Singular Scheme Research Articles

Weakly nonlinear electrophoresis of a highly charged colloidal particle

At large zeta potentials, surface conduction becomes appreciable in thin-double-layer electrokinetic transport. In the linear weak-field regime, where this effect is quantified by the Dukhin number, it is manifested in non-Smoluchowski electrophoretic mobilities. In this paper we go beyond linear response, employing the recently derived macroscale model of Schnitzer and Yariv [“Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction,” Phys. Rev. E 86, 021503 (2012)10.1103/PhysRevE.86.021503] as the infrastructure for a weakly nonlinear analysis of spherical-particle electrophoresis. A straightforward perturbation in the field strength is frustrated by the failure to satisfy the far-field conditions, representing a non-uniformity of the weak-field approximation at large distances away from the particle, where salt advection becomes comparable to diffusion. This is remedied using inner-outer asymptotic expansions in the spirit of Acrivos and Taylor [“Heat and mass transfer from single spheres in Stokes flow,” Phys. Fluids 5, 387 (1962)10.1063/1.1706630], with the inner region representing the particle neighborhood and the outer region corresponding to distances scaling inversely with the field magnitude. This singular scheme furnishes an asymptotic correction to the electrophoretic velocity, proportional to the applied field cubed, which embodies a host of nonlinear mechanisms unfamiliar from linear electrokinetic theories. These include the effect of induced zeta-potential inhomogeneity, animated by concentration polarization, on electro-osmosis and diffuso-osmosis; bulk advection of salt; nonuniform bulk conductivity; Coulomb body forces acting on bulk volumetric charge; and the nonzero electrostatic force exerted upon the otherwise screened particle-layer system. A numerical solution of the macroscale model validates our weakly nonlinear analysis.

Reduced-order, nonlinear approximation of catenary riser dynamics using frequency domain identification

This paper demonstrates an approximation to the numerical solution of the dynamic equilibrium of a catenary riser. The approximant is obtained in the frequency domain when the structure is excited by motions applied at the top. The dynamic equilibrium is formulated mathematically through six nonlinear partial differential equations which involve both geometric and hydrodynamic nonlinearities. The latter are represented by the Morison’s formula. The numerical solution of the six nonlinear differential equations is used to generate spatio-temporal data series for riser bending moments induced by sinusoidal heave motions of various amplitudes and frequencies. The data series are transformed to the frequency domain where a complex singular value decomposition scheme is applied in order to reconstruct the full nonlinear spectrum. The significant harmonics of the riser’s spectrum are then identified as the three lower odd harmonics. The method finally provides a set of orthogonal modes for all significant harmonics; that is, the fundamental, the third and the fifth harmonic of the bending moment in the 2D plane of reference. The nonlinear, frequency-domain modal decomposition proposed is also examined in a typical test case.

GA-based decoupled adaptive FSMC for nonlinear systems by a singular perturbation scheme

Generally, the difficulty with multivariable system control is how to overcome the coupling effects for each degree of freedom. The computational burden and dynamic uncertainty of multivariable systems makes the model-based decoupling approach hard to implement in a real-time control system. In this study, an intelligent adaptive controller is proposed to handle these behaviors. The structure of these model-free new controllers is based on fuzzy systems for which the initial parameter vector values are found based on the genetic algorithm. One modified adaptive law is derived based on Lyapunov stability theory to control the system for tracking a user-defined reference model. The requirement of the Kalman–Yacubovich lemma is fulfilled. In addition, a non-square multivariable system can be decoupled into several isolated reduced-order square multivariable subsystems by using the singular perturbation scheme for different time-scale stability analysis. The adjustable parameters for the intelligent system can be initialized using a genetic algorithm. Novel online parameter tuning algorithms are developed based on the Lyapunov stability theory. A boundary-layer function is introduced into these updating laws to cover parameter and modeling errors and to guarantee that the state errors converge into a specified error bound. Finally, a numerical simulation is carried out to demonstrate the control methodology that can rapidly and efficiently control nonlinear multivariable systems.

ON THE SINGULAR SCHEME OF CODIMENSION ONE HOLOMORPHIC FOLIATIONS IN ℙ3

In this work, we begin by showing that a holomorphic foliation with singularities is reduced if and only if its normal sheaf is torsion-free. In addition, when the codimension of the singular locus is at least two, it is shown that being reduced is equivalent to the reflexivity of the tangent sheaf. Our main results state on one hand, that the tangent sheaf of a codimension one foliation in ℙ3 is locally free if and only if the singular scheme is a curve, and that it splits if and only if it is arithmetically Cohen–Macaulay. On the other hand, we discuss when a split foliation in ℙ3 is determined by its singular scheme.

Bornes pour la régularité de Castelnuovo-Mumford des schémas non lisses

We establish bounds for the Castelnuovo-Mumford regularity of singular scheme, in terms of the degrees of the equations defining the scheme and of the dimension of the singular locus. In the case where the singularities are isolated, we improve the bound given by Chardin and Ulrich, and in the general case we establish a bound doubly exponential in the dimension of the singular locus.

Determination of optimal accelerometer locations using modal sensitivity for identifying a structure

A new algorithm is proposed to determine optimal accelerometer locations (OAL) when a structure is identified by frequency domain system identification (SI) method. As a result, a guideline is presented for selecting OAL which can reflect modal response of a structure properly. The guideline is to provide a minimum number of necessary accelerometers with the variation in the number of measurable target modes. To determine OAL for SI applications effectively, the modal sensitivity effective independence distribution vector (MS-EIDV) is developed with the likelihood function of measurements. By maximizing the likelihood of the occurrence of the measurements relative to the predictions, Fisher Information Matrix (FIM) is derived as a function of mode shape sensitivity. This paper also proposes a statistical approach in determining the structural parameters with a presumed parameter error which reflects the epistemic paradox between the determination of OAL and the application of a SI scheme. Numerical simulations have been carried out to examine the proposed OAL algorithm. A two-span multi-girder bridge and a two-span truss bridge were used for the simulation studies. To overcome a rank deficiency frequently occurred in inverting a FIM, the singular value decomposition scheme has been applied.

Detection of abrupt structural damage induced by an earthquake using a moving time window technique

This paper presents a time domain system identification (SI) scheme for detection of sudden structural damage that occurs during an earthquake. A moving time window technique is proposed to trace abrupt changes in the structural parameters caused by sudden damage. The time window represents a finite time interval, in which the SI procedures are performed assuming time-invariant system parameters. As the time window moves forward, the variation of system parameters in time is identified. The error function is defined as the time integral of the squared errors between measured accelerations and calculated accelerations by a mathematical model. Structural damping is approximated by the Rayleigh damping model, and damping properties as well as stiffness properties of a structure are considered as system parameters. A regularization technique is adopted to alleviate the ill-posed characteristics of SI problems. In the formulation of a new regularization function in time domain, a weighting factor is introduced to balance the relative regularization effect between stiffness and damping parameters. A truncated singular value decomposition scheme is applied to impose the regularization function on the minimization of the error function. Numerical simulation studies are presented to demonstrate the validity of the proposed method.

Exact Solutions of Some Discrete Deconvolution Problems

In this work, we study the existence of solutions of the deconvolution problems in the discrete setting. More precisely, we prove the existence of solutions of the discrete multichannel deconvolution problems DMDP with convolvers being the characteristic functions of finite sets of positive integers. Also, we provide the reader with a simple method and a fast algorithm for finding the closed forms of the discrete deconvolvers with minimal supports that constitute exact solutions of the DMDP. Moreover, we show that unlike the singular value decomposition scheme, the multichannel deconvolution scheme based on the use of these discrete deconvolvers is not very sensitive to small 2-norm perturbation of the data. Finally, we show how to generalize our method for solving the 2-D version of the DMDP.

Dynamics and control designs for internal thermally coupled distillation columns with different purities, Part 2 : close loop analysis and control designs*

Abstract Interaction between overhead and bottom composition loops of internal thermally coupled distillation columns (ITCDIC) with four purities are analyzed by means of relative gain array, condition number and singular value decomposition, which indicates that high and very high-purity ITCDIC are well coupled and ill-conditioned systems with severe gain directionality problem. Based on the above dynamic behaviors, suitable control schemes of four different purity systems are studied. In low-purity system, internal model control (IMC) is better than decentralized proportion integral differential (D-PID) control in terms of response speed and remaining errors. In moderate-purity system, D-PID can effectively reject large load disturbances while IMC fails due to severe mismatch between model and plant. In high-purity system, neither IMC nor D-PID can provide satisfactory control so that modified IMC and multivariable PID with singular value decomposition scheme are presented respectively to improve contro...

In-Situ Determination of the Transformer Core's Magnetization Characteristics on HT-7 Superconducting Tokamak

As a complex physics system, the tokamak plasma is strongly coupled with external poloidal fields, which are defined by electromagnetic circuits. For the HT-7 device with an iron core, the transformer magnetization plays the most important role. With a reasonable two-dimensional magnetizing current filament model, the magnetization curve was numerically derived from in-situ external magnetic experimental data detected by flux loops and small pick-up coils. To solve the ill-posed inverse problem, singular value decomposition scheme and iterative procedures were used and proved to be effective. This provides a practical solution for in-situ determination of the transformer's magnetization characteristics. It paves the way for tokamak experiment prediction and plasma current profile reconstruction.

An iterative singular vectors estimation scheme for beamforming transmission and detection in MIMO systems

An iterative singular vectors estimation scheme for beamforming transmission and detection in MIMO systems

The Singular Sources Method for an Inverse Transmission Problem

We employ the singular sources method introduced in [4] to solve an inverse transmission scattering problem for the Helmholtz equation or D, respectively, where the total field u satisfies the transmission conditions on the boundary of some domain D with some constant β. The main idea of the singular sources scheme is to reconstruct the scattered field of point sources or higher multipoles (·, z) with source point z in its source point from the far field pattern of scattered plane waves. The function (z, z) is shown to become singular for z→∂D. This can be used to detect the shape D of the scattering object. Here, we will show how in addition to reconstructions of the shape D of the scattering object, the constant β can be reconstructed without solving the direct scattering problem. This extends the singular sources method from the reconstruction of geometric properties of an object to the reconstruction of physical quantities.

An iterative singular vectors estimation scheme for beamforming transmission and detection in MIMO systems

A novel iterative singular vector estimation scheme has been proposed for a beamforming transmission and detection in wireless multiple input multiple output (MIMO) systems. Two singular channel matrix vectors, which correspond to the largest singular value, are iteratively obtained at the transmitter and the receiver without estimating the channel coefficients. The proposed singular vectors estimation strategy has advantages over the conventional MIMO channel estimation schemes in terms of both frame-error-rate performance, bandwidth efficiency and computation complexity.

Coherent Sheaves on Configuration Schemes

We introduce and study configuration schemes, which are obtained by “glueing” usual schemes along closed embeddings. The category of coherent sheaves on a configuration scheme is investigated. Smooth configuration schemes provide alternative “resolutions of singularities” of usual singular schemes. We consider in detail the case when the singular scheme is a union of hyperplanes in a projective space.

A plane foliation of degree different from 1 is determined by its singular scheme

We prove that a foliation 877-1 of degree ≠ 1 on P 2 is completely determined by its singular subscheme SingS( 877-2) of P 2. We apply this result to obtain a similar characterization of 877-3 in terms of the configuration of base points associated to its singular scheme, in case every singularity of 877-4 has non-trivial linear part. Our main motivation comes from a well-known fact: in case a foliation 877-5 of degree r ≥ 2 on P n has only isolated singularities of multiplicity 1, then 877-6 is completely determined by its singular set Sing( 877-7).

Singular schemes of hypersurfaces

Let Y be the singular locus of a hypersurface X in a smooth variety M , with the scheme structure defined by the Jacobian ideal of X (we will say then that Y is the singular scheme of X, to emphasize that the scheme structure of Y is important for our considerations). In this note we consider a class in the Chow group of Y which arises naturally in this setup, and which captures much intersection-theoretic information about the situation. The guiding question we have in mind is: which schemes Y can arise as singular schemes of hypersurfaces? We will obtain strong constraints showing for instance that the only hypersurfaces in P whose singular schemes are positive dimensional linear subspaces of P are quadrics, and that no (reduced) nodal curve can be the singular scheme of a hypersurface in a non-singular variety. Many more statements of this sort can be found in section 3. A different type of application is in section 2: we show how our class relates to other invariants of the singularity of a hypersurface; the class can be used to recover results of Holme and Parusiǹski on degree and multiplicity of dual varieties, and leads naturally to a generalization of the notion of ‘ranks’ of a (smooth) projective variety. Also, we obtain a strengthening of Landman’s parity result, and a new proof of a result of Zak on the dimension of the dual of a smooth variety. The duality results follow by applying the framework to hyperplane sections of M : the singular scheme of a section is supported on the locus of contact of the hyperplane with M , and the class can be used to measure this contact. For example, the class measures how ‘general’ a given section is: we show (Corollary 2.6) that if the contact scheme is a linear subspace Pr−1, then the corresponding hyperplane is a smooth point of the dual variety of M , and the dual variety has codimension r. The main general results are in section 1, where we prove (Corollary 1.7) that the class we introduce depends in fact only on Y and on the line bundle L = O(X)|Y , and not on the ambient variety M (provided that Y is the singular scheme of a

Hydrodynamic interaction of two unequal-sized spheres in a slightly rarefied gas: resistance and mobility functions

The problem of the hydrodynamic interaction of two unequal-sized spheres in a slightly rarefied gas is treated following the singular perturbation scheme of Sone & Onishi (1978), valid at small, but finite, particle Knudsen numbers. In this method the solution to the linearized BGKW transport equation governing the gas molecular motion consists of two parts: one describing a Knudsen layer where the actual microscopic boundary conditions are applied and the other describing a Hilbert region where the Stokes equations of continuum hydrodynamics hold. The Knudsen-layer solution establishes the ‘slip’ boundary conditions for the Stokes equations. Here we clearly distinguish between particle ‘slip’ due to the type of boundary conditions and particle ‘slip’ due to lengthscale effects as measured by the Knudsen number. The present analysis has been carried out to first order in particle Knudsen number for the case of diffuse reflective molecular boundary conditions. General relationships between the first- and zero-order velocity fields, both of which are written in the form of Lamb's (1932) solution to the Stokes equation, are established. It is illustrated how these general relationships can be used to determine the force and torque acting on a single sphere translating and rotating in a slightly rarefied gas. Finally, we have treated the two-sphere problem in a slightly rarefied gas using the twin multipole expansion method of Jeffrey & Onishi (1984). Here again, general relationships are established between the solutions of the first-order fluid velocity field and the zero-order velocity field, the latter being shown to recover Jeffrey & Onishi's results for stick boundary conditions. These general relationships are subsequently used to determine the complete resistance and mobility matrices of the two-sphere system. The symmetric properties of the resistance and mobility matrices are demonstrated for slip boundary conditions, in agreement with the general proof of Landau & Lifshitz (1980) and Bedeaux, Albano & Mazur (1977).

New approaches in a 3-D one-carrier device solver

A 3-D one-carrier device solver has been developed on an Intel iPSC2 hypercube multiprocessor which can handle over 130 K nodes. CPU time averages 20 min per bias point on a 50 K-node MOSFET example. Slotboom variables are used in conjunction with the Scharfetter-Gummel current discretization scheme. A scaling scheme is proposed which produces n, p variables from the Slotboom variables. An improved damped-Newton scheme, which maintains the iteration numbers at below fifteen for high gate biases, is used in solving Poisson's equation. The performance of a previously proposed initial guess scheme is improved through the use of a novel update strategy during the Poisson solution stage after the initial guess step. This improvement allows stable calculation for voltage steps as high as 5 V. A modified singular perturbation scheme (MSP) has been proposed whose implementation speeds up the convergence under high-V/sub gs/ and -V/sub ds/ bias conditions by a factor of three to six. A block matrix analysis of the MSP scheme yields insight into its performance. >

Nonlinear waves on a rotating viscous fluid with a cylindrical free surface

An asymptotic theory is developed for the study of nonlinear wave motion of a rotating viscous fluid with a cylindrical free surface. The method used here is based upon a multiple-parameter singular perturbation scheme within the framework of long-wave approximation. Wave speed and a set of asymptotic evolution equations are derived, and a criterion for the instability of the wave motion is defined.