When to Hold and When to Fold: Studies on the topology of origami and linkages

Linkages and mechanisms are pervasive in physics and engineering as models for avariety of structures and systems, from jamming to biomechanics. With the increasein physical realizations of discrete shape-changing materials, such as metamaterials,programmable materials, and self-actuating structures, an increased understandingof mechanisms and how they can be designed is crucial. At a basic level, linkagesor mechanisms can be understood to be rigid bars connected at pivots around whichthey can rotate freely. We will have a particular focus on origami-like materials, anextension to linkages with the added constraint of faces. Self-actuated versions typ-ically start flat and when exposed to an external stimulus - such as a temperaturechange or magnetic field - spontaneously fold. Since these structures fold all at once,and the number of folding patterns accessible to a given origami are exponential, theyare prone to folding to a configuration other than the desired one. Other work hassuggested methods for avoiding this misfolding, but it assumes ideal, rigid origami. Here, we expand on these models to account for the elasticity of real structures andintroduce methods for accounting for Gaussian curvature in them. We also explorehow to find and set an upper bound on minimal forcing sets, or the minimum set offolds required to force an origami, and present a graph theory algorithm for findingthem in arbitrary origami. Taken altogether, these origami studies give insight intohow the physical properties of origami influence folding and a new set of tools foravoiding misfolding. Next, we turn back to a more fundamental study of linkagesand present a new method for finding the manifold of their critical points. We thendemonstrate a design protocol that utilizes this manifold to create linkages with tun-able motions, before turning to several example structures, including the four-barlinkage and the Kane-Lubensky chain

Mechanologic: Designing Mechanical Devices that Compute

Despite their initial success and impact on the development of the modern computer, mechanical computers were quickly replaced once electronic computers became viable. Recently, there has been increased interest in designing devices that compute using modern and unconventional materials. In this dissertation, we investigate multiple ways to realize a mechanical device that can compute, with a main focus on designing mechanical equivalents for wires and transistors. For our first approach at designing mechanical wires, we present results on the propagation of signals in a soft mechanical wire composed of bistable elements. When we send a signal along bistable wires that do not support infinite signal propagation, we find that signals can propagate for a finite distance controlled by a penetration length for perturbations. We map out various parameters for this to occur, and present results from experiments on wires made of soft elastomers. Our second approach for designing mechanical devices that compute focuses on designing the topology of the configuration space of a linkage. By programming the configuration space through small perturbations of the bar lengths in the linkage, we are able to design a linkage that gates the propagation of a soliton in a Kane-Lubensky chain. This dissertation also includes other results related to the study of small length changes in linkages and an analysis of a version of a mechanical transistor compatible with the soft bistable wires

Extremal Reaches in Polynomial Time

Given a 3D polygonal chain with fixed edge lengths and fixed angles between consecutive edges (shortly, a revolutejointed chain or robot arm), the Extremal Reaches Problem asks for those configurations where the distance between the endpoints attains a global maximum or minimum value. In this paper, we solve it with a polynomial time algorithm. Copyright 2011 ACM

Extremal Reaches in Polynomial Time

Given a 3D polygonal chain with fixed edge lengths and fixed angles between consecutive edges (shortly, a revolutejointed chain or robot arm), the Extremal Reaches Problem asks for those configurations where the distance between the endpoints attains a global maximum or minimum value. In this paper, we solve it with a polynomial time algorithm. Copyright 2011 ACM

Biological Systems Workbook: Data modelling and simulations at molecular level

Nowadays, there are huge quantities of data surrounding the different fields of biology derived from experiments and theoretical simulations, where results are often stored in biological databases that are growing at a vertiginous rate every year. Therefore, there is an increasing research interest in the application of mathematical and physical models able to produce reliable predictions and explanations to understand and rationalize that information. All these investigations are helping to overcome biological questions pushing forward in the solution of problems faced by our society. In this Biological Systems Workbook, we aim to introduce the basic pieces allowing life to take place, from the 3D structural point of view. We will start learning how to look at the 3D structure of molecules from studying small organic molecules used as drugs. Meanwhile, we will learn some methods that help us to generate models of these structures. Then we will move to more complex natural organic molecules as lipid or carbohydrates, learning how to estimate and reproduce their dynamics. Later, we will revise the structure of more complex macromolecules as proteins or DNA. Along this process, we will refer to different computational tools and databases that will help us to search, analyze and model the different molecular systems studied in this course

Classical and reactive molecular dynamics: Principles and applications in combustion and energy systems

Molecular dynamics (MD) has evolved into a ubiquitous, versatile and powerful computational method for fundamental research in science branches such as biology, chemistry, biomedicine and physics over the past 60 years. Powered by rapidly advanced supercomputing technologies in recent decades, MD has entered the engineering domain as a first-principle predictive method for material properties, physicochemical processes, and even as a design tool. Such developments have far-reaching consequences, and are covered for the first time in the present paper, with a focus on MD for combustion and energy systems encompassing topics like gas/liquid/solid fuel oxidation, pyrolysis, catalytic combustion, heterogeneous combustion, electrochemistry, nanoparticle synthesis, heat transfer, phase change, and fluid mechanics. First, the theoretical framework of the MD methodology is described systemically, covering both classical and reactive MD. The emphasis is on the development of the reactive force field (ReaxFF) MD, which enables chemical reactions to be simulated within the MD framework, utilizing quantum chemistry calculations and/or experimental data for the force field training. Second, details of the numerical methods, boundary conditions, post-processing and computational costs of MD simulations are provided. This is followed by a critical review of selected applications of classical and reactive MD methods in combustion and energy systems. It is demonstrated that the ReaxFF MD has been successfully deployed to gain fundamental insights into pyrolysis and/or oxidation of gas/liquid/solid fuels, revealing detailed energy changes and chemical pathways. Moreover, the complex physico-chemical dynamic processes in catalytic reactions, soot formation, and flame synthesis of nanoparticles are made plainly visible from an atomistic perspective. Flow, heat transfer and phase change phenomena are also scrutinized by MD simulations. Unprecedented details of nanoscale processes such as droplet collision, fuel droplet evaporation, and CO2 capture and storage under subcritical and supercritical conditions are examined at the atomic level. Finally, the outlook for atomistic simulations of combustion and energy systems is discussed in the context of emerging computing platforms, machine learning and multiscale modelling

COMPUTATIONAL STUDIES TO UNDERSTAND THE ROLE OF ALLOSTERY IN COPPER REGULATION IN Mycobacterium tuberculosis AND IN THE DESIGN OF HPV VACCINES

Thesis (Ph.D.) - Indiana University, Chemistry, 2015Allostery is defined as the change in the structure, function or activity of a specific site on a protein, due to the binding of a substrate or effecter on a different site of the same protein. This phenomenon has been observed and studied in two different protein systems of therapeutic importance. CsoR protein in Mycobacterium tuberculosis adopts classical allostery to regulate the concentration of Cu(I) inside the cell. Cu(I) is speculated to bind in an unusual trigonal planar geometry with two cysteines and one histidine. When CsoR is bound to copper an overall structural change (allostery) is envisioned and its affinity to DNA is lost. In the current computational exploration we focus on the binding mode of Cu(I) and identify different protonation states of copper bound cysteines. MD simulations were performed on the apo and copper bound form with a starting structure from QM/MM calculations to predict the allosteric structural transition. The dynamic properties of the capsid of the human papillomavirus (HPV) type 16 were also examined using classical molecular dynamics simulations. The allostery identified in the components of the HPV is non-classical because the mean structure of the epitope carrying loops remains unchanged as the result of allosteric effect, but the structural fluctuations are altered significantly, which in turn changes the biochemical reactivity profile of the epitopes. Exploiting this novel insight, a new vaccine design strategy is proposed, where a relatively small virus fragment is deposited on a silica nanoparticle in such a way that the fluctuations of the h4 helix are suppressed. The structural and dynamic properties of the epitope carrying loops on this hybrid nanoparticle match the characteristics of epitopes found on the full virus like particle precisely, suggesting that these nanoparticles may serve as potent, cost-effective and safe alternatives to traditionally developed vaccines

Development of High Performance Molecular Dynamics with Application to Multimillion-Atom Biomass Simulations

An understanding of the recalcitrance of plant biomass is important for efficient economic production of biofuel. Lignins are hydrophobic, branched polymers and form a residual barrier to effective hydrolysis of lignocellulosic biomass. Understanding lignin\u27s structure, dynamics and its interaction and binding to cellulose will help with finding more efficient ways to reduce its contribution to the recalcitrance. Molecular dynamics (MD) using the GROMACS software is employed to study these properties in atomic detail. Studying complex, realistic models of pretreated plant cell walls, requires simulations significantly larger than was possible before. The most challenging part of such large simulations is the computation of the electrostatic interaction. As a solution, the reaction-field (RF) method has been shown to give accurate results for lignocellulose systems, as well as good computational efficiency on leadership class supercomputers. The particle-mesh Ewald method has been improved by implementing 2D decomposition and thread level parallelization for molecules not accurately modeled by RF. Other scaling limiting computational components, such as the load balancing and memory requirements, were identified and addressed to allow such large scale simulations for the first time. This work was done with the help of modern software engineering principles, including code-review, continuous integration, and integrated development environments. These methods were adapted to the special requirements for scientific codes. Multiple simulations of lignocellulose were performed. The simulation presented primarily, explains the temperature-dependent structure and dynamics of individual softwood lignin polymers in aqueous solution. With decreasing temperature, the lignins are found to transition from mobile, extended to glassy, compact states. The low-temperature collapse is thermodynamically driven by the increase of the translational entropy and density fluctuations of water molecules removed from the hydration shell

Enabling New Functionally Embedded Mechanical Systems Via Cutting, Folding, and 3D Printing

Traditional design tools and fabrication methods implicitly prevent mechanical engineers from encapsulating full functionalities such as mobility, transformation, sensing and actuation in the early design concept prototyping stage. Therefore, designers are forced to design, fabricate and assemble individual parts similar to conventional manufacturing, and iteratively create additional functionalities. This results in relatively high design iteration times and complex assembly strategies

Disordered proteins and network disorder in network descriptions of protein structure, dynamics and function. Hypotheses and a comprehensive review

During the last decade, network approaches became a powerful tool to describe protein structure and dynamics. Here we review the links between disordered proteins and the associated networks, and describe the consequences of local, mesoscopic and global network disorder on changes in protein structure and dynamics. We introduce a new classification of protein networks into ‘cumulus-type’, i.e., those similar to puffy (white) clouds, and ‘stratus-type’, i.e., those similar to flat, dense (dark) low-lying clouds, and relate these network types to protein disorder dynamics and to differences in energy transmission processes. In the first class, there is limited overlap between the modules, which implies higher rigidity of the individual units; there the conformational changes can be described by an ‘energy transfer’ mechanism. In the second class, the topology presents a compact structure with significant overlap between the modules; there the conformational changes can be described by ‘multi-trajectories’; that is, multiple highly populated pathways. We further propose that disordered protein regions evolved to help other protein segments reach ‘rarely visited’ but functionally-related states. We also show the role of disorder in ‘spatial games’ of amino acids; highlight the effects of intrinsically disordered proteins (IDPs) on cellular networks and list some possible studies linking protein disorder and protein structure networks