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At least 19 records

Geometric transformation and three-dimensional hopping of Hopf solitons

Arising in many branches of physics, Hopf solitons are three-dimensional particle-like field distortions with nontrivial topology described by the Hopf map. Despite their recent discovery in colloids and liquid crystals, the requirement of applied fields or confinement for stability impedes their utility in technological applications. Here we demonstrate stable Hopf solitons in a liquid crystal material without these requirements as a result of enhanced stability by tuning anisotropy of parameters that describe energetic costs of different gradient components in the molecular alignment field. Nevertheless, electric fields allow for inter-transformation of Hopf solitons between different geometric embodiments, as well as for their three-dimensional hopping-like dynamics in response to electric pulses. Numerical modelling reproduces both the equilibrium structure and topology-preserving out-of-equilibrium evolution of the soliton during switching and motions. Our findings may enable myriads of solitonic condensed matter phases and active matter systems, as well as their technological applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Acoustic cloaking: Geometric transform, homogenization and a genetic algorithm

A general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinates in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows cloaking to be performed. To approximate such complex metamaterials we apply results of the theory of homogenization and combine them with a genetic algorithm. To illustrate the power of our approach, we design three types of cloaks composed of isotropic concentric layers structured with three types of perforations: curved rectangles, split rings and crosses. These cloaks have parameters compatible with existing technology and they mimic the behavior of the transformed material. Numerical simulations have been performed to qualitatively and quantitatively study the cloaking efficiency of these metamaterials.

36 MATERIALS SCIENCE↗

Geometric Transformations Afforded by Rotational Freedom in Aramid Amphiphile Nanostructures

Molecular self-assembly in water leads to nanostructure geometries that can be tuned owing to the highly dynamic nature of amphiphiles. There is growing interest in strongly interacting amphiphiles with suppressed dynamics, as they exhibit ultrastability in extreme environments. However, such amphiphiles tend to assume a limited range of geometries upon self-assembly due to the specific spatial packing induced by their strong intermolecular interactions. To overcome this limitation while maintaining structural robustness, we incorporate rotational freedom into the aramid amphiphile molecular design by introducing a diacetylene moiety between two aramid units, resulting in diacetylene aramid amphiphiles (D-AAs). This design strategy enables rotations along the carbon–carbon sp hybridized bonds of an otherwise fixed aramid domain. We show that varying concentrations and equilibration temperatures of D-AA in water lead to self-assembly into four different nanoribbon geometries: short, extended, helical, and twisted nanoribbons, all while maintaining robust structure with thermodynamic stability. In conclusion, we use advanced microscopy, X-ray scattering, spectroscopic techniques, and two-dimensional (2D) NMR to understand the relationship between conformational freedom within strongly interacting amphiphiles and their self-assembly pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nickel‐Based Single‐Molecule Catalysts with Synergistic Geometric Transition and Magnetic Field‐Assisted Spin Selection Outperform RuO 2 for Oxygen Evolution

Overcoming slow kinetics and high overpotential in electrocatalytic oxygen evolution reaction (OER) requires innovative catalysts and approaches that transcend the scaling relationship between binding energies for intermediates and catalyst surfaces. Inorganic complexes provide unique, customizable geometries, which can help enhance their efficiencies. However, they are unstable and susceptible to chemical reaction under extreme pH conditions. Immobilizing complexes on substrates creates single‐molecule catalysts (SMCs) with functional similarities to single‐atom catalysts (SACs). Here, in this work, an efficient SMC, composed of dichloro(1,3‐bis(diphenylphosphino)propane) nickel [NiCl 2 dppp] anchored to a graphene acid (GA), is presented. This SMC surpasses ruthenium‐based OER benchmarks, exhibiting an ultra‐low onset and overpotential at 10 mAcm −2 when exposed to a static magnetic field. Comprehensive experimental and theoretical analyses imply that an interfacial charge transfer from the Ni center in NiCl 2 dppp to GA enhances the OER activity. Spectroscopic investigations reveal an in situ geometrical transformation of the complex and the formation of a paramagnetic Ni center, which under a magnetic field, enables spin‐selective electron transfer, resulting in enhanced OER performance. The results highlight the significance of in situ geometric transformations in SMCs and underline the potential of an external magnetic field to enhance OER performance at a single‐molecule level.

in situ geometrical changes↗

A Level Set Model for Structured Mesh Representation of Fibrous Preforms used in Composites Manufacturing

Here, a model for implicit representation of fibrous and woven preforms used for composites manufacturing is described. The method is based on a level set function defined on a structured mesh to implicitly capture the complex fiber and weave geometries. Since most software packages used to model woven preforms are based on unstructured mesh, a numerical model for transforming a discretized surface to a structured mesh representation and vice-a-versa is presented. Specific emphasis is on scalable computation of a level set function for large and complex 3D woven structures from a triangulated surface of the smallest unit (yarn). The model is applied to capture a periodic 3D layered 5-harness satin (5HS) weave geometry on a structured mesh. Geometric transformations needed to efficiently compute the level set function for the 3D structure on a high resolution mesh are described. Effects of mesh resolution on the geometric features such as number of resolved fibers, effective fiber size, and the surface area to volume ratio of the iso-surface are analyzed. Using the distance property of the level set function, an approach to evaluate the structure function resulting from transient evolving topology representing densification due to matrix phase depositions is also presented. The approach captures transition of the geometric characteristic from fiber governed at early stages of densification to yarn governed at the terminal stage.

36 MATERIALS SCIENCE↗

Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia

Visualizing molecular transformations in real-time requires a structural retrieval method with Ångström spatial and femtosecond temporal atomic resolution. Imaging of hydrogen-containing molecules additionally requires an imaging method sensitive to the atomic positions of hydrogen nuclei, with most methods possessing relatively low sensitivity to hydrogen scattering. Laser-induced electron diffraction (LIED) is a table-top technique that can image ultrafast structural changes of gas-phase polyatomic molecules with sub-Ångström and femtosecond spatiotemporal resolution together with relatively high sensitivity to hydrogen scattering. Here, we image the umbrella motion of an isolated ammonia molecule (NH3) following its strong-field ionization. Upon ionization of a neutral ammonia molecule, the ammonia cation (NH3+) undergoes an ultrafast geometrical transformation from a pyramidal (ΦHNH=107°) to planar (ΦHNH=120°) structure in approximately 8 femtoseconds. Using LIED, we retrieve a near-planar (ΦHNH=117 ± 5°) field-dressed NH3+ molecular structure 7.8−9.8 femtoseconds after ionization. Our measured field-dressed NH3+ structure is in excellent agreement with our calculated equilibrium field-dressed structure using quantum chemical ab initio calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analyticity and the Unruh effect: a study of local modular flow

The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of “weakly analytic” states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown — i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Three-dimensional electronic scaffolds for monitoring and regulation of multifunctional hybrid tissues

Recently, the integration of electronic elements with cellular scaffolds has brought forth the ability to monitor and control tissue function actively by using flexible free-standing two-dimensional (2D) systems. Capabilities for electrically probing complex, physicochemical and biological three-dimensional (3D) microenvironments demand, however, 3D electronic scaffolds with well-controlled geometries and functional-component distributions. This work presents the development of flexible 3D electronic scaffolds with precisely defined dimensions and microelectrode configurations formed using a process that relies on geometric transformation of 2D precursors by compressive buckling. It demonstrates a capability to fabricate these constructs in diverse 3D architectures and/or electrode distributions aimed at achieving an enhanced level of control and regulation of tissue function relatively to that of other approaches. In addition, this work presents the integration of these 3D electronic scaffolds within engineered 3D cardiac tissues, for monitoring of tissue function, controlling tissue contraction through electrical stimulation, and initiating on-demand, local release of drugs, each through well-defined volumetric spaces. These ideas provide opportunities in fields ranging from in vitro drug development to in vivo tissue repair and many others.

3D electronic scaffolds↗

Foundations for high-order, conservative cut-cell methods: Stable discretizations on degenerate meshes

Cut-cell methods for unsteady flow problems can greatly simplify the grid generation process and allow for high-fidelity simulations on complex geometries. However, cut-cell methods have been limited to low orders of accuracy. This is driven, largely, by the variety of procedures typically introduced to evaluate derivatives in a stable manner near the highly irregular embedded geometry. Here, a completely new approach, termed TEMO (truncation error matching and optimization), is taken to solve this problem. The approach is based on two simple and intuitive design principles. These principles directly allow for the construction of stable 8th To the best of the authors' knowledge, these are the highest orders ever achieved for a cut-cell discretization by a significant margin. This is done for both explicit and compact finite differences and is accomplished without any geometric transformations or artificial stabilization procedures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Longitudinal unzipping of 2D transition metal dichalcogenides

Unzipping of the basal plane offers a valuable pathway to uniquely control the material chemistry of 2D structures. Nonetheless, reliable unzipping has been reported only for graphene and phosphorene thus far. The single elemental nature of those materials allows a straightforward understanding of the chemical reaction and property modulation involved with such geometric transformations. Here we report spontaneous linear ordered unzipping of bi-elemental 2D MX 2 transition metal chalcogenides as a general route to synthesize 1D nanoribbon structures. The strained metallic phase (1T') of MX 2 undergoes highly specific longitudinal unzipping owing to the self-linearized oxygenation at chalcogenides. Stable dispersions of 1T' MoS 2 nanoribbons with widths of 10–120 nm and lengths up to ~4 µm are produced in water. Edge abundant 1T' MoS 2 nanoribbons reveal the hidden potential of idealized electrocatalysis for hydrogen evolution reactions at a competitive level with the precious Pt catalyst.

36 MATERIALS SCIENCE↗

Image processing tools for petabyte-scale light sheet microscopy data

Light sheet microscopy is a powerful technique for high-speed three-dimensional imaging of subcellular dynamics and large biological specimens. However, it often generates datasets ranging from hundreds of gigabytes to petabytes in size for a single experiment. Conventional computational tools process such images far slower than the time to acquire them and often fail outright due to memory limitations. To address these challenges, we present PetaKit5D, a scalable software solution for efficient petabyte-scale light sheet image processing. This software incorporates a suite of commonly used processing tools that are optimized for memory and performance. Notable advancements include rapid image readers and writers, fast and memory-efficient geometric transformations, high-performance Richardson–Lucy deconvolution and scalable Zarr-based stitching. These features outperform state-of-the-art methods by over one order of magnitude, enabling the processing of petabyte-scale image data at the full teravoxel rates of modern imaging cameras. The software opens new avenues for biological discoveries through large-scale imaging experiments.

97 MATHEMATICS AND COMPUTING↗

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMD is a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

high-performance computing↗

Monolithic mtesla-level magnetic induction by self-rolled-up membrane technology

Monolithic strong magnetic induction at the mtesla to tesla level provides essential functionalities to physical, chemical, and medical systems. Current design options are constrained by existing capabilities in three-dimensional (3D) structure construction, current handling, and magnetic material integration. We report here geometric transformation of large-area and relatively thick (~100 to 250 nm) 2D nanomembranes into multiturn 3D air-core microtubes by a vapor-phase self-rolled-up membrane (S-RuM) nanotechnology, combined with postrolling integration of ferrofluid magnetic materials by capillary force. Hundreds of S-RuM power inductors on sapphire are designed and tested, with maximum operating frequency exceeding 500 MHz. An inductance of 1.24 μH at 10 kHz has been achieved for a single microtube inductor, with corresponding areal and volumetric inductance densities of 3 μH/mm 2 and 23 μH/mm 3 , respectively. The simulated intensity of the magnetic induction reaches tens of mtesla in fabricated devices at 10 MHz.

42 ENGINEERING↗

Attribute-Guided Adversarial Training for Robustness to Natural Perturbations

We report while existing work in robust deep learning has focused on small pixel-level norm-based perturbations, this may not account for perturbations encountered in several real world settings. In many such cases although test data might not be available, broad specifications about the types of perturbations (such as an unknown degree of rotation) may be known. We consider a setup where robustness is expected over an unseen test domain that is not i.i.d. but deviates from the training domain. While this deviation may not be exactly known, its broad characterization is specified a priori, in terms of attributes. We propose an adversarial training approach which learns to generate new samples so as to maximize exposure of the classifier to the attributes-space, without having access to the data from the test domain. Our adversarial training solves a min-max optimization problem, with the inner maximization generating adversarial perturbations, and the outer minimization finding model parameters by optimizing the loss on adversarial perturbations generated from the inner maximization. We demonstrate the applicability of our approach on three types of naturally occurring perturbations --- object-related shifts, geometric transformations, and common image corruptions. Our approach enables deep neural networks to be robust against a wide range of naturally occurring perturbations. We demonstrate the usefulness of the proposed approach by showing the robustness gains of deep neural networks trained using our adversarial training on MNIST, CIFAR-10, and a new variant of the CLEVR dataset.

97 MATHEMATICS AND COMPUTING↗

An LES-based airborne Doppler lidar simulator and its application to wind profiling in inhomogeneous flow conditions

Wind profiling by Doppler lidar is common practice and highly useful in a wide range of applications. Airborne Doppler lidar can provide additional insights relative to ground-based systems by allowing for spatially distributed and targeted measurements. Providing a link between theory and measurement, a first large eddy simulation (LES)-based airborne Doppler lidar simulator (ADLS) has been developed. Simulated measurements are conducted based on LES wind fields, considering the coordinate and geometric transformations applicable to real-world measurements. The ADLS provides added value as the input truth used to create the measurements is known exactly, which is nearly impossible in real-world situations. Thus, valuable insight can be gained into measurement system characteristics as well as retrieval strategies. As an example application, airborne Doppler lidar wind profiling is investigated using the ADLS. For commonly used airborne velocity azimuth display (AVAD) techniques, flow homogeneity is assumed throughout the retrieval volume, a condition which is violated in turbulent boundary layer flow. Assuming an ideal measurement system, the ADLS allows to isolate and evaluate the error in wind profiling which occurs due to the violation of the flow homogeneity assumption. Overall, the ADLS demonstrates that wind profiling is possible in turbulent wind field conditions with reasonable errors (root mean squared error of 0.36 m s –1 for wind speed when using a commonly used system setup and retrieval strategy for the conditions investigated). Nevertheless, flow inhomogeneity, e.g., due to boundary layer turbulence, can cause an important contribution to wind profiling error and is non-negligible. Results suggest that airborne Doppler lidar wind profiling at low wind speeds (<5 m s –1 ) can be biased, if conducted in regions of inhomogeneous flow conditions.

17 WIND ENERGY↗

Geometric Event-Based Quantum Mechanics

In this work, we propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Geometrical control of topological charge transfer in Shakti-Cairo colloidal ice

Lattice transformations that preserve the system topology, but not its geometry, are common in condensed matter systems. However, how geometric constrains influence the topological properties of the lattices is still unclear. Here we show that a geometric transformation between two mixed coordination lattices, from Shakti to Cairo in an artificial colloidal ice, leads to a breakdown of the ice rule in all but one specific geometry. We observe a transfer of topological charge among sublattices which can be controlled in sign and intensity, vanishing at the ice-rule point. These unusual topological effects are absent in magnetic spin ices and they are due to collective, non-local geometric frustration in the particle ice. By merging numerical simulations, theory and experiments, we demonstrate how the charge transfer occurs in the Cairo geometry. The broader implication of our results is that we demonstrate how geometric constraints can control the topological properties of a mesoscopic colloidal system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗