Regular Problems Research Articles

Parametric Aeroelastic Reduced-Order Model with State-Consistence Enforcement

State-space reduced-order models (ROMs) constructed by traditional system identification methods suffer from the state-inconsistence issue and poor ROM interpolatability for varying flight conditions. This paper presents a novel system identification method and a state-consistence enforcement (SCE) algorithm to generate a state-space aeroelastic (AE)-ROM within a broad flight parameter space. A new regularization term is proposed to modify the traditional autoregressive exogenous formulation and specifically penalize state inconsistence between ROMs at varying flight conditions. The new formulation cast in the form of the generalized Tikhonov regularization problem can be computed very efficiently and produce fundamentally state-consistent ROMs. Rigorous numerical analysis that compares the state-consistent AE-ROM with the full-order model and the ROM without SCE is also conducted. The results convincingly prove that the proposed approach significantly improves the state consistence of ROMs at varying flight conditions. To the best of our knowledge, this research represents the first effort of developing a state-consistent data-driven AE-ROM and enabling aeroelasticity analysis within a broad flight parameter space.

Carleson perturbations for the regularity problem

We prove that the solvability of the regularity problem in L^q(\partial \Omega) is stable under Carleson perturbations. If the perturbation is small, then the solvability is preserved in the same L^q , and if the perturbation is large, the regularity problem is solvable in L^{r} for some other r\in (1,\infty) . We extend an earlier result from Kenig and Pipher to very general unbounded domains, possibly with lower dimensional boundaries as in the theory developed by Guy David and the last two authors. To be precise, we only need the domain to have non-tangential access to its Ahlfors regular boundary, together with a notion of gradient on the boundary.

Hybrid reconstruction framework for model-based multispectral bioluminescence tomography based on Alpha-divergence

Bioluminescence tomography (BLT) is a promising imaging modality that can provide noninvasive three-dimensional visualization information on tumor distribution. In BLT reconstruction, the widely used methods based on regularization or greedy strategy face problems such as over-sparsity, over-smoothing, spatial discontinuity, poor robustness, and poor multi-target resolution. To deal with these problems, combining the advantages of the greedy strategies as well as regularization methods, we propose a hybrid reconstruction framework for model-based multispectral BLT using the support set of a greedy strategy as a feasible region and the Alpha-divergence to combine the weighted solutions obtained by [Formula: see text]1-norm and [Formula: see text]2-norm regularization methods. In numerical simulations with digital mouse and in vivo experiments, the results show that the proposed framework has better localization accuracy, spatial resolution, and multi-target resolution.

Wall laminar nanofluid jet flow and heat transfer

PurposeThis work aims to investigates exact solutions of the classical Glauert’s laminar wall jet mass and heat transfer under wall suction, wall contraction or dilation, and two thermal transport boundary conditions; prescribed constant surface temperature and prescribed constant surface flux in nanofluidic environment.Design/methodology/approachThe flow system arranged in terms of partial dif- ferential equations is non-dimensionalized with suitable dimensionless transformation variables, and this new set of equations is reduced into ordinary differential equations via a set of similarity transformations, where they are treated analytically for closed form solutions.FindingsExact solutions of nanofluid flow for velocity distributions, momentum flux, wall shear stress and heat transfer boundary layers for commonly studied nanoparticles; namely copper, alumina, silver, and titanium oxide are presented. The flow behavior of alumina and titanium oxide is identical, and a similar behavior is seen for copper and silver, making two pairs of identical traits. The mathematical expressions as well as visual analysis of wall shear drag and temperature gradient which are of practical interest are analyzed. It is shown that wall stretching or shrinking, wall transpiration and velocity slip together influences the jet flow mechanism and extends the original Glauert’s jet solutions. The exact solutions for the two temperature boundary layer conditions and temperature gradients are analyzed analytically. It is found that the effect of nanopar- ticles concentration on thermal boundary layer is intense, causing temperature uplift, whereas the wall transpiration causes a decrease in thermal layers.Originality/valueThe analysis carried out in nanofluid environment is genuinely new and unique, as our work generalizes the Glauert’s classical regular wall jet fluid problem.

AN OPTIMAL GRADIENT ESTIMATE FOR ASYMPTOTICALLY REGULAR VARIATIONAL INTEGRALS WITH MULTI-PHASE

We devote this article to the Calderón-Zygmund estimate for the minimizers of asymptotically regular variational integrals with multi-phase integrands. A local gradient Lq-estimate for such problem under a sharp regular assumption is obtained by approximating the solutions of asymptotically regular problems to the solutions of regular problems based on a new perturbation method, while the gradients of solutions close to infinity.

Gradient estimate for asymptotically regular elliptic equations of double phase with variable exponents

AbstractWe devote this paper to the proof of a regularity result for the solutions of asymptotically regular elliptic equations with ‐growth. By approximating the solutions of asymptotically regular problems with the solutions of regular problems based on a new perturbation method while the gradients of solutions close to infinity, we derive an interior Calderón–Zygmund estimate.

An efficient IMEX method for nonlinear functional differential equations with state-dependent delay

Implicit-explicit midpoint (IMEX MP) formula is proposed to solve numerically nonlinear neutral functional differential equations (NFDEs) with state-dependent delay. Since the deviating argument will be explicitly treated, the proposed method is extremely effective. Second order convergence of this method is shown theoretically and numerically for NFDEs with smooth solutions and Volterra functional differential equations (VFDEs). For general NFDEs with nonsmooth solutions, regularization problem by smoothing the initial data is introduced and analyzed. The regularization error is derived in maximum norm. The global errors of IMEX MP method are derived and reveal that it is only first order of convergence for this regularization error or for the non-smoothness of the original problems. Numerical examples are provided to support the theoretical analysis, compared with IMEX Euler method.

Global Well-Posedness of the 2D MHD Equations of Damped Wave Type in Sobolev Space

The magnetohydrodynamic system of damped wave type (abbreviated as MHD-wave system) is formally derived from Maxwell's equations of electromagnetism by keeping the usually ignored small term involving the product of permittivity and magnetic permeability. When this term is ignored in the context of nonrelativistic charged fluid, one obtains the standard MHD system. This extra term in the MHD-wave system assumes the form $\gamma \partial_{tt} b$ with $\gamma>0$ being a small constant and $b$ the magnetic field. Mathematically this term makes the global well-posedness problem much more challenging than the corresponding MHD system. Even the global existence and regularity problem for the 2D MHD-wave system appears to be open. This paper solves the global well-posedness problem in a critical Sobolev setting when $\gamma$ and the size of the initial data satisfy a suitable constraint. In addition, the solution of the MHD-wave system is shown to converge to that of the corresponding MHD system with an explicit rate. The energy method does not work here, and this paper presents a new approach.

An inexact ADMM with proximal-indefinite term and larger stepsize

In this paper, an inexact Alternating Direction Method of Multipliers (ADMM) has been proposed for solving the two-block separable convex optimization problem subject to linear equality constraints. The first resulting subproblem is solved inexactly under relative error criterion, while another subproblem called regularization problem is solved inexactly by introducing an indefinite proximal term. Meanwhile, the dual variable is updated twice with relatively larger stepsizes since an indefinite proximal term is exploited. By reformulating the first-order optimality conditions of the involved subproblems as a monotone inclusion problem, the sublinear convergence rate of the proposed algorithm is established in the pointwise and ergodic sense. Numerical experiments on testing two sparse optimization problems from statistical learning and image restoration indicate that our inexact ADMM performs much better than several well-established algorithms.

Regularization by transport noises for 3D MHD equations

We consider the problem of regularization by noise for the three dimensional magnetohydrodynamical (3D MHD) equations. It is shown that, in a suitable scaling limit, multiplicative noise of transport type gives rise to bounds on the vorticity fields of the fluid velocity and magnetic fields. As a result, if the noise intensity is big enough, then the stochastic 3D MHD equations admit a pathwise unique global solution for large initial data, with high probability.

Determination of the right-hand side in elliptic equations

ABSTRACT The problem of determining a term in the right-hand side of elliptic equations from an observation on a part of the boundary is investigated. The inverse problem is formulated as an operator equation and then stabilized by Tikhonov regularization method. The regularized problem is discretized based on Hinze's variational discretization concept and the regularization parameter is chosen guaranteeing that when noise level and the discretization mesh size tend to zero, the solution of the discretized regularized problem converges to the f ∗ -minimum norm solution of the continuous inverse problem. Some numerical examples are presented for illustrating the performance of the proposed method.

A Comprehensive Review on Journey of Pyrrole Scaffold Against Multiple Therapeutic Targets.

Heterocyclic compounds are that type of substances that are deeply intertwined with biological processes. Heterocycles are found in about 90% of commercially available medicines. In medicinal chemistry, finding new synthetic molecules with drug-like characteristics is a regular problem, which triggered the development of pharmacological molecules, the majority of which are based on N-heterocyclic motifs. Among the heterocycles, the pyrrole scaffold is the most commonly found heterocycle in both natural and synthetic bioactive compounds. Pyrrole has a fivemembered heterocyclic ring with a plethora of pharmacophores, resulting in a library of different lead compounds. Pyrrole derivatives are physiologically active heterocyclic compounds that can be used as scaffolds for antibacterial, antiviral, anticancer, antitubercular, anti-inflammatory, and as enzyme inhibitors. On account of their extensive pharmacological profile, pyrrole and its various synthetic derivatives have drawn much attention from researchers to explore it for the benefit of humankind. This review presents an overview of recent developments in the pyrrole derivatives against multiple therapeutic targets.

Comment on ‘PRISMA: A robust and intuitive tool for high‐throughput processing of chemical spectra’

AbstractThe analysis of spectral data, and in particular the quantification of these, highly depends on curve fitting the spectra with suitable methods. The required methodologies have been known for very long. However, even today it is a regular problem that this, i.e. physically correct analyzing spectral data, is not practiced.

Boundary Feedback Stabilization of Two-Dimensional Shallow Water Equations with Viscosity Term

This paper treats a water flow regularization problem by means of local boundary conditions for the two-dimensional viscous shallow water equations. Using an a-priori energy estimate of the perturbation state and the Faedo–Galerkin method, we build a stabilizing boundary feedback control law for the volumetric flow in a finite time that is prescribed by the solvability of the associated Cauchy problem. We iterate the same approach to build by cascade a stabilizing feedback control law for infinite time. Thanks to a positive arbitrary time-dependent stabilization function, the control law provides an exponential decay of the energy.

Bus Transit Operations Control: Review and an Experiment Involving Tri-Met’s Automated Bus Dispatching System

Tri-Met has implemented an automated bus dispatching system (BDS) employing satellite-based automatic vehicle location (AVL) technology. The BDS is capable of facilitating real-time operations control actions to improve service regularity. This article focuses on a service regularity problem that often occurs during peak periods when regular service is augmented by extra-board trips (“trippers”). In this case, “bus bunching” results when regular service trips experience departure delays while trippers depart on schedule. With the aid of BDS information, field supervisors stationed at a key location on Portland’s (Oregon) bus mall used holding, short turning, and reassignment actions to maintain headways on six selected routes. Analysis of their efforts reveals an improvement in service regularity as well as a leveling of passenger loads.

The Mott-Smith solution to the regular shock reflection problem

The classical Mott-Smith solution for one-dimensional normal shock wave structure is extended to the two-dimensional regular shock reflection problem. The solution for the non-equilibrium molecular velocity distribution function along the symmetry-plane streamline is obtained as a weighted sum of four Maxwellians. An analysis of applicability of the solution has been performed using the results of direct simulation Monte Carlo calculations for a range of incident shock wave intensities. Accuracy of the solution improves with increasing$Ma_n$, the Mach number normal to the shock front, so that the solution becomes rather accurate for strong shocks with$Ma_n>8$.

A parallel discrete unified gas kinetic scheme on unstructured grid for inviscid high-speed compressible flow simulation

The discrete unified gas kinetic scheme (DUGKS) is a recently devised approach to simulate multiscale flows based on the kinetic models, which also shows distinct features for continuum flows. Most of the existing DUGKS are sequential or based on structured grids, thus limiting their scope of application in engineering. In this paper, a parallel DUGKS for inviscid high-speed compressible flows on unstructured grids is proposed. In the framework of the DUGKS, the gradients of the distribution functions are calculated by a least-square method. To parallelize the method, a graph-based partitioning method is employed to guarantee the load balancing and minimize the communication among processors. The method is validated by several benchmark problems, i.e., a two-dimensional (2D) Riemann problem, 2D subsonic flows passing two benchmark airfoils, a 2D regular shock reflection problem, 2D supersonic flows (Mach numbers are 3 and 5) around a cylinder, an explosion in a three-dimensional (3D) box, a 3D subsonic flow around the Office National d'Etudes et de Recherches Aérospatiales M6 wing, a 3D hypersonic flow (Mach number is 10) around a hemisphere, and a supersonic flow over the Northrop YF-17 fighter model. The numerical results show good agreement with the published results, and the present method is robust for a wide range of Mach numbers, from subsonic to hypersonic. The parallel performance results show that the proposed method is highly parallel scalable, where an almost linear scalability with 93% parallel efficiency is achieved for a 3D problem with over 55 × 106 tetrahedrons on a supercomputer with up to 4800 processors.

DIFFERENCE AND PRIMITIVE OPERATORS ON THE DUNKL-TYPE FOCK SPACE $$\mathscr {F}_{\alpha }(\mathbb {C}^{d})$$

In 1961, Bargmann introduced the classical Fock space $$\mathscr {F}(\mathbb {C}^{d})$$ and in 1984, Cholewinsky introduced the generalized Fock space $$\mathscr {F}_{\alpha ,e}(\mathbb {C}^{d})$$ . These two spaces are the aim of many works, and have many applications in mathematics, in physics, and in quantum mechanics. In this work, we introduce and study the Fock space $$\mathscr {F}_{\alpha }(\mathbb {C}^{d})$$ associated to the Dunkl operators $$T_{\alpha _{j}}$$ with $$\alpha _{j}>-1/2$$ for all $$j=1,\ldots ,d$$ . This space is an extension of the Dunkl-type Fock space $$\mathscr {F}_{\alpha }(\mathbb {C})$$ constructed by Sifi and Soltani in 2002. We prove that the space $$\mathscr {F}_{\alpha }(\mathbb {C}^{d})$$ is a Hilbert space with reproducing kernel. Next, we give an application of the classical theory of reproducing kernels to the Tikhonov regularization problem for the bounded linear operator $$\mathscr {L}:\mathscr {F}_{\alpha }(\mathbb {C}^{d})\rightarrow \mathscr {H}$$ , where $$\mathscr {H}$$ is a Hilbert space. Finally, we come up with some results regarding the extremal functions, when $$\mathscr {L}$$ is the difference operator and the primitive operator, respectively.

Robust tensor recovery with nonconvex and nonsmooth regularization

This paper considers the least squares loss minimization problem regularized by tensor average rank and zero norm, to decompose the noisy observation into a low-rank tensor, a sparse tensor and a noise tensor. Due to the nonconvex and nonsmooth of the average rank and the zero norm of tensors, it is not easy to solve the problem directly. We construct the variational characterizations of the tensor average rank and the tensor zero norm, get an equivalent mathematical program with an equilibrium constraint, and then propose an equivalent Lipschitz surrogate for the regularization problem by adding the equality constraint into the objective. Moreover, we design a convex algorithm with multi-stage to verify the efficiency of the proposed method. Numerical experiments are reported for simulation data and actual data to show the performance of the new method.

Existence and regularity of solutions for a 3D coupled parabolic-elliptic equations related to magnetic relaxation

This paper is devoted to the existence and regularity problem of a 3D coupled parabolic-elliptic equations that arises in the study of the magnetostatic equilibria. We first show a uniform a priori estimate and the global existence of the approximation equations, as well as a convergence property of the approximate solutions. These results are used to prove the local well-posedness of the original equations. Then an optimal regularity criterion for strong solutions of the equations is established. Under the assumption that the initial magnetic field is small in some critical Besov spaces, this criterion leads to the global-in-time existence of strong solutions. The proof of which relies on a commutator estimate established in the paper.