Different Degrees Of Freedom Research Articles

A high-order nonlinear limiter for discontinuous Galerkin method on parallel adaptive Cartesian grids

The discontinuous Galerkin (DG) method has been widely adopted due to its excellent properties. However, the problem of designing a class of high-order limiter that takes into account accuracy, compactness, efficiency, and robustness has long been an open question in simulating compressible flow with strong discontinuities. In this paper, a high-order multi-resolution weighted essentially non-oscillatory (MR-WENO) limiter is designed for the DG method on a parallel adaptive Cartesian grid, based directly on the weak solution to a polynomial obtained by the DG method. It can gradually be reduced to first-order accuracy in the vicinity of discontinuities while maintaining the excellent features of the DG method. Thus, it essentially has non-oscillatory characteristics in non-smooth regions with respect to the adaptive Cartesian grids. An improved shock detection technique is adopted as an indicator to identify troubled cells, which forms a high-order limiting procedure. A high-order MR-WENO limiter is used for both two- and three-dimensional cases to reconstruct different degrees of freedom on adaptive Cartesian grids. If the mesh is refined or coarsened, the details of the implementation algorithm are presented to determine how the hanging nodes are modulated and how the numerical solutions are redefined on such adaptive Cartesian grids. The parallelization of this method can be achieved by linking to the octree-based adaptive mesh refinement library called p4est. Finally, the low dissipation, shock capture ability, and load balancing of the high-order DG method with an MR-WENO limiter may enhance the resolutions of nearby strong discontinuities in adaptive Cartesian grids.

Action in Complexity: Entanglement and Emergent Order in Entrepreneurship

When properly understood in the context of entrepreneurship, entanglement explains the complex ingredients in the tangled relations required for entrepreneurial success. However, in examining entrepreneurial success, many scholars overlook a critical consideration—are the right resources (people and materials) in the right place at the right time? How do entanglement and convergence come about? This occurs when a microsystem is entangled with many fine-grained structures with different degrees of freedom, converging to generate emergence. These fine-grained structures are the heterogeneous agents with correlated histories (co-founders, financiers, suppliers, competitors, customers, employees, etc.) that are entangled with the entrepreneurs. This article explains the complex causes in the emergent order arising from several entangled dynamics among the heterogeneous agents and resources. The challenge is understanding what complex ingredients and combinations are necessary for a new emergent order that gives rise to such possibilities. Finally, such emergence arising from entanglement is discussed to explain collaboration and coevolution effects, and suggestions for future research that utilises the intended theorisations of practice are offered.

Temperature‐Dependent Anharmonic Phonons in Quantum Paraelectric KTaO3 by First Principles and Machine‐Learned Force Fields

AbstractUnderstanding collective phenomena in quantum materials from first principles is a promising route toward engineering materials properties and designing new functionalities. This work examines the quantum paraelectric state, an elusive state of matter characterized by the smooth saturation of the ferroelectric instability at low temperature due to quantum fluctuations associated with anharmonic phonon effects. The temperature‐dependent evolution of the soft ferroelectric phonon mode in the quantum paraelectric KTaO3 in the range 0–300 K is modeled by combining density functional theory (DFT) calculations with the stochastic self‐consistent harmonic approximation assisted by an on‐the‐fly machine‐learned force field. The calculated data show that including anharmonic terms is essential to stabilize the spurious imaginary ferroelectric phonon predicted by DFT in the harmonic approximation, in agreement with experiments. Augmenting the DFT workflow with machine‐learned force fields allows for efficient stochastic sampling of the configuration space using large supercells in a wide temperature range, inaccessible to conventional ab initio protocols. This work proposes a robust computational workflow capable of accounting for collective behaviors involving different degrees of freedom and occurring at large time/length scales, paving the way for precise modeling and control of quantum effects in materials.

Optimal cooling of multiple levitated particles: Theory of far-field wavefront shaping

The opportunity to manipulate small-scale objects pushes us to the limits of our understanding of physics. Particularly promising in this regard is the interdisciplinary field of levitation, in which light fields can be harnessed to isolate nano-particles from their environment by levitating them optically. When cooled down towards their motional quantum ground state, levitated systems offer the tantalizing prospect of displaying mesoscopic quantum properties. Currently restricted to single objects with simple shapes, the interest in levitation is currently moving towards the manipulation of more complex structures, such as those featuring multiple particles or different degrees of freedom. Unfortunately, current cooling techniques are mostly designed for single objects and thus cannot easily be multiplexed to address such coupled many-body systems. Here, we present an approach based on the spatial modulation of light in the far-field to cool down multiple nano-objects in parallel. Our procedure is based on the experimentally measurable scattering matrix and on its changes with time. We demonstrate how to compose from these ingredients a linear energy-shift operator, whose eigenstates are identified as the incoming wavefronts that implement the most efficient cooling of complex moving ensembles of levitated particles. Submitted in parallel with arxiv:2103.12592, this article provides a theoretical and numerical study of the expected cooling performance as well as of the robustness of the method against environmental parameters.

Deep‐Learning Assisted Polarization Holograms

AbstractMultiplexing holography with metasurfaces using different degrees of freedom of light has enabled recent applications in display and information processing. In terms of polarization‐multiplexed holograms, the most general form is an arbitrary Jones matrix profile in storing the maximum amount of information. It requires a relaxation to bianisotropic metasurfaces from a conventional single‐layer implementation of nanostructures, but it will also complicate both the inverse design of the nanostructures and the hologram generation algorithm. Here, an integrated neural network approach, being extended from the recent DeepCGH algorithm, is developed to obtain metasurface structural profiles directly from independent holograms from an arbitrary set of polarizations to another, with maximally four different co‐ and cross‐polarization conversion channels. Such an information‐driven approach enables designing complex polarization holograms directly from an existing metamaterial library without detailed physical knowledge on the constraints, and can be extended to other multiplexing holograms to further facilitate an efficient usage of the information stored on a metasurface.

Coarse Graining DNA: Symmetry, Nonlocal Elasticity, and Persistence Length

While the behavior of double-stranded DNA at mesoscopic scales is fairly well understood, less is known about its relation to the rich mechanical properties in the base-pair scale, which is crucial, for instance, to understand DNA-protein interactions and the nucleosome diffusion mechanism. Here, by employing the rigid base-pair model, we connect its microscopic parameters to the persistence length. Combined with all-atom molecular dynamic simulations, our scheme identifies relevant couplings between different degrees of freedom at each coarse-graining step. This allows us to clarify how the scale dependence of the elastic moduli is determined in a systematic way encompassing the role of previously unnoticed off-site couplings between deformations with different parity.

Entropy-enthalpy interplay in aluminum bound neurofilaments.

Considerable amount of work has been shown to understand the preferred chelation modes of metal-binding peptides using quantum mechanical calculations, resulting in a hierarchy of binding affinities. Previous work has shown an increasing stabilization energy for higher coordination complexes. However, as the coordination of a metal increases, the conformational space available for the polypeptide chain is inevitably reduced. Resolving the many entropic contributions from different degrees of freedom is particularly challenging. In this work, we explore this problem focusing on a family of phosphorylated neuropeptides that bind to aluminum. Determination of the configurational entropy is done using Maximum Information Spanning Tree (MIST) scheme implemented in the parallel software PARENT. We find that there is a general negative correlation between both stabilization energy and entropy, and that a subtle interplay determines the population of the most favorable species, rewarding a balance between both contributions. Additionally, we synthesize and discuss the requirements for a possible Metal Ion Hypothesis based on our findings.

Experimental and numerical assessments of new concrete dry connections concerning potentials of robotic CNC manufacturing technique

Coinciding with new manufacturing methods such as robotic additive manufacturing techniques and the gradual transition in construction approaches, new structural elements should be developed that, against the classic approaches, can easily be manufactured by new additive manufacturing techniques. Concrete Dry connections are one of these discussed elements. Appropriate geometries of dry concrete joints, manufactured by robotic CNC technique, accelerate the construction process by eliminating the necessity of formwork, scaffolding and concrete injection. Furthermore, desirable connections with higher interlocking and resistance in different degrees of freedom can be developed by facing the difficulties of traditional construction methods. Through some examples, this paper initially discussed the possibility of constructing dry concrete joints by robotic 3D-printing and robotic milling/sawing methods, and their geometrical accuracy was measured. In addition, 9 geometries of dry concrete joints were proposed and produced by formwork. Then, the performances of the proposed post-tensioned dry joints were discussed and compared to similar monolithic elements. On this basis, certain dry joints, entirely and easily manufactured by additive manufacturing technology (robotic concrete printing and CNC), could achieve up to 64% of the flexural capacity of a dimensional similar monolithic beam.

Effect of Motion Cues on Highway Driving Performance in Simulated Driving

The motion system is a major component of a driving simulator. It provides motion cues in various directions with different degrees of freedom (DOF). Different DOF could influence response variables widely used in highway design safety evaluation conducted in simulators. Few studies, though, have comprehensively explored the effect of driving simulator motion cues on driving performance. The high-fidelity Tongji University Driving Simulator (TUDS) was used to separately compare five dependent variables: speed, speed change, lane deviation, longitudinal acceleration, and lateral acceleration. The Wilcoxon signed-rank test was used to examine the difference for each variable using 8-DOF and fixed-base motion system configurations for nine types of combined highway alignments. A subjective assessment of participants’ driving experience was conducted, and the chi-square test for each term was used to compare the difference in motion system fidelity and adverse reactions between the two configurations. Results show that: (1) speed and lateral acceleration are more likely to be significantly affected by motion cues than speed change, lane deviation, and longitudinal acceleration; (2) the horizontal curve with up-grade is the type of combined alignment where speed and lateral acceleration are mostly affected; (3) characteristics of the five variables in different combined alignments vary between the two simulators; (4) the 8-DOF motion system provides better perceived motion fidelity than the fixed-base system does, and the 8-DOF simulator causes less discomfort and tiredness in simulator sickness; and (5) the presence of motion cues is suggested for highways with complex combined curves when focusing on speed and lateral acceleration.

Effects of Panel Misalignment in a Deployable Origami-Based Optical Array

Abstract Deployable origami-based arrays can offer many benefits for a wide variety of engineering applications. However, alignment in the deployed state is a primary challenge of these arrays; in optical systems, local (single panel) and global (entire array) misalignment can drastically reduce performance. The objective of this work is to compare the relative sensitivities of different degrees-of-freedom (DOFs) of misalignment in deployable origami-based optical arrays and specify which have the greatest effect on performance. To accomplish this, we suggest a practice for defining local and global misalignment in deployable origami-based arrays, we simulate misalignment perturbations and record the resulting power output, and we use compensation techniques to restore as much lost power as possible. We use a deployable LiDAR telescope based on the hexagonal twist origami pattern as a case study, though the conclusions could be extended to other origami-based systems. From simulation, we find that the DOFs which are the most sensitive to misalignment and for which compensation is not effective are the local decenter X (467% power loss per mm misalignment), local decenter Y (463% power loss per mm misalignment), local tilt (357% power loss per degree misalignment), and local tip (265% power loss per degree misalignment) misalignments. These results could help minimize the need for compensation or position sensing and help optical systems designers to know which DOFs should be carefully controlled to maximize energy output.

Design and Application of Jones Matrix Metasurface with Different Degrees of Freedom

Design and Application of Jones Matrix Metasurface with Different Degrees of Freedom

Influence of metal binding on the conformational landscape of neurofilament peptides.

In order to understand the preferred modes of chelation in metal-binding peptides, quantum mechanical calculations can be used to compute energies, resulting in a hierarchy of binding affinities. These calculations often produce increasing stabilization energies the higher the coordination of the complex. However, as the coordination of a metal increases, the conformational freedom of the polypeptide chain is inevitably reduced, resulting in an entropic penalty. Estimating the magnitude of this penalty from the many different degrees of freedom of biomolecular systems is very challenging, and as a result this contribution to the free energy is often ignored. Here we explore this problem focusing on a family of phosphorylated neuropeptides that bind to aluminum. We find that there is a general negative correlation between both stabilization energy and entropy. Our results suggest that a subtle interplay between enthalpic and entropic forces will determine the population of the most favourable species. Additionally, we discuss the requirements for a possible "Metal Ion Hypothesis" based on our findings.

Numerical investigation of wave interaction with two closely spaced floating boxes using particle method

This paper applies Improved Meshless Local Petrov-Galerkin method based on Rankine source function (IMLPG_R) to simulate two-dimensional wave interaction with two closely spaced floating boxes. The present study considers four different box configurations based on the degree of freedom, namely FF (both boxes fixed), HH (only heave allowed), RR (only roll allowed), and MM (both heave and roll allowed). The influences of the different degrees of freedom of the boxes on the wave elevation in the gap, and forces acting on the boxes, are investigated. Regular waves with a wave period ranging from 0.6s to 1.6s and two focused wave groups based on the JONSWAP spectrum with a peak frequency of 0.869Hz and 1.081Hz, respectively, are employed for the analysis. The piston mode resonance frequencies of different configurations were observed to vary slightly depending on the motion restrained. Compared to the FF configuration, the MM configuration showed a 28.3% increase in wave amplification in the gap. Some unique characteristics observed in the response amplitude operator (RAO) and flow patterns around the boxes are explained using instantaneous velocity and vorticity diagrams. The response of various configurations under a nonlinear transient-focused wave is also examined. The first-order and second-order time series of wave elevation in the gap is obtained by using the four-phase combination method.

Multidetection scheme for transient-grating-based spectroscopy.

Time-resolved optical spectroscopy represents an effective non-invasive approach to investigate the interplay of different degrees of freedom, which plays a key role in the development of novel functional materials. Here, we present magneto-acoustic data on Ni thin films on SiO2 as obtained by a versatile pump-probe setup that combines transient grating spectroscopy with time-resolved magnetic polarimetry. The possibility to easily switch from a pulsed to continuous wave probe allows probing of acoustic and magnetization dynamics on a broad time scale, in both transmission and reflection geometry.

Hourglass-shaped grafts are superior to conventional grafts for restoring knee stability and graft force at knee flexion angle of 30° following anterior cruciate ligament reconstruction: A finite element analysis.

Background: Anterior cruciate ligament reconstruction (ACLR) using a generally columnar graft is considered the gold standard for treating anterior cruciate ligament ruptures, but such grafts cannot replicate the geometry and mechanical properties of the native anterior cruciate ligament. Purpose: To evaluate the effectiveness of an innovative hourglass-shaped graft versus a traditional columnar graft for restoring joint stability and graft force, while avoiding notch impingement following anterior cruciate ligament reconstruction. Methods: Finite element models of a human knee were developed to simulate ① An intact state, ② anterior cruciate ligament reconstruction using columnar grafts with different diameters (7.5-12mm in 0.5mm increments), ③ anterior cruciate ligament reconstruction using columnar grafts with different Young's moduli (129.4, 168.0 and 362.2MPa) and ④ anterior cruciate ligament reconstruction using hourglass-shaped grafts with different Young's moduli. The knee model was flexed to 30° and loaded with an anterior tibial load of 103N, internal tibial moment of 7.5Nm, and valgus tibial moment of 6.9Nm. The risk of notch impingement, knee stability and graft forces were compared among the different groups. Results: This study found that columnar grafts could not simultaneously restore knee stability in different degree of freedoms (DOFs) and graft force to a level similar to that of the intact knee. The anterior tibial translation and graft force were restored to a near-normal condition when the internal tibial rotation was over-restrained and valgus tibial rotation was lax. A graft diameter of at least 10mm was needed to restore knee stability and graft force to physiological levels, but such large grafts were found to be at high risk of notch impingement. In contrast, the hourglass-shaped graft was able to simultaneously restore both knee stability and graft force at knee flexion of 30° while also having a much lower risk of impingement. Conclusion: Under knee flexion angle of 30°, an hourglass-shaped graft was better able to restore joint stability and graft force to a near-physiological level than columnar grafts, while also reducing the risk of notch impingement.

A Comprehensive Analysis of Ultraviolet Remote Sensing for Aerosol Layer Height Retrieval from Multi-Angle Polarization Satellite Measurements

Based on the optimal estimation (OE) theory and information content analysis method, we discuss the ability to include the multi-angle satellite ultraviolet polarization channel to retrieve the aerosol layer height (ALH) for ten typical aerosol types in the China region. We also quantitatively evaluate the effects of polarization measurements and the number of viewing angles on ALH retrieval under different conditions (aerosol model, aerosol optical depth, etc.). By comparing the different degree of freedom for signal (DFS) results of ALH caused by the theoretical retrieval error changes in different microphysical parameters in the aerosol and surface model, we identify the key factors affecting ALH retrieval. The results show that the extended ultraviolet band provides important information for ALH retrieval and is closely related to the scattering and absorption characteristics of aerosol models. The polarization measurements in fine mode reduce the posterior error of ALH retrieval by 6–39%; however, this is relatively small for coarse mode. In particular, when it is applied to the transported dust and background dust aerosol types, the posterior error is only reduced by 1–8% after adding polarization measurements. For these two aerosol types with weak absorption at the ultraviolet band, increasing the number of angles observed in addition to increasing the polarization channel will more effectively improve ALH inversion. Compared with other aerosol and surface model parameters, the retrieval errors for the total volume column, effective variance, real part of the complex refractive index, and surface reflectance are the main factors affecting ALH retrieval. Therefore, reducing the theoretical retrieval error of these parameters will be helpful.

Quantum-inspired protocol for measuring the degree of similarity between spatial shapes.

We put forward and demonstrate experimentally a quantum-inspired protocol that allows us to quantify the degree of similarity between two spatial shapes embedded in two optical beams without the need to measure the amplitude and phase across each beam. Instead the sought-after information can be retrieved by measuring the degree of polarization of the combined optical beam, a measurement that is much easier to implement experimentally. The protocol makes use of non-separable optical beams, whose main trait is that different degrees of freedom (polarization and spatial shape here) cannot be described independently. One important characteristic of the method described is that it allows us to compare two unknown spatial shapes.

Evidence for superadiabatic heating and cooling of Alfvénic solar wind

ABSTRACT Alfvénic fluctuations are widespread and crucial in various physical processes of space & astrophysical plasma. However, their role in heating and work done remains unexplored. Here, we have used Wind spacecraft’s data situated at 1 au distance to examine 12 distinct Alfvénic regions using polytropic analysis. The study finds an average polytropic index value α = 2.64, which is consistent with a superadiabatic behaviour for plasma particles with three effective degrees of freedom (f = 3). Moreover, this study examines several scenarios for plasma particles with different degrees of freedom. We noted that the investigated Alfvénic region could be adiabatic only for plasma particles with f = 1.26 degrees of freedom. In addition to this, for α = 2.64, the ratio of work done to the total heat supply within the system is $\frac{\delta w}{\delta q} = -0.68$, indicating that 68 per cent of the total supplied heat is utilized to accomplish work by the system on the surrounding (expansion phenomena), and the remaining is used to increase the internal energy of the system. As a result, we hypothesized that the Alfvénic plasma region is cooling more than the adiabatic expectation, resulting in supercooling phenomena. Thus, we propose that the discovered possible superadiabatic process would be critical in understanding the energy transfer from the Alfvénic zone to the surrounding plasma.

Quantifying 6D tumor motion and calculating PTV margins during liver stereotactic radiotherapy with fiducial tracking

Our study aims to estimate intra-fraction six-dimensional (6D) tumor motion with rotational correction and the related correlations between motions of different degrees of freedom (DoF), as well as quantify sufficient anisotropic clinical target volume (CTV) to planning target volume (PTV) margins during stereotactic body radiotherapy (SBRT) of liver cancer with fiducial tracking technique. A cohort of 12 patients who were implanted with 3 or 4 golden markers were included in this study, and 495 orthogonal kilovoltage (kV) pairs of images acquired during the first fraction were used to extract the spacial position of each golden marker. Translational and rotational motions of tumor were calculated based on the marker coordinates by using an iterative closest point (ICP) algorithm. Moreover, the Pearson product-moment correlation coefficients (r) were applied to quantify the correlations between motions with different degrees of freedom (DoFs). The population mean displacement ( ), systematic error (Σ) and random error (σ) were obtained to calculate PTV margins based on published recipes. The mean translational variability of tumors were 0.56, 1.24 and 3.38mm in the left-right (LR, X), anterior-posterior (AP, Y), and superior-inferior (SI, Z) directions, respectively. The average rotational angles θ X , θ Y and θ Z around the three coordinate axes were 0.88, 1.24 and 1.12, respectively. (|r|>0.4) was obtainted between Y -Z , Y - θ Z , Z -θ Z and θ X - θ Y . The PTV margins calculated based on 13 published recipes in X, Y, and Z directions were 1.08, 2.26 and 5.42mm, and the 95% confidence interval (CI) of them were (0.88,1.28), (1.99,2.53) and (4.78,6.05), respectively. The maximum translational motion was in SI direction, and the largest correlation coefficient of Y-Z was obtained. We recommend margins of 2, 3 and 7mm in LR, AP and SI directions, respectively.

Magnetoresistance relaxation steps originating from dynamic spin-orbital interactions in Ca3Ru2O7

The in-plane magnetoresistance and magnetostriction of ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ single crystals were investigated under pulsed magnetic field. Field-induced resistance steps and structural change were observed for specific field directions and far below the metal-to-insulator transition temperature ${T}_{\mathrm{MI}}=48$ K, which were not observed under static magnetic field. Especially, the resistance steps were only observed in the field-descending branch, indicating the relaxation properties, and no magnetization steps were observed. These results unveil the existence of instantaneous interactions among different degrees of freedom in ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, which are observable under pulsed magnetic field thanks to its fast field sweep rate. Based on the orbital states of ${\mathrm{Ca}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ and the Kugel-Khomskii model, we propose that the resistance steps and the structural change are related to a dynamic spin-orbital interaction, and this interaction can be strongly suppressed by the magnetocrystalline anisotropy.