Mechanical and Thermal Stability of Adhesive Membranes with Nonzero Bending Rigidity

Membranes at a microscopic scale are affected by thermal fluctuations and self-adhesion due to van der Waals forces. Methods to prepare membranes of even molecular scale, e.g., graphene, have recently been developed, and the question of their mechanical and thermal stability is of crucial importance. To this end we modeled microscopic membranes with an attractive interaction and applied Langevin dynamics. Their behavior was also analyzed under external loading. Even though these membranes folded during isotropic compression as a result of energy minimization, the process at high confinement was similar to crumpling of macroscopic nonadhesive sheets. The main difference appeared when the com…

Simulation Software for Flow of Fluid with Suspended Point Particles in Complex Domains: Application to Matrix Diffusion

Matrix diffusion is a phenomenon in which tracer particles convected along a flow channel can diffuse into porous walls of the channel, and it causes a delay and broadening of the breakthrough curve of a tracer pulse. Analytical and numerical methods exist for modeling matrix diffusion, but there are still some features of this phenomenon, which are difficult to address using traditional approaches. To this end we propose to use the lattice-Boltzmann method with point-like tracer particles. These particles move in a continuous space, are advected by the flow, and there is a stochastic force causing them to diffuse. This approach can be extended to include particle-particle and particle-wall…

Solution for the fragment-size distribution in a crack-branching model of fragmentation

It is well established that rapidly propagating cracks in brittle material are unstable such that they generate side branches. It is also known that cracks are attracted by free surfaces, which means that they attract each other. This information is used here to formulate a generic model of fragmentation in which the small-size part of the fragment-size distribution results from merged crack branches in the damage zones along the paths of the propagating cracks. This model is solved under rather general assumptions for the fragment-size distribution. The model leads to a generic distribution S(-gamma) exp(-S/S(0)) for fragment sizes S, where gamma = 2d-1/d with d the Euclidean dimension, an…

Validation of matrix diffusion modeling

Abstract Crystalline rock has been chosen as the host medium for repository of highly radioactive spent nuclear fuel in Finland. Radionuclide transport takes place along water-carrying fractures, and matrix diffusion has been indicated as an important retarding mechanism that affects the transport of mobile fission and activation products. The model introduced here for matrix diffusion contains a flow channel facing a porous matrix with stagnant water into which tracer molecules advected in the channel can diffuse. In addition, the possibility of a finite depth of the matrix and an initial tracer distribution (‘contamination’) in the matrix are included in the model. In order to validate th…

Quasi-Projective Varieties

We have developed the theory of affine and projective varieties separately. We now introduce the concept of a quasi-projective variety, a term that encompasses both cases. More than just a convenience, the notion of a quasi-projective variety will eventually allow us to think of an algebraic variety as an intrinsically defined geometric object, free from any particular embedding in affine or projective space.

Tube transport of water vapor with condensation and desorption

Attenuation and delay of active tracers in tube transport is an important current problem, but its full explanation is still lacking. To this end a model is introduced, where part of a tracer undergoes condensation and evaporation, treated as a diffusion-type process, in addition to Taylor dispersion. Condensation of water was verified by high-speed imaging, and the model solution fitted the breakthrough curves of laboratory measurements with pulses of water vapor of varying relative humidity. The model provides a transfer function whose performance was verified against field measurements. peerReviewed

Interface Detection Using a Quenched-Noise Version of the Edwards-Wilkinson Equation

We report here a multipurpose dynamic-interface-based segmentation tool, suitable for segmenting planar, cylindrical, and spherical surfaces in 3D. The method is fast enough to be used conveniently even for large images. Its implementation is straightforward and can be easily realized in many environments. Its memory consumption is low, and the set of parameters is small and easy to understand. The method is based on the Edwards-Wilkinson equation, which is traditionally used to model the equilibrium fluctuations of a propagating interface under the influence of temporally and spatially varying noise. We report here an adaptation of this equation into multidimensional image segmentation, an…

Dependence of thermal conductivity on structural parameters in porous samples

The in-plane thermal conductivity of porous sintered bronze plates was studied both experimentally and numerically. We developed and validated an experimental setup, where the sample was placed in vacuum and heated while its time-dependent temperature field was measured with an infrared camera. The porosity and detailed three-dimensional structure of the samples were determined by X-ray microtomography. Lattice-Boltzmann simulations of thermal conductivity in the tomographic reconstructions of the samples were used to correct the contact area between bronze particles as determined by image analysis from the tomographic reconstructions. Small openings in the apparent contacts could not be de…

Diffusion through thin membranes: Modeling across scales

From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesosco…

Affine Algebraic Varieties

Algebraic geometers study zero loci of polynomials. More accurately, they study geometric objects, called algebraic varieties, that can be described locally as zero loci of polynomials. For example, every high school mathematics student has studied a bit of algebraic geometry, in learning the basic properties of conic sections such as parabolas and hyperbolas.

Step algebras of quantum sl(n)

Maps to Projective Space

One of the main goals of algebraic geometry is to understand the geometry of smooth projective varieties. For instance, given a smooth projective surface X, we can ask a host of questions whose answers might help illuminate its geometry. What kinds of curves does the surface contain? Is it covered by rational curves, that is, curves birationally equivalent to ℙ1? If not, how many rational curves does it contain, and how do they intersect each other? Or is it more natural to think of the surface as a family of elliptic curves (genus-1 Riemann surfaces) or as some other family? Is the surface isomorphic to ℙ2 or some other familiar variety on a dense set? What other surfaces are birationally …

Sorption-Caused Attenuation and Delay of Water Vapor Signals in Eddy-Covariance Sampling Tubes and Filters

AbstractAdsorption and desorption (together called sorption) processes in sampling tubes and filters of eddy-covariance stations cause attenuation and delay of water vapor signals, leading to an underestimation of water vapor fluxes by tens of percent. The aim of this work was (i) to quantify the effects on sorption in filters and tubes of humidity, flow rate, and dirtiness and (ii) to test a recently introduced sorption model that facilitates correction of fluxes. Laboratory measurements on the transport of water vapor pulses through tubes and filters were carried out, and eddy-covariance field measurements were also used.In the laboratory measurements, the effects of sorption processes we…