Lower Order Part Research Articles

Design and application of weight-on-bit control system for drilling process: A variable-gain integrated controller with multiple-model parameter estimation

Controlling weight-on-bit is essential in the drilling process, which determines the rock-breaking performance, drill bit wear, and wellbore quality. This paper aims to develop a weight-on-bit control system for field implementation, using a variable-gain integrated controller and a multiple-model parameter estimator. First, a weight-on-bit dynamic model for controller synthesis is derived according to the real drilling scenario. Then, the integrated controller is designed with two parts: a variable-gain proportional–integral controller and a dynamic output feedback controller, which separates the design of the system’s high-order from low-order parts. The controller gain is tuned through a multiple-model parameter estimator, which estimates uncertain parameters related to rock strength. The established control system is implemented in a typical electrical drilling rig. It meets the requirement of adapting to different formations, considering the flexible drill string and the variable feed motor speed threshold. Numerical and field application results confirm the effectiveness of the developed system.

Segmented Tag Cache: A Novel Cache Organization for Reducing Dynamic Read Energy

A set-associative cache organization is widely used to achieve a high hit-rate in modern caches, leading to a considerable enhancement in the system performance. In a conventional set-associative cache, tag and data arrays are simultaneously accessed to achieve fast access, but doing so causes a large amount of energy consumption. Previous attempts, such as way prediction and sequential tag access for energy reduction, are still associated with substantial energy consumption due to the tag access. This paper presents a new cache organization termed Segmented Tag Cache (STC), which reduces the amount of energy consumed during the tag access. The proposed organization initially implements a new tag organization that supports partial tag access. More specifically, the tag array is segmented into two parts, and partial tag access only reads low-order part of the tag. A cache access scheme suitable for the proposed tag organization then are developed. Under the scheme, the delay of the tag organization is hidden by the data access delay, avoiding an increase in the overall cache access time to be maintained. Simulation results show that the STC reduces the energy-delay product by approximately 58 percent compared to the conventional cache organizations with a negligible performance penalty.

Approximation in law of locally $\alpha $-stable Lévy-type processes by non-linear regressions

We study a real-valued Levy-type process $X$, which is locally $\alpha $-stable in the sense that its jump kernel is a combination of a ‘principal’ (state dependent) $\alpha $-stable part with a ‘residual’ lower order part. We show that under mild conditions on the local characteristics of a process (the jump kernel and the velocity field) the process is uniquely defined, is Markov, and has the strong Feller property. We approximate $X$ in law by a non-linear regression $\widetilde{X} ^{x}_{t}=\mathfrak{f} _{t}(x)+t^{1/\alpha }U^{x}_{t} $ with a deterministic regressor term $\mathfrak{f} _{t}(x)$ and $\alpha $-stable innovation term $U^{x}_{t}$, and provide error estimates for such an approximation. A case study is performed, revealing different types of assumptions which lead to various choices of regressor/innovation terms and various types of the estimates. The assumptions are quite general, cover the super-critical case $\alpha <1$, and allow non-symmetry of the Levy kernel and unboundedness of the drift coefficient.

Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics

We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J. Comput. Phys. 230(11):4248-4267, 2011, doi:10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J. Comput. Phys. 136(1):83-99, 1997, doi:10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to {sim}50% speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.

Integration by parts and Pohozaev identities for space-dependent fractional-order operators

Consider a classical elliptic pseudodifferential operator P on Rn of order 2a(0<a<1) with even symbol. For example, P=A(x,D)a where A(x,D) is a second-order strongly elliptic differential operator; the fractional Laplacian (−Δ)a is a particular case. For solutions u of the Dirichlet problem on a bounded smooth subset Ω⊂Rn, we show an integration-by-parts formula with a boundary integral involving (d−au)|∂Ω, where d(x)=dist(x,∂Ω). This extends recent results of Ros-Oton, Serra and Valdinoci, to operators that are x-dependent, nonsymmetric, and have lower-order parts. We also generalize their formula of Pohozaev-type, that can be used to prove unique continuation properties, and nonexistence of nontrivial solutions of semilinear problems. An illustration is given with P=(−Δ+m2)a. The basic step in our analysis is a factorization of P, P∼P−P+, where we set up a calculus for the generalized pseudodifferential operators P± that come out of the construction.

On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem

The existence and uniqueness in Sobolev spaces of solutions of the Cauchy problem to parabolic integro-differential equation with variable coefficients of the order α∈(0,2) is investigated. The principal part of the operator has kernel m(t,x,y)/|y|d+α with a bounded nondegenerate m, Hölder in x and measurable in y. The lower order part has bounded and measurable coefficients. The result is applied to prove the existence and uniqueness of the corresponding martingale problem.

Sampling-free linear Bayesian update of polynomial chaos representations

We present a fully deterministic approach to a probabilistic interpretation of inverse problems in which unknown quantities are represented by random fields or processes, described by possibly non-Gaussian distributions. The description of the introduced random fields is given in a “white noise” framework, which enables us to solve the stochastic forward problem through Galerkin projection onto polynomial chaos. With the help of such a representation the probabilistic identification problem is cast in a polynomial chaos expansion setting and the Baye’s linear form of updating. By introducing the Hermite algebra this becomes a direct, purely algebraic way of computing the posterior, which is comparatively inexpensive to evaluate. In addition, we show that the well-known Kalman filter is the low order part of this update. The proposed method is here tested on a stationary diffusion equation with prescribed source terms, characterised by an uncertain conductivity parameter which is then identified from limited and noisy data obtained by a measurement of the diffusing quantity.

On Nontrivial Solutions of Variational-Hemivariational Inequalities with Slowly Growing Principal Parts

This paper is concerned with the inclusion −\mathrm{div}(a(|∇u|)∇u) + ∂_u G(x,u) \ni 0 \quad \text{in } Ω, with Dirichlet boundary condition u = 0 on ∂Ω , in the case where the higher order part has slow growth and the lower order part is locally Lipschitz. By using a Mountain Pass theorem for variational-hemivariational inequalities without the Palais–Smale condition in Orlicz–Sobolev spaces, we show the existence of nontrivial solutions of the above inclusion.

Making Room for Mental Space

According to the consensus cosmological theory of the inflationary big bang, the universe originated about 14 billion years ago with no initial conditions, inherent nature, order, or purpose—from literally nothing. Instantaneously it was randomly fluctuating quantized gravity and Higgs fields that through spontaneous symmetry breaking formed into four fundamental particle-forces. The forces congealed into atomic structures, elements, stars, planets, organic molecules, living cellular organisms, and eventually humans with complex enough nervous systems to generate higher-order conscious mind with apparent causal control of its lower-order parts. How the closed physical causal chain unlinked and inserted a causally efficacious conscious mind at some stage of neural complexity is inexplicable; there is no room for it in the physicalist view—it must be epiphenomenal and a fundamental misperception. A coherent alternative is developing in quantum and quantum gravity theories of a proposed information space or nonlocal mental space underneath the physical. The progression of theories is overviewed with respect to the nature of space, and are shown to be increasingly consistent with holistic interpretations of ancient Vedic science that make room for a causally efficacious conscious mind.

A finite element formulation with stabilization matrix for geometrically non-linear shells

An assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically non-linear problems of isotropic and laminated composite shells. The present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement. The assumed independent strain field is divided into a lower order part and a higher order part. Subsequently, the lower order part is set equal to the displacement-dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix. The strains and the determinant of the Jacobian matrix are assumed to vary linearly in the thickness direction. This assumption allows analytical integration through thickness, independent of the number of plies. A nine-node element with a judiciously chosen set of higher order assumed strain field is developed. Numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation.

A sixteen node shell element with a matrix stabilization scheme

A sixteen node shell element is developed using a matrix stabilization scheme based on the Hellinger-Reissner principle with independent strain. Initially the assumed independent strain is divided into a lower order part and a higher order part. The stiffness matrix corresponding to the lower order assumed strain is equivalent to the stiffness matrix of the assumed displacement model element with the reduced integration scheme. The spurious kinematic modes of the element are suppressed by introducing a stabilization matrix associated with a judiciously chosen set of higher order assumed strain fields. Numerical results show that this element is free of locking even for very thin plates and shells.

Propagation of singularities for operators with constant coefficient hyperbolic-elliptic principal part

In this paper we consider partial differential operators of the type P(x, D)= Pm(D)+Q(x, D), where the constant coefficient principal part Pm is supposed to be hyperbolic-elliptic. We study the propagation of Gevrey singularities for solutions u of the equation P(x, D) u=f, for ultradistributions f, finding exactly to which spaces of ultradistribuiions u microlocally belongs. The results are obtained by constructing a fundamental solution for P when the lower order part Q is with constant coefficients, and a parametrix otherwise.

A new efficient mixed formulation for thin shell finite element models

AbstractA nine node shell element is developed by a new and more efficient mixed formulation. The new shell element formulation is based on the Hellinger–Reissner principle with independent strain and the concept of a degenerate solid shell. The new formulation is made more efficient in terms of computing time than the conventional mixed formulation by dividing the assumed strain fields into a lower order part and a higher order part. Numerical results demonstrate that the present nine node element is free of locking even for very thin plates and shells and is also kinematically stable. In fact the stiffness matrix associated with the higher order assumed strain plays the role of a stabilization matrix.