Shapes and singularities in triatic liquid crystal vesicles

Determining the equilibrium configuration and shape of curved two-dimensional films with (generalized) liquid crystalline (LC) order is a difficult infinite dimensional problem of direct relevance to the study of generalized polymersomes, soft matter and the fascinating problem of understanding the origin and formation of shape (morphogenesis). The symmetry of the free energy of the LC film being considered and the topology of the surface to be determined often requires that the equilibrium configuration possesses singular structures in the form of topological defects such as disclinations for nematic films. The precise number and type of defect plays a fundamental role in restricting the space of possible equilibrium shapes. Flexible closed vesicles with spherical topology and nematic or smectic order, for example, inevitably possess four elementary strength $+1/2$ disclination defects positioned at the four vertices of a tetrahedral shell. Here we address the problem of determining the equilibrium shape of flexible vesicles with generalized LC order. The order parameter in these cases is an element of $S^1/Z_p$, for any positive integer $p$. We will focus on the case $p =3$, known as triatic LCs. We construct the appropriate order parameter for triatics and find the associated free energy. We then describe the structure of the elementary defects of strength $+1/3$ in flat space. Finally, we prove that sufficiently floppy triatic vesicles with the topology of the 2-sphere equilibrate to octahedral shells with strength $+1/3$ defects at each of the six vertices, independently of scale.Comment: New results and new sections added, 4 new figures and updated abstrac

A bound on the free energy of tensionless membranes

Using the proof of Willmore's conjecure by Marques and Neves, we conjecture that the free energy of tensionless fluid membranes of arbitrary genus has an upper bound. This implies that the average genus of such a membrane, in equilibrium, is finite, regardless of external constraints.Comment: 4 pages, 1 figur

Enabling modeling framework with surrogate modeling capabilities and complex networks

Conceptual and physically based environmental simulation models as products of research environments efforts became complex software over time in order to allow describing the behaviour of natural phenomena more accurately. Results from these models are considered accurate but often require to operate an entire system of modeling resources with dedicated knowledge, an extensive set up, and sometimes significant computational time. Model complexity limits wide model adaptation among consultants because of lower available technical resources and capabilities. However, models should be ubiquitous to use in both research and consulting environments. This dissertation aims to address and alleviate two aspects of research model complexity: 1) for researchers, the model design complexity with respect to its internal software structure and 2) for consultants, the model application complexity with respect to data and parameter setup, runtime requirements, and proper model infrastructure setup. The first contribution provides modeling design and implementation support by managing interacting modeling solutions as “Directed Acyclic Graph”, while the second one helps to create surrogate models of complex physical models as a streamlined process. Both contributions are implemented within the OMS/CSIP modeling framework and infrastructure and were applied in various studies. First, a machine learning (ML)-based surrogate model approach is presented to respond to field application requirements to get quick but “accurate enough” model results with limited input and limited a-priori knowledge of the internal physical processes involved. The surrogate model aims to capture the behaviour of a physical model as an ensemble system of artificial neural networks (ANN). Here, the NeuroEvolution of Augmenting Topology (NEAT) technique has been leveraged because of its integration of a genetic approach to build and evolve its ANNs during supervised training. Throughout this phase, the thorough design of the services facilitate seamless monitoring of structural mutations of the artificial neural network and its performances with respect to behavioural emulation of the original model response. This results in a streamlined surrogate model generation. Furthermore, the stochasticity inherent to the evolutionary genetic algorithm combined with a specially designed cross-validation approach allows for straightforward use of the ensemble application. Several, slightly different artificial neural networks are concurrently trained. The ensemble system is built upon the selection of the utmost performant surrogate models and is used collectively to provide uncertainty quantified results when applied against new data. Secondly, a Directed Acyclic Graph (DAG) modeling structure NET3 was developed. NET3 provides appropriate data structures to represent modeling states interactions as relationships based on network topologies. The inherent structure of the DAG commands the execution of modeling tasks. NET3 implicitly manages the parallel computation depending on the network topology. A node of a NET3 modeling structure encapsulates any sort of modeling solution such as a system of ordinary differential equations, a set of statistical rules, or a system of partial differential equations. Each link connects these modeling solutions by handling their data flow. As a result, NET3 simplifies 1) the translation of physical mathematical concepts into model components, and 2) the management of complex interactions of modeling solutions. NET3 also pushes forward the idea of separating concerns between software architecture and scientific model codebase. It manages aspects that relate to the architectural design of the graph modeling structure and lets research scientist focus on their model’s domain. NET3 improves encapsulation and reusability of scientific/mathematical concepts. It avoids code duplication by allowing the same modeling solution to be adopted in different nodes and finely adapted to specific requirements. In summary, NET3 enables a new level of modeling flexibility by allowing to quickly change model representations to explore new modeling solutions. The two presented contributions were integrated into the Object Modeling System/Cloud Services Integrated Platform (OMS/CSIP) environmental modeling framework (EMF). EMFs are standard practice in environmental modeling because they represent a software solution of separating the burden of software architectural design management from scientific research. Here, OMS/CSIP has been identified “advanced” in terms of EMFs design. It offers high flexibility, low language invasiveness, fine and thorough architectural design, and innovative cloud computing deployment infrastructure. These aspects make OMS/CSIP infrastructure the suitable platform to host NEAT based surrogate modeling and NET3 extensions. Framework-enabled NEAT based Surrogate modeling (FeNS) results from the full integration of NEAT based surrogate modeling approach with OMS/CSIP platform. Here, the surrogate model approach was developed as CSIP services to help transitioning from research models to “field models” by enabling the modeling framework to interact with CSIP services, ML libraries, and a NoSQL database to emerge model surrogates for a(ny) modelling solution. OMS/CSIP was extended to harvest data from each model run and automatically derive the surrogate model at the modeling framework level. NET3 extends OMS modeling simulations to run as a graph network of interconnected modeling solutions. Furthermore, it enhances available OMS calibration algorithms to become multi-site calibration procedures. OMS already provided implicit parallel computation of independent components in a modeling solution. NET3 now adds a further layer of implicit parallelism by concurrently running independent modeling solutions. Two studies were carried out to develop and test FeSN while three applications supported the development and testing of NET3. Surrogate models of the Revised Universal Soil Loss Equation, Version 2 (R2) were generated to scale up from simple test cases with a constrained input space to more generic applications including a larger variety of input parameters. The main goal of the surrogate model was to streamline and simplify access to the R2 model behaviour. We performed sensitivity analysis of R2 to limit the input space to only relevant parameters (e.g. soil properties, climate parameter, field geometries, crop rotation description). The main study area was the State of Iowa starting from a single county (Clay county) ending up to four counties (Buena Vista, Cherokee, Clay, and Wright). Clustering methodologies were applied to improve surrogate model accuracy and to accelerate the training process by reducing the dataset size. The overall “goodness-of-fit” against the testing dataset estimated on the median of the uncertainty quantified result of the surrogate models ensemble was always above 0.95 Nash-Sutcliffe (NS), root mean squared error (RMSE) between 0.13 and 0.36, and bias between -0.07 and 0.02. In many cases, accuracy of the surrogate model with respect to testing dataset was above 0.98 NS. Surrogate models of the AgroEcoSystem (AgES) were generated to apply and test FeNS methodology to a semi-distributed hydrologic model. The main goal of the surrogate model was to streamline and simplify access to the AgES model behaviour. Only relevant lumped parameters on watershed centroid were used to train the surrogate models and limit the input space to only relevant parameters (e.g. precipitation, groundwater level, LAI, and potential evapotranspiration). The main study area was the South Fork Iowa River (SFIR) watershed in the State of Iowa across Wright, Franklin, Hamilton, and Hardin counties. The overall “goodness-of-fit” against the testing dataset estimated on the median of the uncertainty quantified result of the surrogate models ensemble was above 0.97 Nash-Sutcliffe (NS), root mean squared error (RMSE) of 2.24, and bias of -0.0794. With respect to NET3, the first application is the real-time modeling of flood forecasting through GEOframe system for the Civil Protection of Regione Basilicata implemented by PhD Bancheri. To scale the computation and finely tune calibration parameters, the Basilicata river basins were split into subcatchments where each was represented by a different NET3 node. The second application was part of Mr. Dalla Torre’s master thesis where the computational core of the rainfall-runoff model of Storm Water Management Model (SWMM by EPA) was componentized. NET3 now allows for reimplementing a concise and lightweight SWMM modeling core and highly parallel model runs. Software architectural design of rainfall-runoff, routing and sewer pipe design components targeted separation of concerns, single responsibility, and encapsulation principles. It resulted in clean and minimized code base. NET3 manages component connections and scalable computation by hosting rainfall-runoff modeling solution into separated nodes from routing and sewer pipe design modeling solution. It also enables each node of the modeling structure to 1) access a shared data structure to fetch input data from and push results to (SWMMobject), and 2) internally analyze the upstream subtree in order to adjust sewer pipe design parameters. The third test case is the application of a “system of systems” of urban models where each node of the graph modeling structure encapsulates a single responsibility system of models. Because of the stochasticity involved in each system of models, the entire graph modeling solution was required to run several times and generate independent realizations. Hence, NET3 was enabled to run a “graph of graphs” modeling structure

Topology and ground state degeneracy of tetrahedral smectic vesicles

Chemical design of block copolymers makes it possible to create polymer vesicles with tunable microscopic structure. Here we focus on a model of a vesicle made of smectic liquid-crystalline block copolymers at zero temperature. The vesicle assumes a faceted tetrahedral shape and the smectic layers arrange in a stack of parallel straight lines with topological defects localized at the vertices. We counted the number of allowed states at $T=0$. For any fixed shape, we found a two-dimensional countable degeneracy in the smectic pattern depending on the tilt angle between the smectic layers and the edge of the tetrahedral shell. For most values of the tilt angle, the smectic layers contain spiral topological defects. The system can spontaneously break chiral symmetry when the layers organize into spiral patterns, composed of a bound pair of $+1/2$ disclinations. Finally, we suggest possible applications of tetrahedral smectic vesicles in the context of functionalizing defects and the possible consequences of the spiral structures for the rigidity of the vesicle.Comment: New figure, extended description of the model in section 2, minor correction in the bibliograph

Multisensory Integration Design in Music for Cochlear Implant Users

Cochlear implant (CI) users experience several challenges when listening to music. However, their hearing abilities are greatly diverse and their musical experiences may significantly vary from each other. In this research, we investigate this diversity in CI users' musical experience, preferences, and practices. We integrate multisensory feedback into their listening experiences to support the perception of specific musical features and elements. Four installations are implemented, each exploring a different sensory modality assisting or supporting CI users' listening experience. We study these installations throughout semi-structured and exploratory workshops with participants. We report the results of our process-oriented assessment of CI users' experience with music. Because the CI community is a minority participant group in music, musical instrument design frameworks and practices vary from those of hearing cultures. We share guidelines for designing multisensory integration that derived from our studies with individual CI users and specifically aimed to enrich their experiences

The design, deployment, and testing of kriging models in GEOframe with SIK-0.9.8

This work presents a software package for the interpolation of climatological variables, such as temperature and precipitation, using kriging techniques. The purposes of the paper are (1) to present a geostatistical software that is easy to use and easy to plug in to a hydrological model; (2) to provide a practical example of an accurately designed software from the perspective of reproducible research; and (3) to demonstrate the goodness of the results of the software and so have a reliable alternative to other, more traditional tools. A total of 11 types of theoretical semivariograms and four types of kriging were implemented and gathered into Object Modeling System-compliant components. The package provides real-time optimization for semivariogram and kriging parameters. The software was tested using a year's worth of hourly temperature readings and a rain storm event (11 h) recorded in 2008 and retrieved from 97 meteorological stations in the Isarco River basin, Italy. For both the variables, good interpolation results were obtained and then compared to the results from the R package gstat

Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices

Periodic lattices in hyperbolic space are characterized by symmetries beyond Euclidean crystallographic groups, offering a new platform for classical and quantum waves, demonstrating great potentials for a new class of topological metamaterials. One important feature of hyperbolic lattices is that their translation group is nonabelian, permitting high-dimensional irreducible representations (irreps), in contrast to abelian translation groups in Euclidean lattices. Here we introduce a general framework to construct wave eigenstates of high-dimensional irreps of infinite hyperbolic lattices, thereby generalizing Bloch's theorem, and discuss its implications on unusual mode-counting and degeneracy, as well as bulk-edge correspondence in hyperbolic lattices. We apply this method to a mechanical hyperbolic lattice, and characterize its band structure and zero modes of high-dimensional irreps.Comment: 10 pages, 4 figure

Audio-Visual Attractors for Capturing Attention to the Screens When Walking in CAVE Systems

International audienceIn four-sided CAVE-like VR systems, the absence of the rear wall has been shown to decrease the level of immersion and can introduce breaks in presence. In this paper it is investigated to which extent user's attention can be driven by visual and auditory stimuli in a four-sided CAVE-like system. An experiment was conducted in order to analyze how user attention is diverted while physically walking in a virtual environment, when audio and/or visual attractors are present. The foursided CAVE used in the experiment allowed to walk up to 9m in straight line. An additional key feature in the experiment is the fact that auditory feedback was delivered through binaural audio rendering techniques via non-personalized head related transfer functions (HRTFs). The audio rendering was dependent on the user's head position and orientation, enabling localized sound rendering. The experiment analyzed how different "attractors" (audio and/or visual, static or dynamic) modify the user's attention. The results of the conducted experiment show that audio-visual attractors are the most efficient attractors in order to keep the user's attention toward the inside of the CAVE. The knowledge gathered in the experiment can provide guidelines to the design of virtual attractors in order to keep the attention of the user and avoid the "missing wall". Index Terms: Audi

Frustrated Self-Assembly of Non-Euclidean Crystals of Nanoparticles

Self-organized complex structures in nature, e.g. viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional (3D) complex structures with simple building blocks, and reach similar or higher level of sophistication in engineered materials? Here we present an analytic theory of tetrahedral nanoparticles (NPs) self-assembling in 3D space, where unavoidable geometrical frustration combined with competing attractive and repulsive inter-particle interactions lead to controllable, high-yield, and enantiopure self-assembly of helicoidal ribbons. This theory, based on crystal structures in non-Euclidean space, predicts morphologies that exhibit qualitative agreement with experimental observations. We expect that this theory will offer a general framework for the self-assembly of simple polyhedral building blocks into complex morphologies with new material capabilities such as tunable optical activity, essential for multiple emerging technologies.Comment: 30 pages, 9 figure