pulses. The technique involves pump-probe measurements of the process of interest from a rotational wavepacket generated by impulsive excitation of asymmetric top molecules. We apply it to make the first measurement of the single ionization probability of an asymmetric top molecule in a strong field as a function of all relevant alignment angles. The measurement and associated calculations help identify the orbital from which the electron is ionized. We expect that this technique will be widely applicable to ultrafast-laser driven processes in molecules and provide unique insight into molecular physics and chemistry.

<p>Resonant states are multiply excited states in atoms and ions that have enough energy to decay by emitting an electron. The ability to emit an electron and the strong electron correlation (which is extra strong in negative ions) makes these states both interesting and challenging from a theoretical point of view. The main contribution in this thesis is a method, which combines the use of <i>B </i>splines and complex rotation, to solve the three-electron Schrödinger equation treating all three electrons equally. It is used to calculate doubly excited and triply excited states of ⁴<i>S</i> symmetry with even parity in He^-. For the doubly excited states there are experimental and theoretical data to compare with. For the triply excited states there is only theoretical data available and only for one of the resonances. The agreement is in general good. For the triply excited state there is a significant and interesting difference in the width between our calculation and another method. A cause for this deviation is suggested. The method is also used to find a resonant state of ⁴<i>S</i> symmetry with odd parity in H^2-. This state, in this extremely negative system, has been predicted by two earlier calculations but is highly controversial.</p><p>Several other studies presented here focus on two-electron systems. In one, the effect of the splitting of the degenerate H(<i>n=</i>2) thresholds in H^-, on the resonant states converging to this threshold, is studied. If a completely degenerate threshold is assumed an infinite series of states is expected to converge to the threshold. Here states of ¹<i>P</i> symmetry and odd parity are examined, and it is found that the relativistic and radiative splitting of the threshold causes the series to end after only three resonant states. Since the independent particle model completely fails for doubly excited states, several schemes of alternative quantum numbers have been suggested. We investigate the so called DESB (Doubly Excited Symmetry Basis) quantum numbers in several calculations. For the doubly excited states of He^-mentioned above we investigate one resonance and find that it cannot be assigned DESB quantum numbers unambiguously. We also investigate these quantum numbers for states of ¹<i>S </i>even parity in He. We find two types of mixing of DESB states in the doubly excited states calculated. We also show that the amount of mixing of DESB quantum numbers can be inferred from the value of the cosine of the inter-electronic angle. In a study on Li^-the calculated cosine values are used to identify doubly excited states measured in a photodetachment experiment. In particular a resonant state that violates a propensity rule is found.</p>

Neste trabalho elaboramos estudos teóricos sobre colisões frias mediadas por fótons em armadilhas magnéto-ópticas. Para isto implementamos algorítimos numéricos de alto desempenho para o cálculo das formas de linha do espectro de fotoassociação do 88Sr. O principal algorítimo utilizado foi o de Numerov renormalizado. Também foram implementados sistemas de construção dos elementos da matriz hamiltoniana para estudos de colisões atômicas levando em consideração a estrutura fina dos potenciais de interação. Por último introduzimos o método de Monte Carlo de Integrais sobre Trajetórias como ferramenta para o estudo da termodinâmica do condensado de Bose-Einstein em armadilhas 2D considerando a interação entre os átomos / In this work we present theoretical studies of cold collisions mediated by photons in magneto-optical traps. We have implemented high-performance numerical algorithms to calculate the photoassociation spectral line shapes of 88Sr. We have mainly utilized the renormalized Numerov algorithm. We have also implemented schemes to write down the Hamiltonian matrix elements to study atomic collisions taking into account the fine structure of the interaction potentials. Finally, we have introduced the Path Integral Monte Carlo method as a tool for studying the thermodynamics of the Bose-Einstein condensate in two-dimensional traps, considering the binary atomic interactions

Neste trabalho resultados experimentais inéditos da taxas de perdas para o sistema Cs-K em função da intensidade do laser de aprisionamento foram obtidos. A análise dos resultados foi auxiliada pelo modelo tipo Gallagher-Pritchard que demonstrou possuir uma dependência muito forte com a velocidade de escape. Um estudo complementar ajudou na determinação dos mecanismos causadores de perdas, a catálise óptica, onde o principal resultado foi a obtenção de um resultado teórico que corresponde a observação experimental para o sistema Na-Rb, onde as perdas foram associadas a atuação do estado duplamente excitado. Compreender os mecanismos causadores de perdas pode ajudar na construção de armadilhas magneto-ópticas de grande eficiência, importantes em experimentos de medidas de propriedades atômicas. / We have investigated trap loss rate as a function of trap laser intensity for the Cs-K system. A model based on Gallagher-Pritchard type considerations, allow understand the obtained results. To correctly interpret the data, we have proposed new mechanisms, which can be proven with recent experiment in Na-Rb system.

As the genetic content is internally located within DNA duplexed form, it has long been hypothesized that DNA undergoes a series of thermally induced conformational changes that assist in protein recognition events. The biological mechanisms for protein-DNA interactions have long been sought after, as little is still known mechanistically about how these complexes form. To study the local contributions to these breathing modes several atomistic simulations of DNA oligonucleotides were generated and analyzed by statistical models to predict metastable conformational states, the system timescales, and the kinetic pathways between states. In order to sample time-series DNA constructs, microsecond molecular dynamics (MD) simulation were performed. MD simulations provide atomstic resolution of macromolecules in explicit solvent and with modern computational workflows can extend well into microsecond timescales. While MD is a powerful tool, it creates a tremendous amount of time-dependent data. In recent years, Markov State Models (MSM), which project the dynamics of MD simulations onto discrete coordinates that follow a Markov chain, have become an invaluable tool to model and describe the kinetics of these large datasets. These models can be coarse-grained for chemical insight, however there does not yet exist a method which consistently and ``crisply'' describe the metastable barriers. To address this, I developed a new method, called Gradient Adaptive Decomposition (GRAD), which optimizes the macrostate model by refining borders with respect to the gradient along the free energy surface. The proposed method requires only a small number of initial microstates because it corrects for errors produced by limited number of seeds. Whereas many methods rely on fuzzy, or overlapping, partitions for proper statstical analysis of timescales, GRAD retains accuracy and crisp decomposition. I present a workflow of GRAD refined MSM to analyze the long timescale MD simulations of DNA oligonucleotides to assess the stacking conformational dynamics of DNA. Evaluating the complex network of transitions accessible found evidence suggesting that chiral directed mechanisms are critical in how DNA bases unstack. I explore how these local effects may be significant to long timescale dynamics and the biological impact in relation to breathing fluctuations. This dissertation includes unpublished co-authored material.