Rigid Translation Research Articles

Quantitative mapping of renal oxygen consumption using pseudo-continuous arterial spin labeling and quantitative susceptibility mapping in humans.

To propose a new method for quantitatively mapping the renal metabolic rate of oxygen (RMRO2) and to evaluate the proposed method using a caffeine challenge. Pseudo-continuous arterial spin labeling (pCASL) and QSM sequences were used to obtain MR images in the kidney. Six healthy volunteers were scanned on caffeine and control days. The pCASL and QSM images were registered using DICOM information and rigid translation. The Fick principle was applied to estimate RMRO2. The results on caffeine and control days were compared to evaluate the capability of the proposed method to estimate renal oxygen consumption. A paired t-test was used to assess the statistical significance. Estimated renal blood flow (RBF), QSM, and RMRO2 maps were consistent with those reported in the literature. RMRO2 values were higher than the cerebral metabolic rate of oxygen (CMRO2) and were significantly reduced on the caffeine days compared to the control days, consistent with findings from non-MRI literature. The feasibility of measuring renal oxygen consumption using pCASL and QSM images was demonstrated. To the best of our knowledge, this work provides quantitative maps of renal oxygen consumption in humans for the first time. The results were consistent with the literature, including the statistically significant reduction in renal oxygen consumption with caffeine challenge. These findings suggest the potential utility of our technique in measuring renal oxygen consumption noninvasively, especially for patients with complications associated with contrast agents.

Utilizing Euler poles for the evaluation of plate rigidity in numerical mantle convection models

SUMMARY Evidence that the Earth’s surface is divided into a tessellation of piece-wise rigidly translating plates is the primary observation supporting the solid-state creep-enabled convection paradigm, utilized to investigate evolution of the Earth’s mantle. Accordingly, identifying the system properties that allow for obtaining dynamically generated plates remains a primary objective in numerical global mantle convection simulations. The first challenge for analysing fluid dynamic model output for the generation of rigid plates is to identify candidate plate boundaries. Here, we utilize a previously introduced numerical tool for plate boundary detection which uses a user specified threshold (tolerance) to automatically detect candidate plate boundaries. The numerical tool is applied with different sensitivities, to investigate the nature of the surface velocity fields generated in three calculations described in earlier work. The cases examined differ by the values that they specify for the model yield stress, a parameter that can allow the formation of tightly focussed bands of surface deformation. The three calculations we examine include zones comprising possible plate boundaries that are characterized by convergence, divergence and strike-slip behaviour. Importance of the potential plate boundaries is assessed by examining the rigidity of the inferred model generated plates. The rigidity is measured by comparing the model velocities to the rigid rotation velocities implied by the statistically determined Euler poles for each candidate plate. We quantify a lack in rigidity by calculating a deformity field based on disagreement of actual surface velocity with rotation about the Euler pole. For intermediate yield stress and boundary detection threshold value, we find that the majority of the model surface can translate almost rigidly about distinct plate Euler poles. Regions that conform poorly to large-scale region rigid translation are also obtained but we find that generally these regions can be decomposed into subsets of smaller plates with a lower tolerance value. Alternatively, these regions may represent diffuse boundary zones. To clarify the degree to which the mantle convection model behaviour shows analogues with Earth’s current-day surface motion, we apply the plate boundary detection and Euler pole calculation methods to previously published terrestrial strain-rate data. Strong parallels are found in the response of the terrestrial data and mantle convection calculations to the threshold value, such that appropriate choice of that parameter results in very good agreement between observations and convection model character. We conclude that plates generated by fluid dynamic convection models can exhibit motion that is markedly rigid, and define statistics (plateness) and fields (deformity) by which the generation of self-consistently determined plate rigidity can be quantified, as well as describing how plate recognition might be optimized. We also note that in agreement with the Earth’s current state, we obtain a dozen dominant plates in the case exhibiting the most plate-like (rigid) surface, suggesting that this approximate number of plates is perhaps intrinsic to the geometry, surface area and physical properties of Earth’s mantle.

Symmetries and covering maps for the minimal tension string on AdS3× S3× T4

This paper considers a recently-proposed string theory on AdS3 × S3 × T4 with one unit of NS-NS flux (k = 1). We discuss interpretations of the target space, including connections to twistor geometry and a more conventional spacetime interpretation via the Wakimoto representation. We propose an alternative perspective on the role of the Wakimoto formalism in the k = 1 string, for which no large radius limit is required by the inclusion of extra operator insertions in the path integral. This provides an exact Wakimoto description of the worldsheet CFT. We also discuss an additional local worldsheet symmetry, Q(z), that emerges when k = 1 and show that this symmetry plays an important role in the localisation of the path integral to a sum over covering maps. We demonstrate the emergence of a rigid worldsheet translation symmetry in the radial direction of the AdS3, for which again the presence of Q(z) is crucial. We conjecture that this radial symmetry plays a key role in understanding, in the case of the k = 1 string, the encoding of the bulk physics on the two-dimensional boundary.

A Pilot Study of Simulation-Free Hippocampal-Avoidance Whole Brain Radiation Therapy Using Diagnostic MRI-Based and Online Adaptive Planning

We aimed to demonstrate the clinical feasibility and safety of simulation-free hippocampal avoidance whole brain radiation therapy (HA-WBRT) in a pilot study (National Clinical Trial 05096286). Ten HA-WBRT candidates were enrolled for treatment on a commercially available computed tomography (CT)-guided linear accelerator with online adaptive capabilities. Planning structures were contoured on patient-specific diagnostic magnetic resonance imaging (MRI), which were registered to a CT of similar head shape, obtained from an atlas-based database (AB-CT). These patient-specific diagnostic MRI and AB-CT data sets were used for preplan calculation, using NRG-CC001 constraints. At first fraction, AB-CTs were used as primary data sets and deformed to patient-specific cone beam CTs (CBCT) to give patient-matched density information. Brain, ventricle, and brain stem contours were matched through rigid translation and rotation to the corresponding anatomy on CBCT. Lens, optic nerve, and brain contours were manually edited based on CBCT visualization. Preplans were then reoptimized through online adaptation to create final, simulation-free plans, which were used if they met all objectives. Workflow tasks were timed. In addition, patients underwent CT-simulation to create immobilization devices and for prospective dosimetric comparison of simulation-free and simulation-based plans. Median time from MRI importation to completion of "preplan" was 1 weekday (range, 1-4). Median on-table workflow duration was 41 minutes (range, 34-70). NRG-CC001 constraints were achieved by 90% of the simulation-free plans. One patient's simulation-free plan failed a planning target volume coverage objective (89% instead of 90% coverage); this was deemed acceptable for first-fraction delivery, with an offline replan used for subsequent fractions. Both simulation-free and simulation CT-based plans otherwise met constraints, without clinically meaningful differences. Simulation-free HA-WBRT using online adaptive radiation therapy is feasible, safe, and results in dosimetrically comparable treatment plans to simulation CT-based workflows while providing convenience and time savings for patients.

A target-free vision-based method for out-of-plane vibration measurement using projection speckle and camera self-calibration technology

In recent decades, computer vision-based methods have been introduced into engineering structures to provide full-field, non-contact vibration measurement. However, the vision-based vibration measurement method is challenging to measure the targetless structures. This paper proposed a target-free out-of-plane vibration measurement method using projection speckle and camera self-calibration technology. In this method, the camera extrinsic parameter estimation result based on the direct method is used as the initial value in the proposed method. Then, a nonlinear inequality constraint on the extrinsic parameters is established regarding the epipolar condition to minimize the reprojection error. Furthermore, the projection relationship between the projection speckle displacement and the actual displacement of the structure is studied so that the deviation of the out-of-plane vibration displacement is corrected. In the experimental verification, 3D reconstruction and rigid translation experiments are designed, respectively. The results show that the self-calibration accuracy of the binocular camera proposed in this paper is notably improved compared with the existing methods. At the same time, the deviation correction effect of the vibration displacement is significant. Finally, the typical flat plate structure and composite wing structure are taken as vibration measurement cases to demonstrate that the proposed approach is reliable and accurate in measuring the dynamic responses of engineering structures.

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables.

The typically rugged nature of molecular free-energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C45H92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

Elastic Stress Field beneath a Sticking Circular Contact under Tangential Load

Based on a potential theoretical approach, the subsurface stress field is calculated for an elastic half-space which is subject to normal and uniaxial tangential surface tractions that—in the case of elastic decoupling—correspond to rigid normal and tangential translations of a circular surface domain. The stress fields are obtained explicitly and in closed form as the imaginary parts of compact complex-valued expressions. The stress state in the surface and on the central axis are considered in detail. As, within specific approximations that have been discussed at length in the literature, any tangential contact problem with friction can be understood as a certain incremental series of such rigid translations, the solutions presented here can serve as the basis of very fast superposition algorithms for the analysis of subsurface stress fields in general tangential contact problems with friction. This idea is demonstrated by means of the frictional tangential contact between an elastic half-space and a rigid cylindrical flat punch with rounded corners.

A Pilot Study of Simulation-Free Hippocampal-Avoidance Whole Brain Radiotherapy Using Diagnostic MR-Based and Online Adaptive Planning

We aimed to demonstrate the clinical feasibility and safety of a simulation-free hippocampal avoidance whole brain radiotherapy (HA-WBRT) workflow in a Phase I clinical trial (NCT05096286). Feasibility was defined as successful completion of the simulation-free HA-WBRT workflow through treatment delivery in at last 70% of treated patients. Ten candidates for HA-WBRT were enrolled for treatment on a ring gantry CT-guided Linac with online adaptive capabilities. Structures were contoured on the diagnostic brain MRI, which was then registered to a separate head computed tomography (CT) of similar head shape, obtained from an atlas-based database. A HA-WBRT "pre-plan" was generated using the atlas-based CT (AB-CT) and the NRG-CC001 constraints. At first fraction, the AB-CT was used as the primary dataset and deformed to the patient's cone-beam CT (CBCT) for dose calculation. The brain, ventricles, and brainstem contours were matched through rigid translation and rotation to the corresponding anatomy on the CBCT to aid in alignment, given the differences in rotational head positioning from diagnostic MRI to CBCT setup. Lastly, the lens, optic nerves, and brain contours were manually edited based on CBCT visualization. Plans were then optimized, and the adaptive plan was chosen for treatment if the plan met all objectives. Workflow tasks were timed. In addition, conventional plans using patients' sim CTs were created for each patient for the purpose of prospective dosimetric comparison. The dosimetric parameters were compared for each patient between the delivered sim-free plan and the conventional sim CT plan using the sign test via statistical software, with p<.05 indicating significance. Median time from approved sim order to first fraction was 4 days (range: 2-7); median time in room (door-to-door) was 49 minutes (range: 35-70). All patients successfully completed all ten fractions and 90% of the simulation-free radiation plans met all NRG-CC001 constraints. For one patient, the sim-free plan at fraction one failed the planning target volume (PTV) coverage objective (coverage of 89%); this was deemed acceptable for delivery by the treating radiation oncologist. An offline replan was then performed to meet NRG-CC001 constraints and used for the subsequent nine fractions. There was no clinically meaningful difference in dosimetric constraints between the sim-free plan (calculated on AB-CT) and conventional CT sim plan. Statistically, the sim-free plans provided improved PTV coverage to higher doses compared to the conventional plans (Table). At a median follow-up of 43 days (range: 9 -280), the intracranial progression-free survival rate was 90%. Simulation-free HA-WBRT is feasible, results in plans that are dosimetrically comparable to conventional CT sim workflows and succeeds in decreasing time to initiation of HA-WBRT by at least 50%. Further studies with a larger cohort are warranted to optimize the workflow.

Evolving a mitigation of the stress response pathway to change the basic chemistry of life

Despite billions of years of evolution, there have been only minor changes in the number and types of proteinogenic amino acids and the standard genetic code with codon assignments across the three domains of life. The rigidity of the genetic code sets it apart from other aspects of organismal evolution, giving rise to key questions about its origins and the constraints it places on innovation in translation. Through adaptive laboratory evolution (ALE) in Escherichia coli, we aimed to replace tryptophan (Trp) in the genetic code with an analogue L-β-(thieno[3,2-b]pyrrolyl)alanine ([3,2]Tpa). This required Escherichia coli to recruit thienopyrrole instead of indole and allowed reassignment of UGG codons. Crossing the stress response system emerged as a major obstacle for ancestral growth in the presence of [3,2]Tp and Trp limitation. During ALE, a pivotal innovation was the deactivation of the master regulon RpoS, which allowed growth solely in the presence of [3,2]Tp in minimal medium. Notably, knocking out the rpoS gene in the ancestral strain also facilitated growth on [3,2]Tp. Our findings suggest that regulatory constraints, not just a rigid translation mechanism, guard Life’s canonical amino acid repertoire. This knowledge will not only facilitate the design of more effective synthetic amino acid incorporation systems but may also shed light on a general biological mechanism trapping organismal configurations in a status quo.

Asymptotic states for kink–meson scattering

The definition of a quantum state corresponding to a wave packet far from a global soliton is considered. We define an asymptotic quantum state corresponding to a localized wave packet of elementary quanta far from a kink. We demand that the state satisfies two properties. First, it must evolve in time via a rigid translation of the wave packet, up to the usual wave packet spreading and corrections which are exponentially suppressed in the distance to the kink. Second, the state must be invariant under a simultaneous translation of the kink and the wave packet. We explicitly construct the leading quantum corrections to an asymptotic state consisting of a meson approaching a kink. We expect this construction to readily generalize to elementary quanta in the presence of any global soliton.

SpikeShip: A method for fast, unsupervised discovery of high-dimensional neural spiking patterns.

Neural coding and memory formation depend on temporal spiking sequences that span high-dimensional neural ensembles. The unsupervised discovery and characterization of these spiking sequences requires a suitable dissimilarity measure to spiking patterns, which can then be used for clustering and decoding. Here, we present a new dissimilarity measure based on optimal transport theory called SpikeShip, which compares multi-neuron spiking patterns based on all the relative spike-timing relationships among neurons. SpikeShip computes the optimal transport cost to make all the relative spike-timing relationships (across neurons) identical between two spiking patterns. We show that this transport cost can be decomposed into a temporal rigid translation term, which captures global latency shifts, and a vector of neuron-specific transport flows, which reflect inter-neuronal spike timing differences. SpikeShip can be effectively computed for high-dimensional neuronal ensembles, has a low (linear) computational cost that has the same order as the spike count, and is sensitive to higher-order correlations. Furthermore, SpikeShip is binless, can handle any form of spike time distributions, is not affected by firing rate fluctuations, can detect patterns with a low signal-to-noise ratio, and can be effectively combined with a sliding window approach. We compare the advantages and differences between SpikeShip and other measures like SPIKE and Victor-Purpura distance. We applied SpikeShip to large-scale Neuropixel recordings during spontaneous activity and visual encoding. We show that high-dimensional spiking sequences detected via SpikeShip reliably distinguish between different natural images and different behavioral states. These spiking sequences carried complementary information to conventional firing rate codes. SpikeShip opens new avenues for studying neural coding and memory consolidation by rapid and unsupervised detection of temporal spiking patterns in high-dimensional neural ensembles.

Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing

One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix O(m) sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution O(n3) via fast Fourier transforms (FFTs) scales as in O(mn3logn) in time and O(mn3) in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).

PSPDNet: Part-aware shape and pose disentanglement neural network for 3D human animating meshes

Disentangled representations of shape and pose are essential for animating human body meshes in computer animation, computer games, and virtual reality applications. While recent deep neural networks have achieved impressive effectiveness, their performance in terms of interpretability, reconstruction precision, and fine-grained control is not satisfactory. To address these issues, we propose the Part-aware Shape and Pose Disentanglement neural network (PSPDNet), a framework for disentangling the shape and pose of 3D human meshes with the same connectivity. PSPDNet utilizes part mesh autoencoders to learn representations of different human body parts, enhancing the interpretability of the latent codes by corresponding them with local motions. While mesh autoencoders alone can decouple shape and pose information from animated meshes, they fail to control local motions. In addition, PSPDNet employs an additional rotation-translation module to remove global rigid motion, i.e., rotation and translation, from the sequence. Finally, we propose a novel loss function which includes disentanglement loss and alignment loss to train PSPDNet in an unsupervised manner. Our experiments show that PSPDNet greatly improves disentangled representation with strong interpretability, insensitivity to global rigid transformation, and locality of editing and controlling.

The energy–momentum complex in non-local gravity

In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here, we generalize the Einstein gravitational energy–momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator [Formula: see text] are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy–momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy–momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy–momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.

Upper bound solution of passive instability on the face of longitudinal inclined shallow buried shield tunnel based on rotation–translation mechanism

To better evaluate the passive failure mode of shallow shield tunnel faces in sandy soil strata, tunnel faces passive failure mode was investigated considering the longitudinal inclination in this study. A three-dimensional rotation–translation mechanism that simultaneously considers the longitudinal inclination of the tunnel and partial failure of the tunnel face based on the upper bound limit analysis method was presented. The mechanism comprised two rigid translation blocks and one rigid rotation block. Subsequently, the reliability of the proposed mechanism was verified using the horizontal rigid translation mechanism and numerical simulation considering the longitudinal inclination. Finally, the effects of tunnel longitudinal inclination (δ), cover depth ratio (C/D), soil internal friction angle (ϕ), and the possible presence of uniform surface surcharge (σS) on the limit support pressure of the tunnel face and the partial failure range was assessed. The results indicated that the partial failure range of the tunnel face gradually increased with δ When C/D<1. Conversely, global failure of the tunnel face occurred at different longitudinal inclinations when C/D≥1. The rotation angle (θ) of the rotational failure zone was sensitive to the longitudinal inclination (δ) and decreased with δ at the same coverage depth ratio.

Compensation for respiratory motion-induced signal loss and phase corruption in free-breathing self-navigated cine DENSE using deep learning.

To introduce a model that describes the effects of rigid translation due to respiratory motion in displacement encoding with stimulated echoes (DENSE) and to use the model to develop a deep convolutional neural network to aid in first-order respiratory motion compensation for self-navigated free-breathing cine DENSE of the heart. The motion model includes conventional position shifts of magnetization and further describes the phase shift of the stimulated echo due to breathing. These image-domain effects correspond to linear and constant phase errors, respectively, in k-space. The model was validated using phantom experiments and Bloch-equation simulations and was used along with the simulation of respiratory motion to generate synthetic images with phase-shift artifacts to train a U-Net, DENSE-RESP-NET, to perform motion correction. DENSE-RESP-NET-corrected self-navigated free-breathing DENSE was evaluated in human subjects through comparisons with signal averaging, uncorrected self-navigated free-breathing DENSE, and breath-hold DENSE. Phantom experiments and Bloch-equation simulations showed that breathing-induced constant phase errors in segmented DENSE leads to signal loss in magnitude images and phase corruption in phase images of the stimulated echo, and that these artifacts can be corrected using the known respiratory motion and the model. For self-navigated free-breathing DENSE where the respiratory motion is not known, DENSE-RESP-NET corrected the signal loss and phase-corruption artifacts and provided reliable strain measurements for systolic and diastolic parameters. DENSE-RESP-NET is an effective method to correct for breathing-associated constant phase errors. DENSE-RESP-NET used in concert with self-navigation methods provides reliable free-breathing DENSE myocardial strain measurement.

The gravitational energy-momentum pseudo-tensor in higher-order theories of gravity

The problem of non-localizability and the non-uniqueness of gravitational energy in general relativity has been considered by many authors. Several gravitational pseudo-tensor prescriptions have been proposed by physicists, such as Einstein, Tolman, Landau, Lifshitz, Papapetrou, Moller, andWeinberg. We examine here the energy-momentum complex in higher-order theories of gravity applying the Noether theorem for the invariance of gravitational action under rigid translations. This, in general, is not a tensor quantity because it is not a covariant object but only an affine tensor, that is, a pseudo-tensor. Therefore we propose a possible prescription of gravitational energy and momentum density for ?k gravity governed by the gravitational Lagrangian L1 = (R + a0R2 + Pp k=1 akR?kR) ??g and generally for n-order gravity described by the gravitational Lagrangian L = L (g??, g??,i1, 1??,i1i2, g??,i1i2i3 ,..., g??,i1i2i3...in). The extended pseudo-tensor reduces to the one introduced by Einstein in the limit of general relativity where corrections vanish. Then, we explicitly show a useful calculation, i.e., the power per unit solid angle ? emitted by a massive system and carried by a gravitational wave in the direction ? x for a fixed wave number k. We fix a suitable gauge, by means of the average value of the pseudo-tensor over a spacetime domain and we verify that the local pseudo-tensor conservation holds. The gravitational energy-momentum pseudo-tensor may be a useful tool to search for possible further gravitational modes beyond the two standard ones of general relativity. Their finding could be a possible observable signatures for alternative theories of gravity.

Many-body quantum chaos and space-time translational invariance

We study the consequences of having translational invariance in space and time in many-body quantum chaotic systems. We consider ensembles of random quantum circuits as minimal models of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor as a sum over many-body Feynman diagrams in the limit of large local Hilbert space dimension q. At sufficiently large t, diagrams corresponding to rigid translations dominate, reproducing the random matrix theory (RMT) behaviour. At finite t, we show that translational invariance introduces additional mechanisms via two novel Feynman diagrams which delay the emergence of RMT. Our analytics suggests the existence of exact scaling forms which describe the approach to RMT behavior in the scaling limit where both t and L are large while the ratio between L and LTh(t), the many-body Thouless length, is fixed. We numerically demonstrate, with simulations of two distinct circuit models, that the resulting scaling functions are universal in the scaling limit.

Microstates and defects of incoherent Σ3 [111] twin boundaries in aluminum

In the last few decades, it has been recognized that a single grain boundary (GB) may exist in several different stable and metastable states, which differ in their atomic structure. However, experimental insights at the atomic structure level are rarely reported. In this study, two different microstates of incoherent Σ3 [111] (112¯) GBs from two different orientation relationships (ORs) in an aluminum thin film grown on sapphire, comprised of slightly different structural units, are reported. The structural units in ORII exhibit hexagonal units while in ORI the hexagonal units are slightly distorted. Molecular statics simulations are utilised to understand the difference in excess properties of both states, which suggest that strain could potentially contribute to the stability of the ORII GB microstate over the ORI microstate. In addition, the atomic structure of the two ORs along the 〈110〉 zone axis reveal the rigid body microscopic translations of different magnitude of {111} planes across the GB experimentally. Furthermore, in the case of asymmetric variants of the same GBs, different types of Σ3 [111] disconnections with Burgers vectors (b1 = 1/6[1¯1¯2]), (b2 = 1/2[1¯01]) and varying step heights (h = 2adsc, 5adsc) are investigated and their implications on the GB mobility are discussed.

Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

An unambiguous definition of gravitational energy remains one of the unresolved issues of physics today. This problem is related to the non-localization of gravitational energy density. In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, Møller, and Weinberg. In this review, we firstly explored the energy–momentum complex in an nth order gravitational Lagrangian L=Lgμν,gμν,i1,gμν,i1i2,gμν,i1i2i3,⋯,gμν,i1i2i3⋯in and then in a gravitational Lagrangian as Lg=(R¯+a0R2+∑k=1pakR□kR)−g. Its gravitational part was obtained by invariance of gravitational action under infinitesimal rigid translations using Noether’s theorem. We also showed that this tensor, in general, is not a covariant object but only an affine object, that is, a pseudo-tensor. Therefore, the pseudo-tensor ταη becomes the one introduced by Einstein if we limit ourselves to General Relativity and its extended corrections have been explicitly indicated. The same method was used to derive the energy–momentum complex in fR gravity both in Palatini and metric approaches. Moreover, in the weak field approximation the pseudo-tensor ταη to lowest order in the metric perturbation h was calculated. As a practical application, the power per unit solid angle Ω emitted by a localized source carried by a gravitational wave in a direction x^ for a fixed wave number k under a suitable gauge was obtained, through the average value of the pseudo-tensor over a suitable spacetime domain and the local conservation of the pseudo-tensor. As a cosmological application, in a flat Friedmann–Lemaître–Robertson–Walker spacetime, the gravitational and matter energy density in f(R) gravity both in Palatini and metric formalism was proposed. The gravitational energy–momentum pseudo-tensor could be a useful tool to investigate further modes of gravitational radiation beyond two standard modes required by General Relativity and to deal with non-local theories of gravity involving □−k terms.