Constant Space Research Articles

Hybrid surface wave propagation through the interface of semiconductor and metal waveguide

Hybrid surface wave propagation through the interface of semiconductor and metal waveguides consisting of CuO/Al and ZnO/Al have been investigated by numerical simulation due to their potential applications. COMSOL Multiphysics is used to simulate the waveguides by adjusting model properties. For the comparative study, the propagation constant (γ), normalized phase (β), attenuation constant (α), propagation length (L), total electric and magnetic energy propagated through the CuO-based Al waveguides and ZnO based Al waveguide is discussed. Comparative studies for both modifications were performed from 0 THz to 12 THz. This study employed boundary conditions to have the continuous behavior of the electric field component of hybrid surface waves (exhibits characteristics of both transverse waves and longitudinal waves) at the interface between metal and semiconductor. The ZnO-based modification shows a higher propagation constant (γ) at all frequencies. Similar trends are observed for propagation length (L) and propagation constant (γ). Meanwhile, the attenuation constant (α) of the CuO-based Al waveguide is higher than that of the ZnO-based Al waveguide. An identical trend was perceived for both electrical and magnetic energy. Maximum parameters favour the ZnO-based Al waveguide, which makes it superior to the CuO-based Al waveguide for high-frequency applications.

Combustion Characteristics of a Swirl-Radial-Injection Composite Fuel Grain with Applications in Hybrid Rockets

The combustion characteristics of a swirl-radial-injection composite fuel grain were experimentally and numerically investigated. This composite grain permits swirl-radial oxidizer injection based on three hollow helical blades, each having a constant hollow space allowing uniform oxidizer injection into the main chamber along the axial direction. The oxidizer enters from channel inlets located along a hollow outer wall. This wall, together with the three blades, is fabricated as one piece from acrylonitrile-butadiene-styrene using three-dimensional printing. Paraffin-based fuel is embedded in the spaces between adjacent blades. Firing tests were conducted with gaseous oxygen as the oxidizer, using oxidizer mass flow rates ranging from 7.45 to 30.68 g/s. Paraffin-based fuel grains using conventional fore-end injection were used for comparison. Regression rate boundaries were determined taking into account the erosion of the oxidizer channels. The data show that the regression rate was significantly increased even at the lower limit. Images of the combustion chamber flame and of the exhaust plume were also acquired. The flame was found to be concentrated in the main chamber and a smoky plume was observed, consistent with the high regression rate. A three-dimensional simulation was employed. The present design was found to improve fuel/oxidizer mixing and combustion efficiency compared with a fuel grain using fore-end injection. Both the experimental results and numerical simulations confirmed the potential of this swirl-radial-injection fuel grain.

Parametric Study on Stone Column for improving Seismic Response of Foundation

Nowadays, due to higher rate of construction activities, useful and effective lands are harder to find for construction purposes. So, the lands which are problematic are now used for construction purposes. The techniques used for improving these problematic lands are called ground improvement techniques. Among all the ground improvement techniques, stone columns are most effective and economical to improve the shear strength and bearing capacity of soil and thus, to reduce the settlement phenomenon. The main objective of the present study is to determine the total displacement of the soil foundation. For this purpose, parametric analysis was carried out to study the effect of two parameters namely stone column diameter and stone column spacing on the total displacement values. Finite element analysis was used to evaluate the displacement of soil strata reinforced with stone column using PlAXIS-2D software. The analysis was carried out for static load applied from top and Bhuj earthquake prescribed as dynamic loading. From present study, it was found that by decreasing the column spacing at a constant diameter of 1m, the maximum total displacement reduction was 36.73% and by increasing the column diameter at constant column spacing of 2m, the maximum total displacement reduction was 39.75%. Thus, it was concluded that by decreasing the column spacing at constant diameter and by increasing the column diameter at constant spacing respectively, there is a tremendous decrease in total displacement of the soil foundation which increases the load bearing capacity of the soils.

Stocking response of Eucalyptus growth depends on site water deficit across a 2100-km gradient in Brazil

Stocking in forests strongly influence stand growth by influencing resource capture, tree survival, and competition between trees and understory vegetation. Many studies have examined these patterns for specific locations and conditions, though with limited populations of inference. The influence of stocking was examined in the TECHS experimental platform, at 16 sites, with 18 clones, across a 2100 km geographic gradient. Stocking was examined by varying spacing within columns, with constant (3-m) spacing between rows. We examined how wood production and quality related to genotypes and environmental conditions, with stocking ranging from 480 to 3300 trees ha−1. Mean annual increment (Mg ha−1 yr−1) for the entire rotation increased with stocking, asymptoting above 1500 trees ha−1. Water-stressed sites had much lower responses to stocking levels than wetter sites. The three driest sites showed only a 25% increase in MAI (7 to 9 Mg ha−1 yr−1) with stocking increases from 480 to 3300 trees ha−1, whereas the 3 most productive sites increased by 50% (20 Mg ha−1 yr−1 to 30 Mg ha−1 yr−1). A similar result occurred for the clones, where the response to the change in stocking was higher in the more productive clones. From a qualitative point of view, tree breakage declined as stocking increased, going from 0% of broken trees in the highest stocking to a maximum of 3% with the stocking of around 480 trees ha−1. Injury to trees increased with stocking, going from about 4 to 9%. Mortality showed a similar pattern, increasing from 8 to 14% with increasing stocking. The percentage of intact (surviving, undamaged) trees at the lowest stocking was 83%, reaching a peak of 94% between 700 and 1100 trees ha−1, declining again to about 85% at the densest stocking. Survival rates declined when stocking exceeded 2900 trees ha−1 on wetter sites, compared with just 900 trees ha−1 on the driest sites. Overall, an increase in stocking from 480 trees ha−1 to 3300 trees ha−1 led to 50% increase in growth. To put this in perspective, the poorest 25% of sites averaged 59% less growth than the top 25%. The poorest 25% of genotypes grew 47% less than the best 25%. The interactions of effects, such as stocking by site, had effects that were of the same magnitude as these main effects. Management decisions about optimal stocking may be substantially improved by considering the main effects and especially their interactions.

DMPC-based string stable platoon control with robustness against communication delays

Communication delays are inevitable in vehicle platoons and may inhibit control performance. To address this issue, existing delay compensation strategies often resort to a greater time headway based on the delay upper bound, which compromises the benefits on traffic throughput. Moreover, it remains a major challenge to strictly ensure string stability with delays for distributed model predictive control (DMPC)-based controller. This paper presents a DMPC method for the cooperation of heterogeneous platoons subject to time-varying communication delays and greatly improves robustness against communication delays by improving the DMPC mechanism. A third-order heterogeneous vehicle dynamics model is integrated into the proposed method to improve control precision when implemented in the field. A synchronization mechanism is designed and the constant spacing policy is applied, which eliminates the delay dependence of the time headway selection and may thus improve traffic throughput. By incorporating a dual-mode scheme, a robustness constraint and a string stability constraint in the optimization problem, feasibility, closed-loop stability, and string stability are theoretically proved. A sufficient condition on the controller parameters is derived to guarantee closed-loop stability under communication delays. Numerical simulations are conducted to demonstrate the effectiveness of the proposed delay-compensating DMPC controller. The results reveal that the proposed controller outperforms the traditional DMPC controller and delay-involved linear controller on string stability, tracking performance and desired spacing selection.

Spatially random disorder in unitary fermion system in (4 − ϵ)-dimensions and effective action at finite temperature

Non-relativistic conformal field theory is significant to understand various aspects of an ultra-cold system. In this paper, we study a non-relativistic system of two-component fermions interacting with a complex boson with Yukawa-like interactions near d = 4-spatial dimensions in the presence of a quenched disorder. The homogeneous theory flows to an interacting fixed point describing a unitary fermion system. In the presence of the disorder, we find that the system has an interesting phase structure in the space of the coupling constants and exhibits an interacting disorder fixed point in ϵ-expansion. The correlation function obeys Lifshitz scaling behaviour at the disorder fixed point with the anisotropic exponent being z = 2 + γE. We also study the disorder system at finite temperature and compute the leading contribution to the 1PI effective action.

An investigation to improve the antifouling properties of the Sharklet topography using computation fluid dynamics

Abstract Biofouling is an undesirable phenomenon that occurs on the surface that is submerged underwater for a long time. With the adhesion of microorganisms, it will defect indsutrie especially the marine industry. By having biofouling on the submerged surface of vessels, it larger the drag force and friction that are experienced by the vessels while travelling and thus increase the cost on fuel consumption. To deal with this issue, mechanical approach and chemical approach were firstly developed which were then attempting significance success on decreasing the occurrence of biofouling. However, these approaches are not a sustainable solution. Hence, surface modification is then proposed and developed by the researchers to control the biofouling. Currently, Sharklet topography is one of the popular micro-structures antifouling technology. Few studies have presented successful results of Sharklet topography on the antifouling performance, but lack of research is relevant to the way on improving the antifouling properties of Sharklet topography. Thus, this project is mainly on modifying the Sharklet topography and make comparison with the initial design by studying the hydrodynamic characteristics around the surface through Computation Fluid Dynamics (CFD) analysis. To carry out this experiment, three-dimensional (3D) models for the non-patterned surface and Sharklet micro-structured surfaces will be created in different channels of flow but with similar settings. The data to be identified and compared from both models are flow velocity, shear strain rate and wall shear stress. From this study, it is observed that as varying the sizes of width between the effective range of microtopography sizes (64 μm – 264 μm) under constant height and spacing, the bigger the size of width, the better the performance of antifouling since the wall shear aspect appears the sharp fluctuation for the geometry with aspect ratio of 1.5 as compared 2.0 and 3.0. With the sharply fluctuating shear stress, it will be an unfavorable environment for the microorganisms to settle down.

Reflection loss-based roadway water depth measurement for driver safety

Flood fatalities generally occur in flood-prone areas such as low water bridges and tunnels, and most are vehiclerelated. The existing water depth measurement solutions are neither cost-efficient nor suitable for roadway scenarios. This paper proposes two water depth measurement methods that can be integrated into cellular networks. The proposed methods reuse the periodic communication signals of 5G and 6G to avoid allocating dedicated sensing signals and conflicting with the communication requirements. The main idea of these methods is based on the fact that the Reflection Loss (RL) induced by a water surface exhibits a strong dependence on the water depth. The peak counting method measures the water depth by counting the successive RL peaks separated by a constant spacing. The RL fingerprinting method integrates the RL peak positions and the measured RL values to determine the water depth. Several factors affecting the water depth measurement resolution are also analyzed. The simulation results show that the measurable water depth range of the proposed methods is larger than the water depth that may pose danger to vehicles, indicating that the proposed methods are feasible for roadway scenarios.

Numerical investigation on a floating self-reacting resonant wave energy converter

A self-reacting resonant C-shaped wave energy converter (SR-C-WEC) consisting of a pair of resonant sub-C-WECs connected by a rigid frame is proposed, which uses the two sub-C-WECs to provide mutual reaction force to solve the efficiency problem caused by floating WECs being hard to provide enough reaction force on WEC and uses the controllable resonant WEC to solve the efficiency problem caused by the temporal variability of waves. Resonant control and equivalent wave force control models are proposed to maximize the absorbed power. The effect of spacing between two sub-C-WECs, natural period, PTO damping and mooring stiffness to absorbed power is investigated. It is found that SR-C-WEC can achieve resonance at each wave condition and the power generation is maximum when the spacing is equal to half wavelength, which is comparable to the power generation when the frame is fixed. In a real sea condition, when the spacing is adjusted or not, the difference in average annual power is only 8.3%. Therefore, constant spacing can be used to simplify the structure and facilitate the application of SR-C-WEC. It is predicted that SR-C-WEC can reach 3638 effective power generation hours per year in real seas off China.

КОНЦЕПТУАЛІЗАЦІЯ ЛОКАЛЬНОГО ПРОСТОРУ КИЄВА В МОВІ ХУДОЖНЬОЇ ПРОЗИ ХХ СТОЛІТТЯ

The article examines the linguistic features of the conceptualization of the local space of the “Kyiv” mindset in the language of artistic prose by two outstanding Ukrainian writers of the 20th century. – V. Pidmohylnyi and P. Zahrebelnyi. Emphasis is placed on the fact that the local-spatial constant of the linguistic-cultural concept of the proper name “Kyiv”, reflected in the artistic discourses of artists, captures many urban and natural objects, which partially reflect the extremely complex topographical and coordinate grid of the real city. The system of urbanonyms, which represent the specifics of the individual and linguistic pictures of the world of novelists in terms of fixing the realities of the same city in different historical periods of its life, is studied. From the point of view of linguistic stylistics, a comparative analysis of expressive and figurative means of addressing the “Kyiv” mindset in the novel “The City” by V. Pidmohylnyi and in a number of historical novels and works about modernity by P. Zahrebelnyi was carried out. It is noted that the study of the verbalized constant of the local space of the city is an important issue not only for integrative linguistic stylistics, but also for cognitive linguistics, conceptology, linguistic and cultural studies, etc. The semantic-stylistic and logical-cognitive transformations of the internal forms of a number of proper names, which in P. Zahrebelnyi's artistic discourse have consistently evolved from an urbanonym to a concept have been traced. It was concluded that V. Pidmohylnyi, having “immersed” Stepan Radchenko, a rural man, in the urbanized space with its anthropogenic landscape, was one of the first Ukrainian writers of the beginning of the 20th century. conceptualized the city as a determining factor in the civilizational and historical development of society. In the artistic discourse of P. Zahrebelnyi, numerous linguistic units that nominate the real landscape of the city reflect the philosophy of the author's vision of Kyiv as a unique, originally Ukrainian city, as it appears in the national-linguistic picture of the world.

Apparent dark matter as a non-local manifestation of emergent gravity

We disclose a close correspondence between Verlinde’s Emergent Gravity (VEG) theory and the non-local gravity theories. Such non-local effects can play crucial role at small distances as well as in large scale structures. In particular, we argue that the emergent gravity effectively is a manifestation of the entanglement entropy and can modify Newton’s law of gravity as well as address the flat rotation curves of spiral galaxies. In the cosmological setup, we have considered three different models for the apparent dark matter density. In the first model, we have found that Friedmann equations get modified due to the presence of the apparent dark matter (DM) in such a way that Newton’s constant of gravity shifts as G→G1+ζ, where ζ is a dimensionless small parameter. Using the flat rotating curves we estimate ζ∼10−7. For such a model, we find out that by rescaling the radial coordinate, r, the curvature space constant, k, and the scale factor of the universe, a, the effect of apparent DM can change the geometry of the universe and can shift the curvature space constant as k⋆=k(1−ζ). To this end, we study a more realistic model with evolving densities where we obtain the ΛCDM model in Verlinde’s gravity and comment on the Hubble tension problem with evolving densities.

A Variable Switching Frequency Space Vector Pulse Width Modulation Control Strategy of Induction Motor Drive System With Torque Ripple Prediction

The constant switching frequency space vector pulse width modulation (CSFSVPWM) generates high-frequency harmonics with integer multiples of the switching frequency, making it fail to fully exploit the potential of pulse width modulation (PWM) technique. In this paper, a variable switching frequency space vector pulse width modulation technique with the function of torque ripple prediction is proposed for induction motor drive system, which could optimize the high-frequency harmonic current distribution and torque ripple. The mathematical correlation between inverter average voltage and instantaneous voltage under the space vector pulse width modulation (SVPWM) is first analyzed, followed by the analysis of current ripple in a switching cycle using the typical seven-segment SVPWM, thus the torque ripple of induction motor during this period can be predicted. The switching period is dynamically adjusted according to the magnitude of predicted torque ripple, and the average switching frequency is maintained to be the same with that of CSFSVPWM. The effectiveness of the proposed method in suppressing high-frequency current harmonics and torque ripple is fully verified by experimenting on a 2.2 kW induction motor drive system, and a comprehensive comparison with CSFSVPWM and random PWM modulation is implemented.

Intelligently Wireless Batteryless RF-Powered Reconfigurable Surface: Theory, Implementation & Limitations

This work exploits ultra-low cost, commodity, radio frequency identification (RFID) tags as elements of a reconfigurable intelligent surface (RIS). Such batteryless tags are powered and controlled by a software-defined radio reader, with properly modified software, so that a source-destination link is assisted, operating at a different band. Signal model includes small-scale and large-scale fading, direct link, as well as specific parameters relevant to reflection (i.e., backscatter) radio, such as antenna structural mode and reflection efficiency, typically overlooked in the literature. An algorithm is offered that computes the optimal RIS configuration with complexity of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> log <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> ) in number of elements <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> , instead of intractable exponential complexity of exhaustive search, while accommodating any number <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> ≥ 2 of loads. With the proposed algorithm, it is shown that performance gains reach a plateau for constant element spacing and increasing number of elements, suggesting that the weak, passive nature of backscattered links limits the performance gains, even with perfect channel estimation. Channel estimation with linear minimum mean squared error (LMMSE) estimator is shown to be effective, provided that there are sufficient number of pilot symbols. A concrete way is offered to design and prototype a wireless, batteryless, RF-powered, reconfigurable surface and a proof-of-concept is experimentally demonstrated.

NSF (Nylon Synthetic Fiber) Effectiveness in Stabilizing Weak Subgrade Soil: An Experimental Investigation

Improvement in subgrade soil has always been an area of concern for highway and geotechnical engineers. Weak subgrade soil results in a greater thickness of the pavement layer, which increases the cost of pavement construction. It further leads to large deformations, which in turn cause continuous deterioration of the paved surface. To solve this problem, various engineering solutions and soil improvement mechanisms were previously proposed. This study was designed to investigate the stabilization of weak subgrade soil with nylon synthetic fiber (NSF) in a compromising combination. Previously, some investigations used a lower fiber content with a higher fiber length, whereas others used a lower fiber length with a higher fiber content. However, this investigation was uniquely designed to stabilize weak subgrade soil with the consideration of appropriate fiber length (10 mm and 20 mm) and content (0.5%, 1%, 1.5%, and 2.5%). The engineering properties of the soil, the effect of NSF on weak subgrade soil, various fiber content and aspect ratios, and the optimum content and critical fiber aspect ratio were investigated in a laboratory. The effect of fibers on compaction, CBR values, and CBR swell values has also been studied. Laboratory results on the modified compaction tests showed that maximum dry density (MDD) was increased with the increment of fiber content, whereas optimum moisture content (OMC) remained constant. The soaked CBR and CBR swell values of natural soil were 1.80% and 8.95%, respectively. Due to reinforcement, the percentage increase in soaked CBR value at the optimum NSF content is 265.3, 310.0, 282.8, and 342.2 for aspect ratios of 33.33, 66.67, 25, and 50, respectively, with reference to natural soil. Also, the percentage decrease in swelling is 34.7, 52.75, 43.55, and 36.9, respectively. Moreover, the CBR value increases with the increase in aspect ratio by keeping the diameter constant and decreases with the increase in aspect ratio by keeping the length constant. It was also observed that increasing the length and diameter of NSF further increased the CBR value of reinforced soil. This increment was substantial at a fiber content of 1.5% for an aspect ratio of 50 (length = 20 mm, diameter = 0.4 mm). There was also a decrease in the CBR swelling value with an increase in fiber content. Finally, this investigation concluded that the use of NSF is a solution to weak soils with regard to moisture and performance problems.

The turbulence development of a vertical natural convection boundary layer

Results from direct numerical simulations of a vertical natural convection boundary layer (NCBL) with $Pr=0.71$ reveal that the turbulence development of such a thermally driven convective flow has two distinct stages: at relatively low Grashof number, the bulk flow is turbulent while the near-wall region is laminar-like or weakly turbulent; at sufficiently high Grashof number, the entire flow becomes turbulent in the sense of von Kármán (cf. Grossmann &amp; Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56, for the ultimate turbulent regime). Investigations on the turbulence statistics show that the near-wall Reynolds shear stress is negligible in the weakly turbulent regime but will grow in magnitude as the flow transitions to the ultimate regime at higher Grashof number. Similar behaviour is also seen in the streamwise turbulence intensity, where it develops from a mono-peak profile into a dual-peak structure as the Grashof number increases. At higher Grashof number, the near-wall energetic site is shown to have an energy distribution similar to that of a canonical wall-bounded turbulence (e.g. Hutchins &amp; Marusic, Phil. Trans. R. Soc.A, vol. 365, 2007, pp. 647–664), with a peak centred at fixed location and wavelength ( $y^+=18$ and $\lambda ^+_x=1000$ ) in viscous coordinates. Investigation on the spanwise spectra also suggests that the turbulent near-wall streaks emerge only at sufficiently high Grashof number, with constant spacing $\lambda _z^+\approx 130$ . The extent of the weakly turbulent regime is identified using the maximum velocity location $\delta_m$ and a laminar length scale $\delta_u$ . The development of near-wall turbulence is also investigated by examining the turbulence kinetic energy budget. In the weakly turbulent regime, the near-wall turbulence is sustained predominantly by the pressure transport in addition to the shear production. At higher Grashof number, the flow becomes fully turbulent, and both turbulent transport and shear production become stronger, while the pressure transport is decreased. These results also reveal that the production–dissipation ratio $P/\varepsilon$ of the NCBL would follow a fundamentally different trend to the canonical wall-bounded flows, which further supports that the near-wall turbulence generation is affected by the bulk flow.

Growth characteristics and post trimming regrowth potential of tropical and sub-tropical landscape hedge plants in response to spacing

Spacing of landscape plants is one of the factors determining the outcome of a design in terms of canopy formation which is one of the variables for aesthetic appearance in terms of shapes and forms. This study was conducted between September 2016 and September 2017, to determine the appropriate intra-row spacing for five plant species in hedge formation. The plant species used were Duranta erecta, Hamelia patens, Ficus retusa, Buxus sempervirens and Acalypha wilkesiana. Transplanting was done at intra-row spacing of 30, 40, 50 and 60cm and a constant inter-row spacing of 100cm. The experiment was a Randomized Complete Block Design in split plot arrangement with three replicates. Plant height, number of leaves, number of branches and canopy space, as indices of species suitability for use as hedge, were measured fortnightly. Plant regrowth and aesthetic characteristics were assessed after periodic trimming. H. patens and B. sempervirens species had the tallest plants. B. sempervirens and D. erecta produced the highest number of leaves while D. erecta and H. patens had the highest number of branches. D. erecta had significantly (p&lt;0.05) the fastest post-trimming shoot regrowth rate relative to other species following the 1st and 2nd trimming (25 and 28 WAT respectively). The effect of spacing on shoot regrowth length was significant after the 3rd, 4th and 5th trimmings (31, 34 and 37 WAT respectively). The highest shoot regrowth height was recorded at 40cm spacing followed by 30cm intra row spacing. All species responded best at 50cm intra-row spacing for the number of branches and canopy space as well as early hedge formation. The study concluded that B. sempervirens was suitable for ideal hedging at 40cm intra-row spacing while A. wilkiesiana and H. patens were only suitable as informal hedges. Hence, B. sempervirens species is recommended as the ideal hedge plant choice based on its early regrowth after trimming, high leaf and branch production as well as overall speed in hedge formation at 31WAT.

Continuous generalized symmetries in three dimensions

We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent theory revealing a ’t Hooft anomaly in the space of coupling constants when suitable compact scalar background fields are activated. Furthermore, the gauging procedure also implies that our main example has infinitely many non-invertible global symmetries. These can be obtained by dressing the continuous symmetry operators with topological quantum field theories. Finally, we comment on the holographic realization of both 2-group global symmetries and non-invertible symmetries discussed here by introducing a corresponding four-dimensional bulk description in terms of dynamical gauge fields.

New genicular joint angle criteria for flexor muscle (Musculus Semimembranosus) during the terrestrial mammals walking.

The genicular or knee joint angles of terrestrial mammals remain constant during the stance phase of walking; however, the angles differ among taxa. The knee joint angle is known to correlate with taxa and body mass among extant mammals, yet several extinct mammals, such as desmostylians, do not have closely related descendants. Furthermore, fossils lose their soft tissues by the time they are unearthed, making body mass estimates difficult. These factors cause significant problems when reconstructing the proper postures of extinct mammals. Terrestrial mammals use potential and kinetic energy for locomotion; particularly, an inverted pendulum mechanism is used for walking. This mechanism requires maintaining the rod length constant, therefore, terrestrial mammals maintain their joint angle in a small range. A muscle reaction referred to as co-contraction is known to increase joint stiffness; both the agonist and antagonist muscles work simultaneously on the same joint at the same time. The musculus semimembranosus flexes the knee joint and acts as an antagonist to muscles that extend it. Twenty-one species of terrestrial mammals were examined to identify the elements that constitute the angle between the m. semimembranosus and the tibia based on the period between the hindlimb touching down and taking off from the ground. Measurements were captured from videos in high-speed mode (420 fps), selecting 13 pictures from the first 75% of each video while the animals were walking. The angles between the main force line of the m. semimembranosus and the tibia, which were defined as θsm-t, were measured. The maximum and minimum angles between the m. semimembranosus and the tibia (θsm-t) of the stance instance (SI) were successfully determined for more than 80% of the target animals (17 out of 21 species) during SI-1 to SI-13 within ±10° from the mean. The difference between each successive SI was small and, therefore, the θsm-t transition was smooth. According to the results of the total stance differences among the target animals, θsm-t was relatively constant during a stance and, therefore, average θsm-t (θave) can represent each animal. Only Carnivora had a significant difference in the correlation between body mass and θave. In addition, there were significant differences in θave between plantigrade and unguligrade locomotion. Our measurements show that θave was 100 ± 10° regardless taxon, body mass, and locomotor mode. Thus, only three points on skeletons need to be measured to determine θave. This offers a new approximation approach for understanding hindlimb posture that could be applied to the study of the hindlimbs of extinct mammals with no closely related extant descendants.

Information metric on the boundary

The information metric on the space of boundary coupling constants in two-dimensional conformal field theories is studied. Such a metric is related to the Casimir energy difference of the theory defined on an interval. We concretely compute the information metric on the boundary conformal manifold of free boson CFT as well as SU(2)k WZW theory, obtaining the result expected from the symmetry of the systems. We also compute the information metric on the space of non-conformal boundary states produced by boundary mass perturbations in the theory of a real free scalar. The holographic dual of the boundary information metric in the context of AdS3/BCFT2 is also discussed. We argue that it corresponds to the area of the minimal cross section of the end-of-the-world brane connecting two boundaries of the asymptotic BCFTs.

Optimal Geometric Multigrid Preconditioners for HDG-P0 Schemes for the reaction-diffusion equation and the Generalized Stokes equations

We present the lowest-order hybridizable discontinuous Galerkin schemes with numerical integration (quadrature), denoted as HDG-P0 for the reaction-diffusion equation and the generalized Stokes equations on conforming simplicial meshes in two- and three-dimensions. Here by lowest order, we mean that the (hybrid) finite element space for the global HDG facet degrees of freedom (DOFs) is the space of piecewise constants on the mesh skeleton. A discontinuous piecewise linear space is used for the approximation of the local primal unknowns. We give the optimal a priori error analysis of the proposed HDG-P0 schemes, which hasn’t appeared in the literature yet for HDG discretizations as far as numerical integration is concerned. Moreover, we propose optimal geometric multigrid preconditioners for the statically condensed HDG-P0 linear systems on conforming simplicial meshes. In both cases, we first establish the equivalence of the statically condensed HDG system with a (slightly modified) nonconforming Crouzeix–Raviart (CR) discretization, where the global (piecewise-constant) HDG finite element space on the mesh skeleton has a natural one-to-one correspondence to the nonconforming CR (piecewise-linear) finite element space that live on the whole mesh. This equivalence then allows us to use the well-established nonconforming geometry multigrid theory to precondition the condensed HDG system. Numerical results in two- and three-dimensions are presented to verify our theoretical findings.