We show that two-dimensional mechanical lattices can generically display topologically protected bulk zero-energy phonon modes at isolated points in the Brillouin zone, analogs of massless fermion modes of Weyl semimetals. We focus on deformed square lattices as the simplest Maxwell lattices, characterized by equal numbers of constraints and degrees of freedom, with this property. The Weyl points appear at the origin of the Brillouin zone along directions with vanishing sound speed and move away to the zone edge (or return to the origin) where they annihilate. Our results suggest a design strategy for topological metamaterials with bulk low-frequency acoustic modes and elastic instabilities at a particular, tunable finite wave vector. DOI: 10.1103/PhysRevLett.116.135503 The topological properties of the energy operator and associated functions in wave vector (momentum) space can determine important properties of physical systems [1][2][3]. In quantum condensed matter systems, topological invariants guarantee the existence and robustness of electronic states at free surfaces and domain walls in polyacetylene [4,5], quantum Hall systems [6,7], and topological insulators [8-13] whose bulk electronic spectra are fully gapped (i.e., conduction and valence bands separated by a gap at all wave numbers). More recently, topological phononic and photonic states have been identified in suitably engineered classical materials as well [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], provided that the band structure of the corresponding wavelike excitations has a nontrivial topology.A special class of topological mechanical states occurs in Maxwell lattices, periodic structures in which the number of constraints equals the number of degrees of freedom in each unit cell [34]. In these mechanical frames, zero-energy modes and states of self-stress (SSSs) are the analogs of particles and holes in electronic topological materials [16]. A zero-energy (frequency) mode is the linearization of a mechanism, a motion of the system in which no elastic components are stretched [19,20]. States of self-stress on the other hand guide the focusing of an applied stress and can be exploited to selectively pattern buckling or failure [18]. Such mechanical states can be topologically protected in Maxwell lattices, such as the distorted kagome lattices of Ref. [16], in which no zero modes exist in the bulk phonon spectra (except those required by translational invariance at wave vector k ¼ 0). These lattices are the analog of a fully gapped electronic material. They are characterized by a topological polarization equal to a lattice vector R T (which can be zero) that, along with a local polarization R L , determines the number of zero modes localized at free surfaces, interior domain walls separating different polarizations, and dislocations [17]. Because R T only changes upon closing the bulk phonon gap, these modes are robust against disorder or imperfections.In this Letter we demonstrate how to create topolo...

Abstract

Figure 1: Simulation of the ERK pathway within a simplified cell model (25 billion atoms, center). With our optimized visualization algorithm, it is possible to render this data set at 3.6 fps. Left: close-up view rendered with depth of field. Right: close-up view showing the cytoskeleton and signal proteins. For molecules near the camera, individual atoms are discernible. AbstractMolecular visualization is an important tool for analyzing the results of biochemical simulations. With modern GPU ray casting approaches it is only possible to render several million of atoms interactively unless advanced acceleration methods are employed. Whole-cell simulations consist of at least several billion atoms even for simplified cell models. However, many instances of only a few different proteins occur in the intracellular environment, which can be exploited to fit the data into the graphics memory. For each protein species, one model is stored and rendered once per instance. The proposed method exploits recent algorithmic advances for particle rendering and the repetitive nature of intracellular proteins to visualize dynamic results from mesoscopic simulations of cellular transport processes. We present two out-of-core optimizations for the interactive visualization of data sets composed of billions of atoms as well as details on the data preparation and the employed rendering techniques. Furthermore, we apply advanced shading methods to improve the image quality including methods to enhance depth and shape perception besides non-photorealistic rendering methods. We also show that the method can be used to render scenes that are composed of triangulated instances, not only implicit surfaces.

We present a novel application for the interactive exploration of cavities within proteins in dynamic data sets. Inside a protein, cavities can often be found close to the active center. Therefore, when analyzing a molecular dynamics simulation trajectory it is of great interest to find these cavities and determine if such a cavity opens up to the environment, making the binding site accessible to the surrounding substrate. Our user-driven approach enables expert users to select a certain cavity and track its evolution over time. The user is supported by different visualizations of the extracted cavity to facilitate the analysis. The boundary of the protein and its cavities is obtained by means of volume ray casting, where the volume is computed in real-time for each frame, therefore allowing the examination of time-dependent data sets. A fast, partial segmentation of the volume is applied to obtain the selected cavity and trace it over time. Domain experts found our method useful when they applied it exemplarily on two trajectories of lipases from Rhizomucor miehei and Candida antarctica. In both data sets cavities near the active center were easily identified and tracked over time until they reached the surface and formed an open substrate channel.

The complexity of today's visualization applications demands specific visualization systems tailored for the development of these applications. Frequently, such systems utilize levels of abstraction to improve the application development process, for instance by providing a data flow network editor. Unfortunately, these abstractions result in several issues, which need to be circumvented through an abstraction-centered system design. Often, a high level of abstraction hides low level details, which makes it difficult to directly access the underlying computing platform, which would be important to achieve an optimal performance. Therefore, we propose a layer structure developed for modern and sustainable visualization systems allowing developers to interact with all contained abstraction levels. We refer to this interaction capabilities as usage abstraction levels, since we target application developers with various levels of experience. We formulate the requirements for such a system, derive the desired architecture, and present how the concepts have been exemplary realized within the Inviwo visualization system. Furthermore, we address several specific challenges that arise during the realization of such a layered architecture, such as communication between different computing platforms, performance centered encapsulation, as well as layer-independent development by supporting cross layer documentation and debugging capabilities.