Nuts and bolts of supersymmetry

A topological mechanism is a zero elastic-energy deformation of a mechanical structure that is robust against smooth changes in system parameters. Here, we map the nonlinear elasticity of a paradigmatic class of topological mechanisms onto linear fermionic models using a supersymmetric field theory introduced by Witten and Olive. Heuristically, this approach consists of taking the square root of a non-linear Hamiltonian and generalizes the standard procedure of obtaining two copies of Dirac equation from the square root of the linear Klein Gordon equation. Our real space formalism goes beyond topological band theory by incorporating non-linearities and spatial inhomogeneities, such as domain walls, where topological states are typically localized. By viewing the two components of the real fermionic field as site and bond displacements respectively, we determine the relation between the supersymmetry transformations and the Bogomolny-Prasad-Sommerfield (BPS) bound saturated by the mechanism. We show that the mechanical constraint, which enforces a BPS saturated kink into the system, simultaneously precludes an anti-kink. This mechanism breaks the usual kink-antikink symmetry and can be viewed as a manifestation of the underlying supersymmetry being half-broken.Comment: 14 pages, 5 figure

Kink-antikink asymmetry and impurity interactions in topological mechanical chains

We study the dynamical response of a diatomic periodic chain of rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In the continuum description, we derive a nonlinear field theory which admits topological kinks and antikinks as nonlinear excitations but where a topological boundary term breaks the symmetry between the two and energetically favors the kink configuration. Using a cobweb plot, we develop a fixed-point analysis for the kink motion and demonstrate that kinks propagate without the Peierls-Nabarro potential energy barrier typically associated with lattice models. Using continuum elasticity theory, we trace the absence of the Peierls-Nabarro barrier for the kink motion to the topological boundary term which ensures that only the kink configuration, and not the antikink, costs zero potential energy. Further, we study the eigenmodes around the kink and antikink configurations using a tangent stiffness matrix approach appropriate for pre-stressed structures to explicitly show how the usual energy degeneracy between the two no longer holds. We show how the kink-antikink asymmetry also manifests in the way these nonlinear excitations interact with impurities introduced in the chain as disorder in the spring stiffness. Finally, we discuss the effect of impurities in the (bond) spring length and build prototypes based on simple linkages that verify our predictions.Comment: 20 pages, 21 figure

Brownian Dynamics Simulation of Dusty Plasma: Comparison with Generalized Hydrodynamics

Brownian dynamics (BD) simulation method has been widely used for studying problems in dispersed systems, such as polymer solutions, colloidal suspensions and more recently, complex (dusty) plasmas. The main problem addressed with this simulation technique is that of time scale separation, which occurs when one form of motion in the system is much faster than the other. This can be a serious problem in Molecular dynamics (MD) simulation where very short time steps are needed to handle the fast motions and thus, requiring very long time runs for the proper evolution of slower modes making the simulation very expensive. More importantly, the fast motions may not be of much interest within themselves, as will be the case in a dusty plasma. The motion of neutral atoms or molecules comprising the plasma occurs at a very fast time scale with respect to the motion of dust particles, and is usually of very little interest, though a large number of such neutrals are present. In such cases, an approximate method is usually adopted, whereby the neutral particles are omitted from the simulation and their effect upon the dynamics of dust particles modeled by a combination of random forces and frictional terms. This leads to a recasting of the Newton's Equation of motion solved in MD, to a Langevin equation, solved in BD. Adopting this approach, we simulate a system of charged dust particles interacting via Yukawa potential in a 2-Dimensional layer, and extract relevant equilibrium statistical features such as the radial distribution function, static structure factor and the low frequency dust wave modes. We then propose the use of a Generalized Hydrodynamical (GH) approach to provide a semi-analytical model for the dust collective modes, which not only provides us with good predictions of the wave dispersion but also provides reasonable estimates for wave-number dependent wave damping, both of which will be compared against the results obtained from BD simulation. Finally, through our simulations, we also observe the equilibrium configuration of dust particles in the presence of cold ions streaming perpendicularly into the 2-Dimensional layer of dust particles. This provides us with novel results in the regime of sub-sonic ion flow speeds

Nonlinear conduction via solitons in a topological mechanical insulator

Networks of rigid bars connected by joints, termed linkages, provide a minimal framework to design robotic arms and mechanical metamaterials built out of folding components. Here, we investigate a chain-like linkage that, according to linear elasticity, behaves like a topological mechanical insulator whose zero-energy modes are localized at the edge. Simple experiments we performed using prototypes of the chain vividly illustrate how the soft motion, initially localized at the edge, can in fact propagate unobstructed all the way to the opposite end. We demonstrate using real prototypes, simulations and analytical models that the chain is a mechanical conductor, whose carriers are nonlinear solitary waves, not captured within linear elasticity. Indeed, the linkage prototype can be regarded as the simplest example of a topological metamaterial whose protected mechanical excitations are solitons, moving domain walls between distinct topological mechanical phases. More practically, we have built a topologically protected mechanism that can perform basic tasks such as transporting a mechanical state from one location to another. Our work paves the way towards adopting the principle of topological robustness in the design of robots assembled from activated linkages as well as in the fabrication of complex molecular nanostructures.Comment: 9 pages, 9 figures, see http://lorentz.leidenuniv.nl/~chen/kinks for Supporting movies. v2: New section in appendix, new figure

Candoia: a platform for building and sharing mining software repositories tools as apps

We propose Candoia, a novel platform and ecosystem for building and sharing Mining Software Repositories (MSR) tools. Using Candoia, MSR tools are built as apps and Candoia ecosystem, acting as an appstore, allows effective sharing. Candoia platform provides, data extraction tools for curating custom datasets for user projects, and data abstractions for enabling uniform access to MSR artifacts from disparate sources, which makes apps portable and adoptable across diverse software project settings of MSR researchers and practitioners. The structured design of a Candoia app and the languages selected for building various components of a Candoia app promotes easy customization. To evaluate Candoia we have built over two dozen MSR apps for analyzing bugs, software evolution, project management aspects, and source code and programming practices showing the applicability of the platform for building a variety of MSR apps. For testing portability of apps across diverse project settings, we tested the apps using ten popular project repositories, such as Apache Tomcat, JUnit, Node.js, etc, and found that apps required no changes to be portable. We performed a user study to test customizability and we found that five of eight Candoia users found it very easy to customize an existing app. Candoia is available for download

Candoia: A Platform and an Ecosystem for Building and Deploying Versatile Mining Software Repositories Tools

Research on mining software repositories (MSR) has shown great promise during the last decade in solving many challenging software engineering problems. There exists, however, a ‘valley of death’ between these significant innovations in the MSR research and their deployment in practice. The significant cost of converting a prototype to software; need to provide support for a wide variety of tools and technologies e.g. CVS, SVN, Git, Bugzilla, Jira, Issues, etc, to improve applicability; and the high cost of customizing tools to practitioner-specific settings are some key hurdles in transition to practice. We describe Candoia, a platform and an ecosystem that is aimed at bridging this valley of death between innovations in MSR research and their deployment in practice. We have implemented Candoia and provide facilities to build and publish MSR ideas as Candoia apps. Our evaluation demonstrates that Candoia drastically reduces the cost of converting an idea to an app, thus reducing the barrier to transitioning research findings into practice. We also see versatility, in Candoia app’s ability to work with a variety of tools and technologies that the platform supports. Finally, we find that customizing Candoia app to fit project-specific needs is often well within the grasp of developers

Modeling electrolytically top gated graphene

We investigate doping of a single-layer graphene in the presence of electrolytic top gating. The interfacial phenomena is modeled using a modified Poisson-Boltzmann equation for an aqueous solution of simple salt. We demonstrate both the sensitivity of graphene's doping levels to the salt concentration and the importance of quantum capacitance that arises due to the smallness of the Debye screening length in the electrolyte.Comment: 7 pages, including 4 figures, submitted to Nanoscale Research Letters for a special issue related to the NGC 2009 conference (http://asdn.net/ngc2009/index.shtml

Nuts and bolts of supersymmetry

A topological mechanism is a zero-elastic-energy deformation of a mechanical structure that is robust against smooth changes in system parameters. Here, we map the nonlinear elasticity of a paradigmatic class of topological mechanisms onto a supersymmetric field theory introduced by Witten and Olive. Heuristically, this approach entails taking the square root of a nonlinear Hamiltonian. It generalizes the standard procedure of obtaining two copies of the Dirac equation by taking the square root of the linear Klein-Gordon equation. Our real-space formalism goes beyond topological band theory by incorporating nonlinearities and spatial inhomogeneities, such as domain walls (i.e., kinks), where topological states are typically localized. We interpret the two components of the real fermionic field as site and bond displacements, respectively. The constraint of zero elastic energy insures that kinks in the mechanical system saturate the Bogomolny-Prasad-Sommerfield bound, while forbidding antikinks. This mechanism can be viewed as a manifestation of the underlying supersymmetry being half broken

Candoia: a platform for building and sharing mining software repositories tools as apps

We propose Candoia, a novel platform and ecosystem for building and sharing Mining Software Repositories (MSR) tools. Using Candoia, MSR tools are built as apps and Candoia ecosystem, acting as an appstore, allows effective sharing. Candoia platform provides, data extraction tools for curating custom datasets for user projects, and data abstractions for enabling uniform access to MSR artifacts from disparate sources, which makes apps portable and adoptable across diverse software project settings of MSR researchers and practitioners. The structured design of a Candoia app and the languages selected for building various components of a Candoia app promotes easy customization. To evaluate Candoia we have built over two dozen MSR apps for analyzing bugs, software evolution, project management aspects, and source code and programming practices showing the applicability of the platform for building a variety of MSR apps. For testing portability of apps across diverse project settings, we tested the apps using ten popular project repositories, such as Apache Tomcat, JUnit, Node.js, etc, and found that apps required no changes to be portable. We performed a user study to test customizability and we found that five of eight Candoia users found it very easy to customize an existing app. Candoia is available for download.This article is published as Tiwari, Nitin M., Ganesha Upadhyaya, Hoan Anh Nguyen, and Hridesh Rajan. "Candoia: a platform for building and sharing mining software repositories tools as apps." In Proceedings of the 14th International Conference on Mining Software Repositories, pp. 53-63. IEEE Press, 2017. Posted with permission.</p