1,076 research outputs found
Positive definiteness of the blended force-based quasicontinuum method
No full textThe development of consistent and stable quasicontinuum models for multidimensional crystalline solids remains a challenge. For example, proving the stability of the force-based quasicontinuum (QCF) model [M. Dobson and M. Luskin, M2AN Math. Model. Numer. Anal., 42 (2008), pp. 113--139] remains an open problem. In one and two dimensions, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width
Big tight closure test elements for some non-reduced excellent rings
No full textAbstractThis paper is concerned with existence of big tight closure test elements for a commutative Noetherian ring R of prime characteristic p. Let R∘ denote the complement in R of the union of the minimal prime ideals of R. A big test element for R is an element of R∘ which can be used in every tight closure membership test for every R-module, and not just the finitely generated ones. The main results of the paper are that, if R is excellent and satisfies condition (R0), and c∈R∘ is such that Rc is Gorenstein and weakly F-regular, then some power of c is a big test element for R if (i) R is a homomorphic image of an excellent regular ring of characteristic p for which the Frobenius homomorphism is intersection-flat, or (ii) R is F-pure, or (iii) R is local. The Gamma construction is not used
Relation between enstrophy production and geometry near the turbulent/non-turbulent interface in free shear flows
No full textIn many free shear flows, such as mixing layers, wakes and jets exhibit a sharp turbulent/non-turbulent interface (TNTI) separating regions of turbulent and non-turbulent or potential flow. In the present work the dependence of enstrophy production on the interface geometry near the TNTI is investigated by using direct numerical simulations (DNS) of a shear free turbulence (SFT) and a temporally developing planar jet (PJET). It is shown that the geometry of the TNTI has impacts on the mechanism governing enstrophy dynamics within the interface layer itself. In particular it is shown that enstrophy production within the turbulent sublayer is primarily associated with a convex shape of the interface both the SFT and PJET
A theoretical framework for discontinuity capturing: Joining variational multiscale analysis and variation entropy theory
No full textIn this paper we show that the variational multiscale method together with the variation entropy concept form the underlying theoretical framework of discontinuity capturing. The variation entropy [M.F.P. ten Eikelder and I. Akkerman, Comput. Methods Appl. Mech. Engrg. 355 (2019) 261-283] is the recently introduced concept that equips total variation diminishing solutions with an entropy foundation. This is the missing ingredient in order to show that the variational multiscale method can capture sharp layers. The novel framework naturally equips the variational multiscale method with a class of discontinuity capturing operators. This class includes the popular YZβ method and methods based on the residual of the variation-entropy. The discontinuity capturing mechanisms do not contain ad hoc devices and appropriate length scales are derived. Numerical results obtained with quadratic NURBS are virtually oscillation-free and show sharp layers, which confirms the viability of the methodology.Accepted Author ManuscriptShip Hydromechanics and Structure
Right and left modules over the Frobenius skew polynomial ring in the f-finite case
No full textAbstractThe main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ringRof prime characteristic for which the Frobenius homomorphismfis finite, the appropriate restrictions of the Matlis-duality functor provide an equivalence between the category of left modules over the Frobenius skew polynomial ringR[x,f] that are Artinian asR-modules and the category of rightR[x,f]-modules that are Noetherian asR-modules.</jats:p
Foam Generation by Capillary Snap-Off in Flow Across a Sharp Permeability Transition
No full textAbstract
Foam reduces gas mobility and can improve sweep efficiency in an enhanced-oil-recovery process. Previous studies show that foam can be generated in porous media by exceeding a critical velocity or pressure gradient. Such pressure gradients are typically encountered only near a well and therefore, it is uncertain whether foam can propagate far from wells. Theoretical studies show that foam can be generated independent of pressure gradient during flow across an abrupt increase in permeability. In subsurface flow, such sharp permeability changes occur across different length scales. Laminations and cross-laminations, for example, are commonly found small-scale features, whereas unconformities, including layer boundaries and erosional surfaces, are field-scale features that are associated with sharp permeability contrasts across them. In this study, we validate theoretical predictions of foam generation through a variety of experimental evidence. We perform coreflood experiments involving simultaneous injection of gas and surfactant solution at field-like velocities into a model consolidated porous medium made of sintered glass. The core has a well-characterized, sharp permeability transition achieved by sintering glass of different grain sizes. Pressure gradient is measured across several sections of the core to identify foam-generation events and the subsequent propagation of foam. X-ray computerized tomography (CT) provides dynamic images of the coreflood in the form of phase saturations as they develop through the experiment. We investigate the effects of the magnitude of the permeability change and injected gas fractional flow on foam generation and mobilization.</jats:p
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