Self-similar fault slip in response to fluid injection

There is scientific and industrial interest in understanding how geologic faults respond to transient sources of fluid. Natural and artificial sources can elevate pore fluid pressure on the fault frictional interface, which may induce slip. We consider a simple boundary value problem to provide an elementary model of the physical process and to provide a benchmark for numerical solution procedures. We examine the slip of a fault that is an interface of two elastic half-spaces. Injection is modelled as a line source at constant pressure and fluid pressure is assumed to diffuse along the interface. The resulting problem is an integro-differential equation governing fault slip, which has a single dimensionless parameter. The expansion of slip is self-similar and the rupture front propagates at a factor $\lambda$ of the diffusive length scale $\sqrt {\alpha t}$ . We identify two asymptotic regimes corresponding to $\lambda$ being small or large and perform a perturbation expansion in each limit. For large $\lambda$ , in the regime of a so-called critically stressed fault, a boundary layer emerges on the diffusive length scale, which lags far behind the rupture front. We demonstrate higher-order matched asymptotics for the integro-differential equation, and in doing so, we derive a multipole expansion to capture successive orders of influence on the outer problem for fault slip for a driving force that is small relative to the crack dimensions. Asymptotic expansions are compared with accurate numerical solutions to the full problem, which are tabulated to high precision.

FZZT branes in JT gravity and topological gravity

We study Fateev-Zamolodchikov-Zamolodchikov-Teschner (FZZT) branes in Witten-Kontsevich topological gravity, which includes Jackiw-Teitelboim (JT) gravity as a special case. Adding FZZT branes to topological gravity corresponds to inserting determinant operators in the dual matrix integral and amounts to a certain shift of the infinitely many couplings of topological gravity. We clarify the perturbative interpretation of adding FZZT branes in the genus expansion of topological gravity in terms of a simple boundary factor and the generalized Weil-Petersson volumes. As a concrete illustration we study JT gravity in the presence of FZZT branes and discuss its relation to the deformations of the dilaton potential that give rise to conical defects. We then construct a non-perturbative formulation of FZZT branes and derive a closed expression for the general correlation function of multiple FZZT branes and multiple macroscopic loops. As an application we study the FZZT-macroscopic loop correlators in the Airy case. We observe numerically a void in the eigenvalue density due to the eigenvalue repulsion induced by FZZT-branes and also the oscillatory behavior of the spectral form factor which is expected from the picture of eigenbranes.

R-Function and variation method for bending problem of clamped thin plate with complex shape

Solving ordinary thin plate bending problem in engineering, only a few analytical solutions with simple boundary shapes have been proposed. When using numerical methods (e.g. the variational method) to solve the problem, the trial functions can be found only it exhibits a simple boundary shape. The R-functions can be applied to solve the problem with complex boundary shapes. In the paper, the R-function theory is combined with the variational method to study the thin plate bending problem with the complex boundary shape. The paper employs the R-function theory to express the complex area as the implicit function, so it is easily to build the trial function of the complex shape thin plate, which satisfies with the complex boundary conditions. The variational principle and the R-function theory are introduced, and the variational equation of thin plate bending problem is derived. The feasibility and correctness of this method are verified by five numerical examples of rectangular, I-shaped, T-shaped, U-shaped, and L-shaped thin plates, and the results of this method are compared with that of other literatures and ANSYS finite element method (FEM). The results of the method show a good agreement with the calculation results of literatures and FEM.

Benchmark for scale-resolving simulation with curved walls: the Taylor Couette flow

Flow between rotating concentric cylinders, or the Taylor Couette flow, has been studied extensively because of its rich physics, ranging from axisymmetric steady laminar flow, to fully developed turbulent flow. In the present study, we advocate the use of this problem as a benchmark case for scale-resolving simulation, such as large eddy simulation (LES) and direct numerical simulation (DNS). The problem is attractive because of its simple geometry, simple boundary conditions, and complex physics involving wall-shear induced and centrifugal instability. Unlike the well-known fully developed channel flow, this problem has a curved wall boundary, and it is unnecessary to add a source term to the governing equations to sustain the fully developed turbulent flow. A p-refinement study for Re = 4000 is performed first to establish DNS data, including the time history of enstrophy, which can be used as an accuracy and resolution indicator to evaluate numerical methods, and is orders of magnitude faster than using the mean flow quantities and Reynolds stresses to evaluate solution quality. Finally, an hp-refinement study is performed to establish the relative accuracy and efficiency of high-order schemes of various accuracy.

Modelization of dispersion of swimming bacteria in Poiseuille flow

<p>We study the shear-induced migration of dilute suspensions of swimming bacteria (modelled as Active elongated Brownian Particles or ABPs) subject to plane Poiseuille flow in a confined channel. By incorporating very simple boundary conditions, we perform numerical simulations of the 3D equations of motion describing the change in position and orientation of the particles. We investigate the effects of confinement, of non-uniform shear and of aspect ratio of the particles on the overall dynamics of the ABPs population.</p><p>We particularly study the coupling between the local shear and the change in the orientation of the particles. We thus perform numerical simulations on both the case where the change in the orientation of the ABPs is purely diffusive (decoupled case) and the case where their orientation is coupled to the shear flow (coupled case). We observe that the decoupled case exhibits a Taylor dispersion <em>i.e.</em>  the effective dispersion coefficient of the ABPs along the direction of the flow is proportional to the square of the imposed shear at all shears. </p><p>However, for all the coupled cases we observe a transition from a Taylor to an active-Taylor regime at a critical shear rate, indicating the effect of shear coupling on the orientation dynamics of the particles. This critical shear rate is directly correlated to the degree of confinement. The change in the dispersion coefficient along the direction of the flow as function of the shear rate is in qualitative agreement with previous studies[1]. </p><p>To further understand these results, we also investigate the change in the dispersion coefficient in the other two directions along with the effect of the shape of the particles. We believe that this study should enhance our understanding of dispersion of bacteria through porous media, on surfaces etc. where shear flows are ubiquitous. </p><p>[1] Sandeep Chilukuri, Cynthia H.Collins, and Patrick T. Underhill. Dispersionof flagellated swimming microorganisms in planar poiseuille flow.Physics offluids, 27, (031902):1 –17, 2015</p>

Evaluating the response of the diurnal range of surface and air temperature to evaporative conditions across vegetation types in ERA5 and FLUXNET data

<p>The diurnal variations of surface and air temperature are related but their different responses to evaporative conditions can inform us about land-atmosphere interactions, extreme events, and their response to global change. Here, we evaluate the sensitivity of the diurnal ranges of surface (DT<sub>s</sub>R) and air (DT<sub>a</sub>R) temperature to evaporative fraction, across short vegetation, savanna, and forests at 106 Fluxnet observational sites and in the ERA5 global reanalysis. We show that the sensitivity of DT<sub>s</sub>R to evaporative fraction depends on vegetation type, whereas for DT<sub>a</sub>R it does not. Using FLUXNET data we found that on days with low evaporative fraction, DT<sub>s</sub>R is enhanced by up to 20 °C (30 °C in ERA5) in short vegetation, whereas only by 8 °C (10 °C in ERA5) in forests. Particularly, in short vegetation, ERA5 shows stronger responses, which is attributable to a negative bias on days with the high evaporative fraction. ERA5 also tends to have lower shortwave and longwave radiation input when compared to FLUXNET data. Contrary to DT<sub>s</sub>R, DT<sub>a</sub>R responds rather similarly to evaporative fraction irrespective of vegetation type (8 °C in FLUXNET, 10 °C in ERA5). To explain this, we show that the DT<sub>a</sub>R response to the evaporative fraction is compensated for differences in atmospheric boundary layer height by up to 2000 m, which is similar across vegetation types. We demonstrate this with a simple boundary layer heat storage calculation, indicating that DT<sub>a</sub>R is primarily shaped by changes in boundary layer heat storage whereas DT<sub>s</sub>R mainly responds to solar radiation, evaporation, and vegetation.  Our study reveals some systematic biases in ERA5 that need to be considered when using its temperature products for understanding land-atmosphere interactions or extreme events. To conclude, this study demonstrates the importance of vegetation and the dynamics of the atmospheric boundary layer in regulating diurnal variations in surface and air temperature under different evaporative conditions.</p>

Chemical graph generators

Chemical graph generators are software packages to generate computer representations of chemical structures adhering to certain boundary conditions. Their development is a research topic of cheminformatics. Chemical graph generators are used in areas such as virtual library generation in drug design, in molecular design with specified properties, called inverse QSAR/QSPR, as well as in organic synthesis design, retrosynthesis or in systems for computer-assisted structure elucidation (CASE). CASE systems again have regained interest for the structure elucidation of unknowns in computational metabolomics, a current area of computational biology.

Identification of Young’s Modulus and Equivalent Spring Constraint Boundary Conditions of the Object With Incomplete Displacement Boundary Conditions

In endoscopic surgery, the surgical navigation needs to calculate the internal deformation of the soft tissue by biomechanical model which needs to determine the elastic properties and boundary conditions. However, these information cannot be obtained accurately in a real operation scenario. For example, only a limited portion of a liver surface can be observed in a hepatic surgery under endoscope while its elastic properties remain unknown. In addition, simple boundary conditions such as fixed constraints and free-force constraints are not physically adequate to simulate the elastic effect of ligaments attached to the liver. Biomechanical models of the soft tissue have been thoroughly studied in recent years. In these studies, boundary conditions play an important role in identification of elastic properties for mechanical model based methods. But they rarely combine these unknown conditions together to construct the model, and instead set boundary conditions or elastic properties as known for simplification. In this paper, we present a novel method to identify the Young’s modulus and equivalent spring constraint boundary conditions of a partially observed soft object with incomplete boundary conditions. The spring constraint boundary condition is applied to alternate the conventional displacement boundary conditions (e.g. free constraint and fixed constraint) and an inverse algorithm based on the standard finite element method (FEM) and Gauss-Newton (GN) method is developed, which takes external forces and displacements of observable nodes as inputs. A series of numerical simulation experiments are implemented and the analysis of simulation results show the feasibility of the proposed method.

Use of a bounding surface model in predicting element tests and capacity in boundary value problems

The paper examines the merit of a two surface plasticity model through an optimised calibration procedure and assesses the model performance in capturing the response at both element and system level. The governing equations are based essentially on the parent two surface plasticity model developed by Dafalias and Manzari (2004) with some simple yet practical changes to enable realistic predictions for monotonic loading along different load paths. This is achieved by scaling the influence of state parameter based on a normalised measure of anisotropy, thus leading to suitable change in dilatancy and plastic modulus for different loading directions. The paper presents a simple optimisation technique for calibrating the model parameters, providing an objective approach to reduce the uncertainties in parameter determination that leads to good agreement with responses measured in drained and undrained triaxial tests. The model has also been implemented for the boundary value problem of a buried circular plate anchor and a surface circular footing. Comparisons of the simulated responses with those measured in centrifuge tests demonstrate the potential of the model, whilst also pointing to the challenges in capturing the global response at all strain levels, even for rather simple boundary value problems.

Oceanic Density/Pressure Gradients and Slope Currents

Eastern boundary currents are some of the most energetic features of the global ocean, contributing significantly to meridional mass, heat, and salt transports. We take a new look at the form of an oceanic slope current in equilibrium with oceanic density gradients. We depth integrate the linearized x and y momentum and continuity equations and assume an equilibrium force balance in the along-slope direction (no along-slope variation in the along-slope flow) and zero cross-slope flow at a coastal boundary. We relate the bottom stress to a bottom velocity via a simple boundary friction law (the precise details are easily modified) and then derive an expression for the slope current velocity by integrating upward including thermal wind shear. This provides an expression for the slope current as a function of depth and of cross-slope coordinate, dependent on the oceanic density field and surface and bottom stresses. This new expression for the slope current allows for more general forms of oceanic density fields than have been treated previously. Wind stress is also now considered. The emphasis here is on understanding the simplified equilibrium force balance rather than the evolution toward that balance. There is a direct relationship between the slope current strength, friction, and along-slope forcing (e.g., wind), and also between the total along-slope forcing and bottom Ekman transport, illustrating that “slippery” bottom boundaries in literature are a direct consequence of unrealistically assuming zero along-slope pressure gradient. We demonstrate the utility of the new expression by comparison with a high-resolution hydrodynamic numerical model.