Commodity spot prices tend to revert to some long-term mean level and most commodity derivatives are based on futures prices, not on spot prices. So, we consider spread options on futures instead of spot or spot index, where the log spot price follows a mean-reverting process. The volatility of the mean-reverting process is driven by two different (fast and slow) scale factors. We use asymptotic analysis to obtain a closed-form approximation of the futures prices and a closed-form formula for the approximate prices of spread options on the futures. The overall improvement of our analytic formula over the classical Kirk–Bjerksund–Sternsland (KBS) formula is discussed via numerical experiments.

We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are well-behaved, we do not assume any asymptotic behaviour of the linear system. Moreover, the control on the nonlinear perturbations may differ along finitely many mutually complementary directions. We consider both the cases of one-sided discrete and continuous dynamics.

Mechanical properties of hydrogels are of considerable interest for applications including tissue engineering and drug delivery. However, mechanical characterization of hydrogels is inherently challenging due to their multiphasic construction. Under mechanical loading, internal fluid redistribution affects the gel response, leading to a time- and length-scale-dependent material behavior, known as poroelasticity. Traditional mechanical tests are effective for determining instantaneous flow-independent gel response, and they are limited in characterizing poroelastic behavior as a function of loading time- and length-scales. Here, micro- and nanoindentation experiments are combined to characterize the full range of poroelastic behavior of a hydrogel. A master curve is presented to demonstrate that the relative competition of poroelastic relaxation time with ramp loading time determines gel response across different time- and length-scales. The master curve provides a novel mechanism to establish the instantaneous and equilibrium limits on the elastic modulus for a material, useful for designing hydrogel biomaterials.

Thermal conductivity behaviors are one of the most important evaluations of carbon fiber-reinforced carbon matrix (C/C) composites in the field of thermal protective structures. In order to deepen the understanding of the thermal conductivity behaviors of C/C composites, the out-of-plane thermal conductivity of C/C composites is studied by considering voids and the fiber volume fractions. The representative volume element (RVE) models of microscale and mesoscale are proposed. The parameters of the RVE models are captured by X-ray micro-computed tomography. The carbon matrix equivalent models and fiber volume fraction models along the z-direction were established. The effects of the porosity and fiber volume fraction along the z-direction on the thermal conductivity were analyzed. The proposed model was validated by experimental results at room temperature. Further, the numerical methods developed in this study can provide guidance for predicting the thermal conductivity of C/C composites with complex structures.

The thermodynamic solubility product for baryte, determined at standard conditions, from data in commonly used compilations, was compared with published experimental solubility products for baryte and with the solubility products from databases used by the PHREEQC geochemical speciation code and MultiScale, which is often used by oil companies to predict or describe baryte scaling. The values in the various databases agree well with experimental data (10–10.05–10–9.96; Melcher, 1910; Neuman, 1933; Templeton, 1960; Davis and Collins, 1971; Blount, 1977; Felmy et al., 1990), which agree within uncertainty with the values presented in the compilations of Robie et al. (1979), Wagman et al. (1982), Lide (2005), Raju and Atkinson (1988), as well as Nordstrom and Munoz (1994), whose values have the least uncertainty. In solutions of 50% seawater mixed with 50% reservoir formation waters, the data predict baryte supersaturation, both at standard temperature and at the temperatures expected in the reservoir, completely consistent with field observations. This provides confidence that the Pitzer approach for activity correction and the database is valid for investigations of baryte precipitation rates in high ionic strength solutions.

We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our discrete model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of Γ-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role.

We develop a mathematical model for a three-phase free boundary problem in one dimension that involves interactions between gas, water and ice. The dynamics are driven by melting of the ice layer, while the pressurized gas also dissolves within the meltwater. The model incorporates the Stefan condition at the water–ice interface along with Henry's law for dissolution of gas at the gas–water interface. We employ a quasi-steady approximation for the phase temperatures and then derive a series solution for the interface positions. A non-standard feature of the model is an integral free boundary condition that arises from mass conservation owing to changes in gas density at the gas–water interface, which makes the problem non-self-adjoint. We derive a two-scale asymptotic series solution for the dissolved gas concentration, which because of the non-self-adjointness gives rise to a Fourier series expansion in eigenfunctions that do not satisfy the usual orthogonality conditions. Numerical simulations of the original governing equations are used to validate series approximations.

We propose a derivation of a nonequilibrium Langevin dynamics for a large particleimmersed in a background flow field. A single large particle is placed in an ideal gasheat bath composed of point particles that are distributed consistently with thebackground flow field and that interact with the large particle through elasticcollisions. In the limit of small bath atom mass, the large particle dynamics converges inlaw to a stochastic dynamics. This derivation follows the ideas of [P. Calderoni, D. Dürrand S. Kusuoka, J. Stat. Phys. 55 (1989) 649–693. D. Dürr,S. Goldstein and J. Lebowitz, Z. Wahrscheinlichkeit 62(1983) 427–448. D. Dürr, S. Goldstein and J.L. Lebowitz. Comm. Math. Phys.78 (1981) 507–530.] and provides extensions to handle the nonzerobackground flow. The derived nonequilibrium Langevin dynamics is similar to the dynamicsin [M. McPhie, P. Daivis, I. Snook, J. Ennis and D. Evans, Phys. A299 (2001) 412–426]. Some numerical experiments illustrate the useof the obtained dynamic to simulate homogeneous liquid materials under shear flow.

This work establishes a multiscale and multitechnique nondestructive approach as valid methodology for monitoring surface properties and evaluating the effectiveness of enzymatic removal of varnishes from paintings/polychrome artefacts.

Mock-up samples (documented reconstructions of oil, tempera, and gilded layers on canvas and wooden supports) were covered with different proteinaceous varnishes (egg white, animal and fish glue, casein) and then characterized before and after the removal of these coatings with enzyme-based solutions. The varnish was cleaned in several steps (two dry swabs and two wet swabs) with a clearance step for removing the residues from proteinaceous varnish or from enzyme solution.

Microscopy [stereomicroscopy (SM), optical microscopy (OM), atomic force microscopy (AFM), and scanning electron microscopy (SEM)] and colorimetric (CIE L*a*b* system) techniques were used for characterization of the reconstruction surfaces at different scales (macro-scale by SM and OM; micro-scale by SEM and nano-scale by AFM). These techniques were also used to monitor the cleaning treatment.

Although results presented in this work were obtained for the specific treatment of enzyme removal, the methodology could be extended to other types of materials and cleaning. Further experiments on real works of art are needed for a complete validation of the methodology.

A new algorithm, called boosted hybrid method, is proposed for the simulation of chemical reaction systems with scale-separation in time and disparity in species population. For such stiff systems, the algorithm can automatically identify scale-separation in time and slow down the fast reactions while maintaining a good approximation to the original effective dynamics. This technique is called boosting. As disparity in species population may still exist in the boosted system, we propose a hybrid strategy based on coarse-graining methods, such as the tau-leaping method, to accelerate the reactions among large population species. The combination of the boosting strategy and the hybrid method allow for an efficient and adaptive simulation of complex chemical reactions. The new method does not need a priori knowledge of the system and can also be used for systems with hierarchical multiple time scales. Numerical experiments illustrate the versatility and efficiency of the method.

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method.

Virtual three-dimensional (3-D) environments have become pervasive tools in a number of professional and recreational tasks. However, interacting with these environments can be challenging for users, especially as these environments increase in complexity and scale. In this paper, we argue that the design of 3-D interaction techniques is an ill-defined problem. This claim is elucidated through the context of data-rich and geometrically complex multiscale virtual 3-D environments, where unexpected factors can encumber intellection and navigation. We develop an abstract model to guide our discussion, which illustrates the cyclic relationship of understanding and navigating; a relationship that supports the iterative refinement of a consistent mental representation of the virtual environment. Finally, we highlight strategies to support the design of interactions in multiscale virtual environments, and propose general categories of research focus.

Les roues aubagées assemblées peuvent posséder beaucoup de zones de contact. À cause des déplacements relatifs aux interfaces, l’usure par fretting est possible, elle affecte négativement la durée de vie de la structure. Il existe des méthodes pour prédire l’usure par fretting dans une analyse quasi-statique. Cependant elles ne permettent pas de prédire tous les phénomènes observés dans les attaches d’aubes de systèmes industriels. Un traitement numérique de l’usure par fretting sous chargement vibratoire est proposé. La méthode est basée sur la DLFT (Dynamical Lagrangian Frequency Time method). Elle permet de modéliser un contact unilatéral avec la loi de frottement de Coulomb. L’idée de base est de séparer le temps en deux échelles : l’échelle lente pour les phénomènes tribologiques et une échelle rapide pour la dynamique. Sur un nombre choisi de périodes l’état est supposé stationnaire et les variables sont décomposées en séries de Fourier. Des investigations numériques, sur roues aubagées avec une interface de contact avec frottement, illustrent les performances de la méthode et montrent le couplage entre dynamique et tribolologie.

Since cancer is a complex phenomenon that incorporates events occurring on differentlength and time scales, therefore multiscale models are needed if we hope to adequately addresscancer specific questions. In this paper we present three different multiscale individual-cell-basedmodels, each motivated by cancer-related problems emerging from each of the spatial scales: extracellular,cellular or subcellular, but also incorporating relevant information from other levels.We apply these hybrid models to investigate the influence of the microenvironement on tumourinvasion, cell-cell collaboration and competition leading to the initiation and growth of epithelialtumours, and to evolution of cell phenotypes/genotypes arising in tumours growing in differentoxygen concentrations. We also discuss how these models relate to one another and can be used tobridge biological scales relevant to cancer.

Siegmund and Worsley (1995) considered the problem of testing for signals with unknown location and scale in a Gaussian random field defined on ℝN. The test statistic was the maximum of a Gaussian random field in an N+1 dimensional ‘scale space’, N dimensions for location and 1 dimension for the scale of a smoothing filter. Scale space is identical to a continuous wavelet transform with a kernel smoother as the wavelet, though the emphasis here is on signal detection rather than image compression or enhancement. Two methods were used to derive an approximate null distribution for N=2 and N=3: one based on the method of volumes of tubes, the other based on the expected Euler characteristic of the excursion set. The purpose of this paper is two-fold: to show how the latter method can be extended to higher dimensions, and to apply this more general result to χ2 fields. The result of Siegmund and Worsley (1995) then follows as a special case. In this paper the results are applied to the problem of searching for activation in brain images obtained by functional magnetic resonance imaging (fMRI).

The minimization of nonconvex functionals naturally arises inmaterials sciences where deformation gradients in certain alloys exhibitmicrostructures. For example, minimizing sequences of the nonconvexEricksen-James energy can be associated with deformations in martensitic materials thatare observed in experiments[2,3]. — From the numericalpoint of view, classical conforming and nonconforming finite elementdiscretizations have been observed to give minimizerswith their quality being highlydependent on the underlying triangulation, see [8,24,26,27] for a survey. Recently, a newapproach has been proposed and analyzed in [15,16]that is based on discontinuous finite elements to reduce the pollution effectof a general triangulation on the computed minimizer.The goal of the present paper isto propose and analyzean adaptive method,giving a more accurate resolution of laminated microstructure on arbitrary grids.