Search Results (15)

The precision and predictive power of perturbative QCD (pQCD) prediction depends on both a precise, convergent, fixed-order series and a reliable way of estimating the contributions of unknown higher-order (UHO) terms. It has been shown that by applying the principle of maximum conformality (PMC), which applies the renormalization group equation recursively to set the effective magnitude of ${\alpha }_s$ of the process, the remaining conformal coefficients will be well matched with the corresponding ${\alpha }_s$ at each order, leading to a scheme-and-scale invariant and more convergent perturbative series. The PMC series, being satisfied with the standard renormalization group invariance, has a rigorous foundation. Thus it not only can be widely applied to virtually all high-energy hadronic processes, but also can be a reliable platform for estimating UHO contributions. In this paper, by using the total decay width $\Gamma (H\to \gamma \gamma )$ which has been calculated up to N⁴LO QCD corrections, we first derive its PMC series by using the PMC single-scale setting approach and then estimate its unknown N⁵LO contributions by using a Bayesian analysis. The newly suggested Bayesian-based approach estimates the magnitude of the UHO contributions based on an optimized analysis of the probability density distribution, and the predicted UHO contribution becomes more accurate when more loop terms have been known to tame the probability density function. Using the top-quark pole mass $M_t$ = 172.69 GeV and the Higgs mass $M_H$ = 125.25 GeV as inputs, we obtain $\Gamma (H\to \gamma \gamma )=9.56504\mathrm{keV}$, and the estimated N⁵LO contribution to the total decay width is $\Delta {\Gamma }_H=\pm 1.65\times {10}^{-4}\mathrm{keV}$ for the smallest credible interval of $95.5\%$ degree of belief. Full article

Exoskeletal robots are of critical importance in the domain of mechanical boosting. The pneumatic artificial muscle (PAM) is commonly used as a flexible actuator in exoskeletal robots designed for upper limbs due to its high power-to-weight ratio, conformability, and safety. This study establishes a new model based on the existing model to improve its control precision by implementing elastic and frictional forces and empirical coefficients, battling against the time-variant hysteresis that PAM’s output force exhibits. In the meantime, a BP neural network is employed in reverse modeling, followed by the adoption of the least-square-based particle swarm optimization algorithm in order to determine the optimized parameter values. PAM provides the Upper Limb Exoskeletal Robot with appropriate auxiliary power, which can be adjusted to accommodate variations in posture change during the lifting process. PAM is also capable of handling variable loads based on the principle of torque balance, constructing a control system according to the inverse dynamics of exoskeletal robots accompanied by an inverse model of PAM’s output force, and finally, rendering tracking control of the elbow angle during the auxiliary process possible. Finally, the tracking error results are calculated and shown; the maximum angular error in the tracking process is 0.0175 rad, MAE value is 0.0038 rad, RMSE value is 0.0048 rad, and IEAT value is 4.6426 rad. This control method is able to improve the precision of tracking control of the elbow angle of the upper limb–exoskeleton coupled system during the process of lifting goods. Full article

In this paper, we investigate properties of solutions to a space-time fractional variable-order conformable nonlinear differential equation with a generalized tempered fractional Laplace operatorby using the maximum principle. We first establish some new important fractional various-order conformable inequalities. With these inequalities, we prove a new maximum principle with space-time fractional variable-order conformable derivatives and a generalized tempered fractional Laplace operator. Moreover, we discuss some results about comparison principles and properties of solutions for a family of space-time fractional variable-order conformable nonlinear differential equations with a generalized tempered fractional Laplace operator by maximum principle. Full article

The setting of the renormalization scale (${\mu }_r$) in the perturbative QCD (pQCD) is one of the crucial problems for achieving precise fixed-order pQCD predictions. The conventional prescription is to take its value as the typical momentum transfer Q in a given process, and theoretical uncertainties are then evaluated by varying it over an arbitrary range. The conventional scale-setting procedure introduces arbitrary scheme-and-scale ambiguities in fixed-order pQCD predictions. The principle of maximum conformality (PMC) provides a systematic way to eliminate the renormalization scheme-and-scale ambiguities. The PMC method has rigorous theoretical foundations; it satisfies the renormalization group invariance (RGI) and all of the self-consistency conditions derived from the renormalization group. The PMC has now been successfully applied to many physical processes. In this paper, we summarize recent PMC applications, including event shape observables and heavy quark pair production near the threshold region in $e^{+}{e}^{-}$ annihilation and top-quark decay at hadronic colliders. In addition, estimating the contributions related to the uncalculated higher-order terms is also summarized. These results show that the major theoretical uncertainties caused by different choices of ${\mu }_r$ are eliminated, and the improved pQCD predictions are thus obtained, demonstrating the generality and applicability of the PMC. Full article

Hypotrochoidal profile contours have been produced in industrial applications in recent years using two-spindle processes, and they are considered effective high-quality solutions for form-fit shaft and hub connections. This study mainly concerns analytical approaches to determine the stresses and deformations in hypotrochoidal profile shafts due to pure bending loads. The formulation was developed according to bending principles using the mathematical theory of elasticity and conformal mappings. The loading was further used to investigate the rotating bending behaviour. The stress factors for the classical calculation of maximum bending stresses were also determined for all those profiles presented and compiled in the German standard DIN3689-1 for practical applications. The results were also compared with the corresponding numerical and experimental results, and very good agreement was observed. Additionally, based on previous work, the stress factor was determined for the case of torsional loading to calculate the maximum torsional stresses in the standardised profiles, and the results are listed in a table. This study contributes to the further refinement of the current DIN3689 standard. Full article

This paper presents a wearable metasurface multiple-input multiple-output (MIMO) antenna for biomedical applications in a 5 GHz wireless body area network (WBAN) with broadband, circular polarization (CP), and high gain. The physical properties of the MIMO antenna element and the principles of polarization conversion are analyzed in-depth using characteristic mode analysis. For the proposed MIMO antenna, the measured −10 dB impedance bandwidth is 34.87% (4.76–6.77 GHz), and the 3 dB axial ratio bandwidth is 22.94% (4.9–6.17 GHz). By adding an isolation strip, the measured isolation of the two antenna elements is greater than 19.85 dB. The overall size of the MIMO antenna is 1.67λ₀ × 0.81λ₀ × 0.07λ₀ at 5.6 GHz, and the maximum gain is 7.95 dBic. The envelope correlation coefficient (ECC) is less than 0.007, with the maximum diversity gain greater than 9.98 dB, and the channel capacity loss is less than 0.29 b/s/Hz. The specific absorption rate (SAR) of the wearable MIMO antenna is simulated by the human tissue model, which proves that the proposed antenna conforms to international standards and is harmless to humans. The proposed wearable metasurface MIMO antenna has CP, broadband, high gain, low ECC, and low SAR, which can be used in wearable devices for biomedical applications. Full article

Sensitivity analysis and parameter optimization of stand models can improve their efficiency and accuracy, and increase their applicability. In this study, the sensitivity analysis, screening, and optimization of 63 model parameters of the Physiological Principles in Predicting Growth (3PG) model were performed by combining a sensitivity analysis method and the Markov chain Monte Carlo (MCMC) method of Bayesian posterior estimation theory. Additionally, a nine-year observational dataset of Chinese fir trees felled in the Shunchang Forest Farm, Nanping, was used to analyze, screen, and optimize the 63 model parameters of the 3PG model. The results showed the following: (1) The parameters that are most sensitive to stand stocking and diameter at breast height (DBH) are nWs(power in stem mass vs. diameter relationship), aWs(constant in stem mass vs. diameter relationship), alphaCx(maximum canopy quantum efficiency), k(extinction coefficient for PAR absorption by canopy), pRx(maximum fraction of NPP to roots), pRn(minimum fraction of NPP to roots), and CoeffCond(defines stomatal response to VPD); (2) MCMC can be used to optimize the parameters of the 3PG model, in which the posterior probability distributions of nWs, aWs, alphaCx, pRx, pRn, and CoeffCond conform to approximately normal or skewed distributions, and the peak value is prominent; and (3) compared with the accuracy before sensitivity analysis and a Bayesian method, the biomass simulation accuracy of the stand model was increased by 13.92%, and all indicators show that the accuracy of the improved model is superior. This method can be used to calibrate the parameters and analyze the uncertainty of multi-parameter complex stand growth models, which are important for the improvement of parameter estimation and simulation accuracy. Full article

Reinforcement learning is one of the most promising machine learning techniques to get intelligent behaviors for embodied agents in simulations. The output of the classic Temporal Difference family of Reinforcement Learning algorithms adopts the form of a value function expressed as a numeric table or a function approximator. The learned behavior is then derived using a greedy policy with respect to this value function. Nevertheless, sometimes the learned policy does not meet expectations, and the task of authoring is difficult and unsafe because the modification of one value or parameter in the learned value function has unpredictable consequences in the space of the policies it represents. This invalidates direct manipulation of the learned value function as a method to modify the derived behaviors. In this paper, we propose the use of Inverse Reinforcement Learning to incorporate real behavior traces in the learning process to shape the learned behaviors, thus increasing their trustworthiness (in terms of conformance to reality). To do so, we adapt the Inverse Reinforcement Learning framework to the navigation problem domain. Specifically, we use Soft Q-learning, an algorithm based on the maximum causal entropy principle, with MARL-Ped (a Reinforcement Learning-based pedestrian simulator) to include information from trajectories of real pedestrians in the process of learning how to navigate inside a virtual 3D space that represents the real environment. A comparison with the behaviors learned using a Reinforcement Learning classic algorithm (Sarsa($\lambda$)) shows that the Inverse Reinforcement Learning behaviors adjust significantly better to the real trajectories. Full article

Magnetized particle motion around black holes in conformal gravity immersed in asymptotically uniform magnetic field has been studied. We have also analyzed the behavior of magnetic fields near the horizon of the black hole in conformal gravity and shown that with the increase of conformal parameters L and N the value of angular component of magnetic field at the stellar surface decreases. The maximum value of the effective potential corresponding to circular motion of the magnetized particle increases with the increase of conformal parameters. It is shown that in all cases of neutral, charged and magnetized particle collisions in the black hole environment the center-of-mass energy decreases with the increase of conformal parameters L and N. In the case of the magnetized and negatively charged particle collisions, the innermost collision point with the maximum center-of-mass energy comes closer to the central object due to the effects of the parameters of the conformal gravity. We have applied the results to the real astrophysical scenario when a pulsar treated as a magnetized particle is orbiting the super massive black hole (SMBH) Sgr A* in the center of our galaxy in order to obtain the estimation of magnetized compact object’s orbital parameter. The possible detection of pulsar in Sgr A* close environment can provide constraints on black hole parameters. Here we have shown that there is degeneracy between spin of SMBH and ambient magnetic field and consequently the interaction of magnetic field $\sim {10}^2$ Gauss with magnetic moment of magnetized neutron star can in principle mimic spin of Kerr black holes up to $0.6$ . Full article

Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state variables. The method is based on explicit recognition of the state and conjugate variables, which can relax towards the respective quasi-equilibria in different ways. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of conjugate variables guarantees that the reduced equations are closed. Moreover, an infinite chain of consecutive DynMaxEnt approximations can be constructed. The method is demonstrated on a particle with friction, complex fluids (equipped with conformation and Reynolds stress tensors), hyperbolic heat conduction and magnetohydrodynamics. Full article

There are two components in this work that allow for solutions of the turbulent channel flow problem: One is the Galilean-transformed Navier-Stokes equation which gives a theoretical expression for the Reynolds stress (u′v′); and the second the maximum entropy principle which provides the spatial distribution of turbulent kinetic energy. The first concept transforms the momentum balance for a control volume moving at the local mean velocity, breaking the momentum exchange down to its basic components, u′v′, u′², pressure and viscous forces. The Reynolds stress gradient budget confirms this alternative interpretation of the turbulence momentum balance, as validated with DNS data. The second concept of maximum entropy principle states that turbulent kinetic energy in fully-developed flows will distribute itself until the maximum entropy is attained while conforming to the physical constraints. By equating the maximum entropy state with maximum allowable (viscous) dissipation at a given Reynolds number, along with other constraints, we arrive at function forms (inner and outer) for the turbulent kinetic energy. This allows us to compute the Reynolds stress, then integrate it to obtain the velocity profiles in channel flows. The results agree well with direct numerical simulation (DNS) data at Re_τ = 400 and 1000. Full article

Conformal design of the island-bridge structure is the key to construct high-performance inorganic stretchable electronics that can be conformally transferred to non-developable surfaces. Former studies in conformal problems of epidermal electronics are mainly focused on soft surfaces that can adapt to the deformation of the electronics, which are not suitable for applications in hard, non-developable surfaces because of their loose surface constraints. In this paper, the conformal design problem for the island-bridge structure on a hard, non-developable surface was studied, including the critical size for island and stiffness and the demand for stretchability for the bridge. Firstly, the conformal model for an island on a part of torus surface was established to determine the relationship between the maximum size of the island and the curvatures of the surface. By combining the principle of energy minimization and the limit of material failure, a critical non-dimensional width for conformability was given for the island as a function of its thickness and interfacial adhesion energy, and the ratio of two principal curvatures of the surface. Then, the dependency of the tensile stiffness of the bridge on its geometric parameters was studied by finite element analysis (FEA) to guide the deterministic assembly of the islands on the surface. Finally, the location-dependent demands for the stretchability of the bridges were given by geometric mapping. This work will provide a design rule for stretchable electronics that fully conforms to the non-developable surface. Full article

Kurchatovite and clinokurchatovite, both of ideal composition CaMgB₂O₅, from the type localities (Solongo, Buryatia, Russia, and Sayak-IV, Kazakhstan, respectively) have been studied using electron microprobe and single-crystal X-ray diffraction methods. The empirical formulae of the samples are Ca_1.01Mg_0.87Mn_0.11Fe²⁺_0.02B_1.99O₅ and Ca_0.94Mg_0.91Fe²⁺_0.10Mn_0.04B_2.01O₅ for kurchatovite and clinokurchatovite, respectively. The crystal structures of the two minerals are similar and based upon two-dimensional blocks arranged parallel to the c axis in kurchatovite and parallel to the a axis in clinokurchatovite. The blocks are built up from diborate B₂O₅ groups, and Ca²⁺ and Mg²⁺ cations in seven- and six-fold coordination, respectively. Detailed analysis of geometrical parameters of the adjacent blocks reveals that symmetrically different diborate groups have different degrees of conformation in terms of the δ angles between the planes of two BO₃ triangles sharing a common O atom, featuring two discrete sets of the δ values of ca. 55° (B’ blocks) and 34° (B” blocks). The stacking of the blocks in clinokurchatovite can be presented as …(+B’)(+B”)(+B’)(+B”)… or [(+B’)(+B”)], whereas in kurchatovite it is more complex and corresponds to the sequence …(+B’)(+B”)(+B’)(−B’)(−B”)(−B’)(+B’)(+B”)(+B’)(−B’)(−B”)(−B’)… or [(+B’)(+B”)(+B’)(−B’)(−B”)(−B’)]. The B’:B” ratios for clinokurchatovite and kurchatovite are 1:1 and 2:1, respectively. According to this description, the two minerals cannot be considered as polytypes and their mutual relationship corresponds to the term modular polymorphs. From the viewpoint of information-based measures of structural complexity, clinokurchatovite (I_G = 4.170 bits/atom and I_G,total = 300.235 bits/cell) is structurally simpler than kurchatovite (I_G = 4.755 bits/atom and I_G,total = 1027.056 bits/cell). The high structural complexity of kurchatovite can be inferred from the modular character of its structure. The analysis of structural combinatorics in terms of the modular approach allows to construct the whole family of theoretically possible “kurchatovite”-type structures that bear the same structural features common for kurchatovite and clinokurchatovite. However, the crystal structures of the latter minerals are the simplest and are the only ones that have been observed in nature. The absence of other possible structures is remarkable and can be explained by either the maximum-entropy of the least-action fundamental principles. Full article

Based on the maximum entropy (MaxEnt) principle for a generalized entropy functional and the conjugate representations introduced by Zhang, we have reformulated the method of information geometry. For a set of conjugate representations, the associated escort expectation is naturally introduced and characterized by the generalized score function which has zero-escort expectation. Furthermore, we show that the escort expectation induces a conformal divergence. Full article

The formation of the F₃B–NH₃ supermolecule by chemical interaction of its fragment parts, BF₃ and NH₃, and the dynamics of internal rotation about the ‘B–N’ bond have been studied in terms of parameters provided by the molecular orbital and density functional theories. It is found that the pairs of frontier orbitals of the interacting fragments have matching symmetry and are involved in the charge transfer interaction. The donation process stems from the HOMO of the donor into the LUMO of the acceptor and simultaneously, back donation stems from the HOMO of acceptor into the LUMO of the donor. The density functional computation of chemical activation in the donor and acceptor fragments, associated with the physical process of structural reorganization just prior to the event of chemical reaction, indicates that BF3 becomes more acidic and NH₃ becomes more basic, compared to their separate equilibrium states. Theoretically it is observed that the chemical reaction event of the formation of the supermolecule from its fragment parts is in accordance with the chemical potential equalization principle of the density functional theory and the electronegativity equalization principle of Sanderson. The energetics of the chemical reaction, the magnitude of the net charge transfer and the energy of the newly formed bond are quite consistent, both internally and with the principle of maximum hardness, PMH. The dynamics of the internal rotation of one part with respect to the other part of the supermolecule about the ‘B–N’ bond mimics the pattern of the conformational isomerism of the isostructural ethane molecule. It is also observed that the dynamics and evolution of molecular conformations as a function of dihedral angles is also in accordance with the principle of maximum hardness, PMH. Quite consistent with spectroscopic predictions, the height of the molecule’s barrier to internal rotation is very small. A rationale for the low height of the barrier has been put forward in terms of the energy partitioning analysis. On the question of origin of the barrier to internal rotation, we conclude that the conformational barrier to internal rotation does not originate from a particular region of the molecule, but rather it is a result of the subtle conjoint interplay of a number of opposing effects of one- and two-center bonded and nonbonded energy terms involving the entire skeleton of the molecule. Full article