On Limits of Dense Packing of Equal Spheres in a Cube

We examine packing of $n$ congruent spheres in a cube when $n$ is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of $\lceil p^{3}/2\rceil$ spheres. For this family of packings, the previous best-known arrangements were usually derived from a ccp by omission of a certain number of spheres without changing the initial structure. In this paper, we show that better arrangements exist for all $n\leq\lceil p^{3}/2\rceil-2$. We introduce an optimization method to reveal improvements of these packings, and present many new improvements for $n\leq4629$

Persistent reshaping of cohesive sediment towards stable flocs by turbulence.

Cohesive sediment forms flocs of various sizes and structures in the natural turbulent environment. Understanding flocculation is critical in accurately predicting sediment transport and biogeochemical cycles. In addition to aggregation and breakup, turbulence also reshapes flocs toward more stable structures. An Eulerian-Lagrangian framework has been implemented to investigate the effect of turbulence on flocculation by capturing the time-evolution of individual flocs. We have identified two floc reshaping mechanisms, namely breakage-regrowth and restructuring by hydrodynamic drag. Surface erosion is found to be the primary breakup mechanism for strong flocs, while fragile flocs tend to split into fragments of similar sizes. Aggregation of flocs of sizes comparable to or greater than the Kolmogorov scale is modulated by turbulence with lower aggregation efficiency. Our findings highlight the limiting effects of turbulence on both floc size and structure

Mapping the microscale origins of magnetic resonance image contrast with subcellular diamond magnetometry

Magnetic resonance imaging (MRI) is a widely used biomedical imaging modality that derives much of its contrast from microscale magnetic field gradients in biological tissues. However, the connection between these sub-voxel field patterns and MRI contrast has not been studied experimentally. Here, we describe a new method to map subcellular magnetic fields in mammalian cells and tissues using nitrogen vacancy diamond magnetometry and connect these maps to voxel-scale MRI contrast, providing insights for in vivo imaging and contrast agent design

Computational virtual measurement for trees

National forest inventory (NFI) is a systematic sampling method to collect forest information, including tree parameters, site conditions, and auxiliary data. The sample plot measurement is the key work in NFI. However, compared to the techniques 100 years ago, measuring methods and data-processing (modeling) approaches for NFI sample plots have been improved to a minor extent. The limit was that the newly-developed methods introduced additional validation workflows and would increase the workload in NFI. That was due to that these methods were usually developed based on species-specific and site-specific strategies. In order to overcome these obstacles, the integration of the novel measuring instruments is in urgent need, e.g., light detection and ranging (LiDAR) and the corresponding data processing methods with NFI. Given these situations, this thesis proposed a novel computational virtual measurement (CVM) method for the determination of tree parameters without the need for validation. Primarily, CVM is a physical simulation method and works as a virtual measuring instrument. CVM measures raw data, e.g., LiDAR point clouds and tree models, by the simulation of the physical mechanism of measuring instruments and natural phenomena. Based on the theory of CVM, this thesis is a systematic description of how to develop virtual measuring instruments. The first work is to introduce the CVM theory. CVM is a conceptual and general methodology, which is different from a specific measurement of tree parameters. Then, the feasibility of CVM was tested using a conceptual implementation, i.e., virtual ruler. The development of virtual ruler demonstrated the two key differences between CVM and conventional modeling methods. Firstly, the research focus of CVM is to build an appropriate physical scenario instead of finding a mathematical relationship between modeling results and true values. Secondly, the CVM outputs can approach true values, whereas the modeling results could not. Consequently, in a virtual space, tree parameters are determined by a measuring process without mathematical predictions. Accordingly, the result is free of validation and can be regarded as true values, at least in virtual spaces. With the knowledge from the virtual ruler development, two exceptional implementations are further developed. They are the virtual water displacement (VWD) method and sunlight analysis method. Both of them employ the same CVM workflow, which is firstly measured in reality and secondly measured in virtual space. The VWD aims to virtually measure the point clouds using the simulation of water displacement methods in reality. There are two stages in this method. The first stage is to apply the simulation of water displacement using massive virtual water molecules (VWMs). Some empirical regressions have to be employed in this stage, due to the limitation of computer performance. In the second stage, a single (or few) VWM (or VWMs) is developed to remove those empirical processes in VWD. Finally, VWD can function as a fully automatic method to measure point clouds.The sunlight analysis method aims to virtually measure the tree models using the simulation of solar illumination during daylight. There are also two stages in this method. The first stage is to develop sunlight analysis for a single tree. The second stage is to analyze the interference from neighboring trees. The results include default tree attributes, which can be collected in the future NFI. The successful developments of CVM, along with implementations of VWD and sunlight analysis methods, prove the initial assumptions in this thesis. It is the conversion of mathematical processing of data into virtual measurements. Accordingly, this is a different philosophy, i.e., the role of data is extended to the digital representative of trees. It opens an avenue of data processing using a more natural approach and is expected to be employed in the near future as a standard measuring instrument, such as a diameter tape, in NFI.Die Nationale Waldinventur (NFI) ist eine systematische Stichprobenmethode zur Erfassung von Waldinformationen, einschließlich Baumparameter, Standortbedingungen und Hilfsdaten. Die Messung von Stichprobenparzellen ist die Schlüsselarbeit der NFI. Im Vergleich zu den Techniken vor 100 Jahren wurden die Messmethoden und Datenverarbeitungsansätze (Modellierung) für NFI-Stichprobenparzellen jedoch in geringem Umfang verbessert. Die Grenze lag darin, dass die neu entwickelten Methoden zusätzliche Validierungsabläufe einführten und den Arbeitsaufwand in der NFI erhöhen würden. Dies war darauf zurückzuführen, dass diese Methoden in der Regel auf der Grundlage art- und standortspezifischer Strategien entwickelt wurden. Um diese Hindernisse zu überwinden, ist die Integration der neuartigen Messinstrumente dringend erforderlich, z.B. Light Detection and Ranging (LiDAR) und die entsprechenden Datenverarbeitungsmethoden mit NFI. Vor diesem Hintergrund wird in dieser Arbeit ein neuartiges rechnergestütztes virtuelles Messverfahren (CVM) zur Bestimmung von Baumparametern ohne Validierungsbedarf vorgeschlagen. CVM ist in erster Linie eine physikalische Simulationsmethode und arbeitet als virtuelles Messinstrument. CVM misst Rohdaten, z.B. LiDAR-Punktwolken und Baummodelle, durch die Simulation des physikalischen Mechanismus von Messinstrumenten und Naturphänomenen. Basierend auf der Theorie des CVM ist diese Arbeit eine systematische Beschreibung, wie virtuelle Messinstrumente entwickelt werden können. Die erste Arbeit dient der Einführung in die Theorie des CVM. CVM ist eine konzeptuelle und allgemeine Methodik, die sich von einer spezifischen Messung von Baumparametern unterscheidet. Anschliessend wird die Durchführbarkeit des CVM anhand einer konzeptuellen Implementierung, d.h. eines virtuellen Lineals, getestet. Die Entwicklung des virtuellen Lineals zeigte die beiden Hauptunterschiede zwischen CVM und konventionellen Modellierungsmethoden auf. Erstens besteht der Forschungsschwerpunkt von CVM darin, ein geeignetes physisches Szenario zu erstellen, anstatt eine mathematische Beziehung zwischen Modellierungsergebnissen und wahren Werten zu finden. Zweitens können sich die Ergebnisse des CVM den wahren Werten annähern, während die Modellierungsergebnisse dies nicht konnten. Folglich werden in einem virtuellen Raum die Baumparameter durch einen Messprozess ohne mathematische Vorhersagen bestimmt. Dementsprechend ist das Ergebnis frei von Validierung und kann, zumindest in virtuellen Räumen, als wahre Werte betrachtet werden. Mit dem Wissen aus der Entwicklung des virtuellen Lineals werden zwei aussergewöhnliche Implementierungen weiterentwickelt. Es handelt sich um die Methode der virtuellen Wasserverdrängung (VWD) und die Methode der Sonnenlichtanalyse. Beide verwenden den gleichen CVM-Workflow, der erstens in der Realität und zweitens im virtuellen Raum gemessen wird. Das VWD zielt darauf ab, die Punktwolken virtuell zu messen, wobei die Simulation von Wasserverdrängungsmethoden in der Realität verwendet wird. Diese Methode besteht aus zwei Stufen. Die erste Stufe besteht in der Anwendung der Simulation der Wasserverdrängung unter Verwendung massiver virtueller Wassermoleküle (VWMs). Aufgrund der begrenzten Computerleistung müssen in dieser Phase einige empirische Regressionen angewandt werden. In der zweiten Stufe wird ein einzelnes (oder wenige) VWM (oder VWMs) entwickelt, um diese empirischen Prozesse im VWD zu entfernen. Schließlich kann VWD als vollautomatische Methode zur Messung von Punktwolken fungieren. Die Methode der Sonnenlichtanalyse zielt darauf ab, die Baummodelle virtuell zu messen, indem die Simulation der Sonneneinstrahlung bei Tageslicht verwendet wird. Auch bei dieser Methode gibt es zwei Stufen. In der ersten Stufe wird die Sonnenlichtanalyse für einen einzelnen Baum entwickelt. Die zweite Stufe ist die Analyse der Interferenz von benachbarten Bäumen. Die Ergebnisse umfassen Standard-Baumattribute, die in der zukünftigen NFI gesammelt werden können. Die erfolgreichen Entwicklungen von CVM, zusammen mit Implementierungen von VWD- und Sonnenlichtanalysemethoden, beweisen die anfänglichen Annahmen in dieser Arbeit. Es handelt sich um die Umsetzung der mathematischen Verarbeitung von Daten in virtuelle Messungen. Dementsprechend handelt es sich um eine andere Philosophie, d.h. die Rolle der Daten wird auf die digitale Darstellung von Bäumen ausgedehnt. Sie eröffnet einen Weg der Datenverarbeitung unter Verwendung eines natürlicheren Ansatzes und wird voraussichtlich in naher Zukunft als Standard-Messinstrument, wie z.B. ein Durchmesser-Band, in der NFI eingesetzt werden

Mechanistic Insights for Magnetic Imaging and Control of Cellular Function

The vast biomolecular toolkit for optical imaging and control of cellular function has revolutionized the study of in vitro samples and superficial tissues in living organisms but leaves deep tissue unexplored. To look deeper in tissue and observe system-level biological function in large organisms requires a modality that exploits a more penetrant form of energy than visible light. Magnetic imaging with MRI reveals the previously unseen, with endogenous tissue contrast and practically infinite penetration depth. While these clear advantages have made MRI a cornerstone of modern medical imaging, the sparse library of molecular agents for MRI have severely limited its utility for studies of cellular function in vivo. The development of new molecular agents for MRI has suffered from a lack of tools to study the connection between changes in the microscale cellular environment and the corresponding millimeter-scale MRI contrast. Bridging this gap requires revisiting the mechanistic underpinnings of MRI contrast, casting aside some of the simplifications that smooth over sub-voxel heterogeneity that is rich with information pertinent to the underlying cell state. Here, we will demonstrate theoretical, computational, and experimental connections between subtle changes in microscale cellular environment and resultant MRI contrast. After reviewing some foundational principles of MRI physics in the first chapter, the second chapter of the thesis will explore computational models that have significantly enhanced the development of genetically encoded agents for MRI, including the first genetically encoded contrast agent for diffusion weighted imaging. By improving the efficacy of these genetically encoded agents, we unlock MRI reporter genes for in vivo studies of cellular dynamics much in the same way that the engineering of Green Fluorescent Protein has dramatically improved in vitro studies of cellular function. In the third chapter, we introduce our study that maps microscale magnetic fields in cells and tissues and connects those magnetic fields to MRI contrast. Such a connection has previously been experimentally intractable due to the lack of methods to resolve small magnetic perturbations with microscale resolution. To overcome this challenge, we leverage nitrogen vacancy diamond magnetometry to optically probe magnetic fields in cells with sub-micron resolution and nanotesla sensitivity, together with iterative localization of field sources and Monte Carlo simulation of nuclear spins to predict the corresponding MRI contrast. We demonstrate the utility of this technology in an in vitro model of macrophage iron uptake and histological samples from a mouse model of hepatic iron overload. In addition, we show that this technique can follow dynamic changes in the magnetic field occurring during contrast agent endocytosis by living cells. This approach bridges a fundamental gap between an MRI voxel and its microscopic constituents and provides a new capability for noninvasive imaging of opaque tissues. In the fourth chapter, we focus on the use of magnetic fields to perturb, rather than image, biological function. Recent suggestions of nanoscale heat confinement on the surface of synthetic and biogenic magnetic nanoparticles during heating by radiofrequency alternating magnetic fields have generated intense interest due to the potential utility of this phenomenon in non-invasive control of biomolecular and cellular function. However, such confinement would represent a significant departure from classical heat transfer theory. We present an experimental investigation of nanoscale heat confinement on the surface of several types of iron oxide nanoparticles commonly used in biological research, using an all-optical method devoid of potential artifacts present in previous studies. By simultaneously measuring the fluorescence of distinct thermochromic dyes attached to the particle surface or dissolved in the surrounding fluid during radiofrequency magnetic stimulation, we found no measurable difference between the nanoparticle surface temperature and that of the surrounding fluid for three distinct nanoparticle types. Furthermore, the metalloprotein ferritin produced no temperature increase on the protein surface, nor in the surrounding fluid. Experiments mimicking the designs of previous studies revealed potential sources of artifacts. These findings inform the use of magnetic nanoparticle hyperthermia in engineered cellular and molecular systems and can help direct future resources towards tractable avenues of magnetic control of cellular function.</p

Imaging and Control of Engineered Cells using Magnetic Fields

Making cells magnetic is a long-standing goal of synthetic biology, aiming to enable the separation of cells from complex biological samples and their non-invasive visualization in vivo using Magnetic Resonance Imaging (MRI). Previous efforts towards this goal, focused on engineering cells to biomineralize superparamagnetic or ferromagnetic iron oxides, have largely been unsuccessful due to the stringent required chemical conditions. In this thesis, we introduce an alternative approach to making cells magnetic, focusing on biochemically maximizing cellular paramagnetism. Here, we show that a novel genetic construct combining the functions of ferroxidation and iron-chelation enables engineered bacteria to accumulate iron in 'ultraparamagnetic' macromolecular complexes, which subsequently allows for these cells to be trapped using strong magnetic field gradients and imaged using MRI in vitro and in vivo. We characterize the properties of these cells and complexes using magnetometry, an array of spectroscopic techniques, biochemical assays, and computational modeling to elucidate the unique mechanisms and implications of this 'ultraparamagnetic' concept. In addition to making cells magnetic, remote control of cellular localization in deep tissue is another long-standing goal of synthetic biology. Such an ability to non-invasively direct cells to sites of interest will not only improve therapeutic outcomes by minimizing off-target activity, but more broadly enable new research on complex cellular communities, such as the gut microbiome, in living animals. Given their deep penetrance through tissues, magnetic fields are ideally suited for facilitating non-invasive targeting of cells; however, the rapid decay of magnetic flux density from its source currently limits the depths to which magnetic targeting can be employed to within 1-2 mm from the surface. Here, we demonstrate a new approach wherein the retention of orally-administered and synthetically magnetized cell-like-particles is selectively enhanced within the murine intestinal tract to depths of up to 13 mm from the surface. Our cellular localization assisted by magnetic particles (CLAMP) strategy can potentially be generalized to any cell (bacterial, mammalian) or drug-containing nanoparticle of interest, and can be combined with existing non-invasive imaging modalities thereby facilitating remote environmental sensing at sites of interest. Finally, while magnetic fields in MRI scanners are widely used today to safely and non-invasively image anatomical structures in living animals, much of the image contrast in MRI is the result of microscale magnetic-field variations in tissues. However, the connection between these microscopic patterns and the appearance of macroscopic MR images has not been the subject of direct experimental studies due to a lack of methods to map microscopic fields in biological samples under ambient conditions. Here, we optically probed magnetic fields in mammalian cells and tissues with submicron resolution and nanotesla sensitivity using nitrogen-vacancy (NV) diamond magnetometry and combined these measurements with simulations of nuclear-spin precession to predict the corresponding MRI contrast. Additionally, we demonstrate the broad utility of this technology for imaging an in vitro model of cellular iron uptake, as well as imaging histological samples from a mouse model of hepatic iron overload. Taken together, our approach bridges a fundamental intellectual gap between a macroscopic MRI voxel and its microscopic constituents.</p

Heat and electron conduction in microporous catalyst layers of polymer electrolyte membrane fuel cells

Recent movement toward zero-emission mobility has propelled significant technological advancements in commercialization of polymer electrolyte membrane fuel cells (PEMFCs). PEMFCs provide electricity by reacting hydrogen with oxygen through two half-reactions occurring inside two respective anodic/cathodic microporous catalyst layers (CLs) with thicknesses of ~2-8 µm. Other products of the overall reaction include water and waste heat. All the electricity generation/consumption and most of the heat generation modes occur inside the CLs through a set of highly coupled multi-physics phenomena (a coupling between the electrochemical reactions, transport of species, electron conduction, and heat conduction). This necessitates knowing thermal and electronic conductivities of CLs for optimizing the fuel cell performance in various operating conditions. In this thesis, novel procedures are developed to measure thermal and electronic conductivities of CLs at low error rates. The procedures are based on novel methods to increase the amount of catalyst in the testbeds for enhancing the signal to noise ratio while ensuring complete deconvolution of the CL bulk signal. Further, a comprehensive platform is developed to characterize microstructure of CLs from different aspects, including a complete scheme for characterizing cracks for the first time. Separate measurements of in-plane and through-plane electronic conductivities, for the first time, uncovers anisotropic microstructure of CLs. CL designs with various compositions and structures are made and characterized. Observed trends in the conductivity data are linked to various structural properties of the CLs to understand structure-property correlations. A complete set of closed-form multi-scale structural models are developed for the conductivities in different directions to understand the underlying physics and provide tools for development of CLs with desired conductivities. The developed models agree well with the experimental data and precisely predict the structural trends. The models also explain and predict effects of different operating conditions. Using the developed tools, design guidelines are proposed for fabricating CLs with desired thermal and electronic conductivities, whose proof of concepts were made and successfully tested in the experimental phase of this research. Order of magnitude analyses show significant potentials for enhancing the fuel cell performance by tuning the conductivities through engineering the microstructure