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971.
972.
973.
Lynnette E.S. RamirezCarlos F.M. Coimbra 《Physica D: Nonlinear Phenomena》2011,240(13):1111-1118
In this work we develop a variable order (VO) differential equation of motion for a spherical particle sedimenting in a quiescent viscous liquid. In particular, we examine the various force terms in the equation of motion and propose a new form for the history drag acting on the particle. We show that the variable order formulation allows for an effective way to express the dynamic transition of the dominant forces over the entire time of the motion of the particle from rest to terminal velocity. The use of VO operators also allows us to examine the evolving dynamics of the wake during sedimentation. Using numerical data from a finite element simulation of a sedimenting particle, we first solve for the order of the derivative that returns the correct decay of the history force. We then propose a relatively simple expression for the history force that is a function of the Reynolds number and particle-to-fluid density ratio. The new history drag expression correlates very well (R2>0.99) with the numerical data for terminal Reynolds numbers ranging from 2.5 to 20, and for particle-to-fluid density ratios of interest in practice (1<β<10). 相似文献
974.
Li Li 《Physics letters. A》2011,375(3):511-516
In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs. 相似文献
975.
In this study, time fractional radial diffusion has been modeled in cylindrical coordinates in order to analyze the anomalous diffusion in an annulus. By using an integral transform technique, the analytical solution of the concentration distribution formula is obtained. The establishing of the concentration distribution is found to be controlled by the fractional derivative α, and the influences of α on the concentration field, the total amount diffused and the quantity of mass passing through the inner wall are presented graphically and studied in detail. Asymptotic expressions for the exact solutions are developed in order to explain the numerical results at small and large time, respectively, and the physical mechanism explanation for the paradoxical behavior shown in the numerical results is given. 相似文献
976.
Arlinghaus LR Thornton-Wells TA Dykens EM Anderson AW 《Magnetic resonance imaging》2011,29(9):1165-1174
Diffusion tensor imaging (DTI) was used to investigate the involvement of brain white matter in Williams syndrome (WS), a genetic neurodevelopmental disorder. Whole-brain DTIs were obtained from 16 young adults with WS and 16 normal controls. A voxel-based analysis was performed to compare fractional anisotropy (FA) values between the two groups. A tract-based analysis was also performed to compare FA values between the two groups along two major white matter tracts that pass through the external capsule: the uncinate and inferior fronto-occipital fasciculi. Several regions of both increased and decreased FA were found within major white matter tracts that connect functional regions that have previously been implicated in the cognitive and neurological symptoms of the syndrome. The tract-based analysis provided additional insight into the involvement of specific white matter tracts implicated in the voxel-based analysis within the external capsule. The results from this study support previously reported changes in white matter diffusion properties in WS and demonstrate the potential usefulness for tract-based analysis in future studies of the disorder. 相似文献
977.
Zalesky A 《Magnetic resonance imaging》2011,29(1):111-125
An evaluative methodology and five accompanying performance measures were developed to quantitatively assess the performance of the skeleton projection algorithm constituting the heart of tract-based spatial statistics (TBSS). The performance measures were designed to quantify the accuracy of skeleton projection in its indented task of alleviating any residual misalignment that may remain after image registration. A ground truth fractional anisotropy (FA) image was slightly warped using a realistic warp field that served to model post-registration residual misalignment of varying magnitudes. Skeleton projection was then used to register the warped FA image to the ground truth. Performing skeleton projection was found to yield up to 50% better correspondence between the values of FA compared to smoothing, despite the fact that less than 10% of post-registration misalignment was corrected. The align-max-with-max strategy underlying TBSS was posited as a potential explanation for this high correspondence in the values of FA, at the expense of lesser alignment between anatomically concordant voxels. 相似文献
978.
979.
Through an Euler–Hopf-type formula, we establish existence result to a Nirenberg-type problem involving the square root of the Laplacian in sphere S2. 相似文献
980.
In this article, a recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas [1998, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, 161–168] is used to investigate the existence and uniqueness of solutions for fractional order functional differential equations with infinite delay. 相似文献