First-order Ones Research Articles

Bifurcation of singularities of fluctuational paths for a noise-driven overdamped two-well system.

Noise-induced escape in a 2D generalized Maier-Stein model with two parameters μ and α is investigated in the weak noise limit. With the WKB approximation, the patterns of extreme paths and singularities are displayed. By employing the Freidlin-Wentzell action functional and the asymptotic series, critical parameters α inducing singularity bifurcation are determined analytically for μ=1. The switching line will appear with singularities and is equivalent to the sliding set in the Filippov system. The pseudo-saddle-node bifurcation on the switching line is found. Then, when -1<μ<1, it is found that all bifurcation values α will decrease as μ decreases and the second-order bifurcation values are bigger than all first-order ones. In addition, the variation of the switching line is also analyzed and a new switching line will emerge when the location of the minimum quasi-potential on the boundary changes. At last, when the noise is anisotropic, only the noise intensity ratio will affect the bifurcation value α.

Taking Better Advantage of Fold Axis Data to Characterize Anisotropy of Complex Folded Structures in the Implicit Modeling Framework

When too few field measurements are available for the geological modeling of complex folded structures, the results of implicit methods typically exhibit an unsatisfactory bubbly aspect. However, in such cases, anisotropy data are often readily available but not fully exploited. Among them, fold axis data are a straightforward indicator of this local anisotropy direction. Focusing on the so-called potential field method, this work aims to evaluate the effect of the incorporation of such data into the modeling process. Given locally sampled fold axis data, this paper proposes to use the second-order derivatives of the scalar field in addition to the existing first-order ones. The mathematical foundation of the approach is developed, and the respective efficiencies of both kinds of constraints are tested. Their integration and impact are discussed based on a synthetic case study, thereby providing practical guidelines to geomodeling tool users on the parsimonious use of data for the geological modeling of complex folded structures.

Reversibility of the Magnetocaloric Effect in the Bean-Rodbell Model

The applicability of magnetocaloric materials is limited by irreversibility. In this work, we evaluate the reversible magnetocaloric response associated with magnetoelastic transitions in the framework of the Bean-Rodbell model. This model allows the description of both second- and first-order magnetoelastic transitions by the modification of the η parameter (η&lt;1 for second-order and η&gt;1 for first-order ones). The response is quantified via the Temperature-averaged Entropy Change (TEC), which has been shown to be an easy and effective figure of merit for magnetocaloric materials. A strong magnetic field dependence of TEC is found for first-order transitions, having a significant increase when the magnetic field is large enough to overcome the thermal hysteresis of the material observed at zero field. This field value, as well as the magnetic field evolution of the transition temperature, strongly depend on the atomic magnetic moment of the material. For a moderate magnetic field change of 2 T, first-order transitions with η≈1.3−1.8 have better TEC than those corresponding to stronger first-order transitions and even second-order ones.

Comparative study of the magnetic phase diagrams and spin-flop-driven magnetodielectric responses of the pure and Mn3+-doped Pb2Fe2Ge2O9 single crystals

The Pb2Fe2-xMnxGe2O9 (x = 0.43) orthorhombic antiferromagnet single crystals have been synthesized by a modified pseudo-flux technique and their magnetic and magnetodielectric properties have been investigated. It has been established that partial substitution of highly anisotropic Mn3+ ions for iron ones significantly affects the magnetic structure of the crystal. Under magnetization of the crystal along the rhombic b and c axes, magnetization jumps have been detected, which are indicative of the occurrence of orientational transitions identified as first-order ones. No weak ferromagnetism characteristic of the pure crystal in the rhombic a axis direction has been detected. The field dependences of the magnetization for the pure and Mn-doped crystals have been analyzed using the thermodynamic potential that takes into account the crystal symmetry. It has been shown that, in the Mn-substituted crystal, the antiferromagnetic vector in the ground state is parallel to the rhombic b axis; in this state, weak ferromagnetism has not been observed. Under magnetization along the b axis, a conventional spin-flop transition occurs. The orientational transition under magnetization along the c axis has been attributed to the reorientation of the antiferromagnetic vector relative to the a axis with the simultaneous occurrence of a weak ferromagnetic moment along the c axis. Magnetic phase diagrams of the Mn-doped crystal for the magnetic fields H||b and H||c have been built.In the Mn-doped crystal, at E||c and H||c, the orientational transition-induced magnetodielectric response jump has been detected, which is higher than the jumps observed for the undoped crystal by a factor of 3. The magnetodielectric properties of the pure and Mn-doped crystals have been analyzed using their magnetic phase diagrams.

Attention-Aware Residual Network Based Manifold Learning for White Blood Cells Classification.

The classification of six types of white blood cells (WBCs) is considered essential for leukemia diagnosis, while the classification is labor-intensive and strict with the clinical experience. To relieve the complicated process with an efficient and automatic method, we propose the Attention-aware Residual Network based Manifold Learning model (ARML) to classify WBCs. The proposed ARML model leverages the adaptive attention-aware residual learning to exploit the category-relevant image-level features and strengthen the first-order feature representation ability. To learn more discriminatory information than the first-order ones, the second-order features are characterized. Afterwards, ARML encodes both the first- and second-order features with Gaussian embedding into the Riemannian manifold to learn the underlying non-linear structure of the features for classification. ARML can be trained in an end-to-end fashion, and the learnable parameters are iteratively optimized. 10800 WBCs images (1800 images for each type) is collected, 9000 images and five-fold cross-validation are used for training and validation of the model, while additional 1800 images for testing. The results show that ARML achieving average classification accuracy of 0.953 outperforms other state-of-the-art methods with fewer trainable parameters. In the ablation study, ARML achieves improved accuracy against its three variants: without manifold learning (AR), without attention-aware learning (RML), and AR without attention-aware learning. The t-SNE results illustrate that ARML has learned more distinguishable features than the comparison methods, which benefits the WBCs classification. ARML provides a clinically feasible WBCs classification solution for leukemia diagnose with an efficient manner.

Modelling and verification of parameterized architectures: A functional approach

The merit of higher order functions for hardware description and transformation is widely acknowledged by hardware designers. However, the use of higher order types makes their correctness proof very difficult. Herein, a new proof approach based on the principle of partial application is proposed which transforms higher order functions into partially applied first-order ones. Therefore, parameterised architectures modelled by higher order functions could be easily redefined only over first-order types. The proof could be performed by induction within the same specification framework that avoids translating the higher order properties between different semantics, which remains extremely difficult. Using the notion of parameterisation where verified components are used as parameters to build more complex ones, the approach fits elegantly in the incremental bottom-up design where both the design and its proof could be developed in a systematic way. The potential features of the proposed methodological proof approach are demonstrated over a detailed example of a circuit design and verification within a functional framework.

Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface

In this research, the three-dimensional (3D) steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed. The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation. The slip for viscous fluid is considered. The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate. The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method. Dual solutions are obtained for the velocity, skin friction coefficient, temperature, and Nusselt number subject to sundry flow parameters, magnetic parameter, Darcy-Forchheimer number, thermal radiation parameter, suction parameter, and dimensionless slip parameter. In this research, the main consideration is given to the engineering interest like skin friction coefficient (velocity gradient or surface drag force) and Nusselt number (temperature gradient or heat transfer rate) and discussed numerically through tables. In conclusion, it is noticed from the stability results that the upper branch solution (UBS) is more reliable and physically stable than the lower branch solution (LBS).

High-order fully actuated system approaches: Part IV. Adaptive control and high-order backstepping

Three types of high-order system models with parametric uncertainties are introduced, namely, the high-order fully actuated (HOFA) models, and the second- and high-order strict-feedback system (SFS) models, which possess a common full-actuation structure. Direct design approaches of adaptive stabilising controllers and adaptive tracking controllers of the HOFA models are firstly proposed based on the Lyapunov stability theory. Using the obtained result, direct second- and high-order backstepping methods for the designs of adaptive stabilising controllers of the second- and high-order SFSs with parametric uncertainties are also proposed. These approaches do not need to convert the high-order systems into first-order ones, and are thus more direct and effective. Furthermore, for a specific second- or higher-order SFS, applications of the proposed high-order backstepping methods need fewer steps than the usual first-order backstepping method, hence save much design and computation complexity.

High-order fully actuated system approaches: Part III. Robust control and high-order backstepping

In this paper, three types of uncertain high-order nonlinear models are firstly proposed, namely, a single high-order fully actuated (HOFA) model with nonlinear uncertainties, an uncertain second-order strict-feedback system (SFS) and an uncertain high-order SFS, and the relations among these types of models are also discussed. Secondly, a direct approach for the design of robust stabilising controllers and robust tracking controllers for an uncertain single HOFA model are proposed based on the Lyapunov stability theory. Using the obtained robust control design result, the second- and high-order backstepping methods for the designs of robust stabilising controllers of the introduced second- and high-order SFSs are also proposed. The proposed approaches do not need to convert the high-order systems into first-order ones, and for a specific system design, the proposed high-order backstepping methods need fewer steps than the usual first-order backstepping method, hence are generally more direct and simpler. An illustrative example demonstrates both the effect and the application procedure of the proposed HOFA robust control approaches.

Passivity-based synchronization for Markov switched neural networks with time delays and the inertial term

The passivity-based synchronization issue of Markov switched inertial neural networks with time delays is addressed in this work. Different from many articles, the influence of inertial term on neural network is taken into account, namely, the second-order derivative of the system model is emphasized. For this issue, the second-order differential equations are processed to establish the first-order ones by means of the variable transformation. Next, under the framework of drive-response, a mode dependent feedback controller is designed to implement passive synchronization of Markov switched inertial neural networks. Meanwhile, by an optimized inequality technique and Lyapunov stability theory, some sufficient conditions are established. Ultimately, through a comparative example displayed, the effectiveness and superiority of the results derived can be fully illustrated.

High-order fully actuated system approaches: Part II. Generalized strict-feedback systems

An advantage of a high-order fully-actuated (HOFA) system is that there exists a controller such that a constant linear closed-loop system with an arbitrarily assignable eigenstructure can be obtained. In this paper, a generalised form of the conventional first-order strict-feedback systems (SFSs) is firstly proposed, and a recursive solution is proposed to convert equivalently the generalised SFS into a HOFA model. Then the second- and high-order SFSs are defined and their equivalent HOFA models are also derived. It is further shown that, under certain common conditions, the recursive solutions for converting the generalised SFSs into HOFA models can be rearranged into direct analytical explicit solutions. Such a high-order system approach is more direct and simpler than the first-order system approach since it avoids the process of converting firstly these second- and high-order SFSs into first-order ones for control, and can finally produce a constant linear closed-loop system. Particularly, it is more effective than the well-known method of backstepping since, for the generalised complicated SFSs with more subsystems, the method of backstepping may simply be not applicable due to more serious ‘differential explosion’ problem. Two examples are worked out to demonstrate the effect of the approach.

Phase transitions in optimized network models

We consider network connection growing models that aim at minimizing the wiring cost while at the same time maximizing the network connections. By mapping the system to an Ising spin model, we obtain analytic results for two such models, both of them show interesting, but different phase transition behaviors for general wiring cost distributions. The phase diagrams for these transitions are also obtained. These results are also extended for networks optimized with weighted node degree for connections. Depending on the properties of the edge and node weight distributions, the system can exhibit a variety of phase transitions, including first-order, second-order and hybrid ones, from no connection to a network of finite fraction of connections. Furthermore, mean-field theory leads to an effective algorithm for finding the fully optimized network configurations in these models. All these results are also verified by numerical simulations.

Relaxed Euler systems and convergence to Navier-Stokes equations

We consider the approximation of Navier-Stokes equations for a Newtonian fluid by Euler type systems with relaxation both in compressible and incompressible cases. This requires to decompose the second-order derivative terms of the velocity into first-order ones. Usual decompositions lead to approximate systems with tensor variables. We construct approximate systems with vector variables by using Hurwitz-Radon matrices. These systems are written in the form of balance laws and admit strictly convex entropies, so that they are symmetrizable hyperbolic. For smooth solutions, we prove the convergence of the approximate systems to the Navier-Stokes equations in uniform time intervals. Global-in-time convergence is also shown for the initial data near constant equilibrium states of the systems. These convergence results are established not only for the approximate systems with vector variables but also for those with tensor variables.

Numerical investigations of gap resonance excited by focused transient wave groups

Two or more structures arranged side by side with narrow gaps may be suffered from large-amplitude free-surface oscillations, which could cause green water on the deck and lead to dramatic increase of hydrodynamic loading acting on structures. Here, transient resonant motions of the free surface inside a narrow gap between two fixed boxes triggered by focused transient wave groups with various focused wave amplitudes are simulated using a two-dimensional numerical wave tank. The free-surface amplifications not only inside the gap but in the vicinity of the two-box system, the response time and the damping time of the transient gap resonance, the maximum wave loads on both boxes and the relative importance of the higher-order wave loads to the first-order ones are systematically investigated. It is found that the most vulnerable position to green water closely depends on the incident focused wave amplitude. The damping time decreases gradually with increasing focused wave amplitude, while the response time seems insensitive to the latter. As the focused wave amplitude increases, the normalized maximum wave loads on both boxes are also shown to decline gradually overall, while the relative importance of the higher-order wave loads to the first-order ones becomes more and more remarkable.

Tricritical Physics in Two-Dimensional p-Wave Superfluids.

We study effects of quantum fluctuations on two-dimensional p+ip superfluids near resonance. In the standard paradigm, phase transitions between superfluids and zero density vacuum are continuous. When strong quantum fluctuations near resonance are present, the line of continuous phase transitions terminates at two tricritical points near resonance, between which the transitions are expected to be first-order ones. The size of the window where first-order phase transitions occur is shown to be substantial when the coupling is strong. Near first-order transitions, superfluids self-contract due to phase separations between superfluids and vacuum.

Non-fragile [formula omitted] synchronization for switched inertial neural networks with random gain fluctuations: A persistent dwell-time switching law

This paper investigates the synchronization control issue for a set of switched inertial neural networks in the discrete-time domain, in which the persistent dwell-time switching law is employed to depict the switchings among system parameters. Thereinto, the foregoing networks having the second-order differential equations are degraded to the first-order differential ones through applying the variable transformation. In addition, in order to cope with random gain fluctuations caused by noise or harsh environments, in the controller, two random variables obeying the Bernoulli distribution are employed to simulate the occurrence of gain fluctuations. Based on Lyapunov stability theory, persistent dwell-time concept and stochastic analysis theory, some sufficient criteria are derived under which the synchronization error system is exponentially mean-square stable with a prescribed l2-l∞ property. Finally, a numerical example, including some illustrative simulations, is given to present the feasibility of the derived analytical results.

Method for Studying the Asymptotic Properties of Solutions to a System of Second-Order Linear Differential Equations on the Half-Line

A special method is proposed for reducing an $$n $$-dimensional system of second-order ordinary differential equations to a $$2n$$-dimensional system of first-order ones. Using matrix weight functions (which can be chosen arbitrarily when applying the method), we establish sufficient conditions for the boundedness and power-law absolute integrability on the half-line of the components of all solutions to a linear system of second-order differential equations and their first derivatives as well as for their decay (in particular, exponential or power-law) as the independent variable tends to infinity. An illustrative example is provided.

Elastic phononic plates with first-order and second-order topological phases

Topologically protected 1D edge states and the 2D surface states have been observed in variant classical wave systems. By extending the quantized polarization, Berry phase, to higher multipole moments, the higher-order topological phases, expressed as 0D corner states, have been theoretically predicted and recently experimentally observed in electric, electromagnetic and acoustic systems. In this paper, we design an elastic phononic plate consisting of a bi-layered hexagonal lattice. The valley-polarized gapless 1D edge state is observed in the elastic phononic plate, by lifting the Dirac cones at the Brillouin zone (BZ) corners. When the bi-layered phononic plates are stacked one by one, the chirality of the oblique columns along the z axis guarantees this 2D elastic phononic plate to be a 3D chiral phononic system. Weyl cones and topologically protected gapless 2D surface states are yielded in this 3D chiral phononic system. The above topological phases are first-order ones with gapless (d-1)-dimensional edge/surface states. By defining a composite cell consisting of three-unit cells and modulating the intra- and inter-coupling within/among the composite cells, the folded double Dirac cone at the BZ center will be gapped and the topological phase of the elastic phononic plate will evolve to a second-order one, expressed as the robust 0D corner state, instead of the gapless 1D edge state. The realization of the first-order edge/surface states and second-order corner states in a unified elastic phononic platform opens up a new path for the design of on-chip topological devices for advanced elastic wave manipulation among the bulk, edge/surface and corner modes.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: II. Computed Sensitivities

This work presents the results of the exact computation of (180)3 = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3rd-order sensitivities are significantly larger than their corresponding 1st- and 2nd-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3rd-order relative sensitivity is the mixed sensitivity of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of 1H (“isotope 6”) and 239Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1st-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope 1H, having the value , while the largest 2nd-order sensitivity is . The 3rd-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.

Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: I. Effects of Imprecisely Known Microscopic Total and Capture Cross Sections

The subcritical polyethylene-reflected plutonium (PERP) metal fundamental physics benchmark, which is included in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook, has been selected to serve as a paradigm illustrative reactor physics system for the application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) that was developed by Cacuci. The 2nd-ASAM enables the exhaustive deterministic computation of the exact values of the 1st-order and 2nd-order sensitivities of a system response to the parameters underlying the respective system. The PERP benchmark is numerically modeled in this work by using the deterministic multigroup neutron transport equation discretized in the spatial and angular independent variables. Thus, the numerical model of the PERP benchmark developed includes the following imprecisely known uncertain parameters: 180 group-averaged total microscopic cross sections, 21,600 group-averaged scattering microscopic cross sections, 120 fission process parameters, 60 fission spectrum parameters, 10 parameters describing the experiment’s nuclear sources, and six isotopic number densities. Thus, the numerical simulation model for the PERP benchmark comprises 21,976 uncertain parameters, which implies that, for any response of interest, there are a total of 21,976 first-order sensitivities and 482,944,576 second-order sensitivities with respect to the model parameters. Computing these sensitivities exactly represents the largest sensitivity analysis endeavor ever carried out in the field of reactor physics. Only 241,483,276 are distinct from each other, and some of these turned out to be zero due to the symmetry of the 2nd-order sensitivities. The numerical results for all of these sensitivities, together with discussions of their major impacts, will be presented in a sequence of publications in the Special Issue of Energies dedicated to “Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling of Nuclear Energy Systems”. This work is the first in this sequence, presenting formulas of general use for neutron transport problems, along with the numerical results that were produced by these formulas for the 180 first-order and 32,400 second-order sensitivities of the PERP leakage response with respect to the neutron transport model’s group-averaged isotopic total cross sections. For comparison, this work also presents formulas of general use and numerical results for the 180 first-order and 32,400 second-order sensitivities of the PERP leakage response with respect to the neutron transport model’s group-averaged isotopic capture cross sections. It has been widely believed hitherto that, for reactor physics systems modeled by the neutron transport or diffusion equations, the second-order sensitivities are all much smaller than the first-order ones. However, contrary to this widely held belief, the numerical results that were obtained in this work prove, for the first time ever, that many of the 2nd-order sensitivities are much larger than the corresponding 1st-order ones, so their effects can become much larger than the corresponding effects stemming from the 1st-order sensitivities. For example, the 2nd-order sensitivities of the PERP leakage response cause the expected value of this response to be significantly larger than the corresponding computed value. The importance of the 2nd-order sensitivities increases as the relative standard deviations for the cross sections increase. For the extreme case of fully correlated cross sections, for example, neglecting the 2nd-order sensitivities would cause an error as large as 2000% in the expected value of the leakage response and up to 6000% in the variance of the leakage response. The significant effects of the mixed 2nd-order sensitivities underscore the need for reliable values for the correlations that might exist among the total cross sections, which are unavailable at this time. The 2nd-order sensitivities with respect to the total cross sections also cause the response distribution to be skewed towards positive values relative to the expected value. Hence, neglecting the 2nd-order sensitivities could potentially cause very large non-conservative errors by under-reporting of the response variance and expected value.