Asymptotics for the heat kernel in multicone domains

A multi cone domain $\Omega \subseteq \mathbb{R}^n$ is an open, connected set that resembles a finite collection of cones far away from the origin. We study the rate of decay in time of the heat kernel $p(t,x,y)$ of a Brownian motion killed upon exiting $\Omega$, using both probabilistic and analytical techniques. We find that the decay is polynomial and we characterize $\lim_{t\to\infty} t^{1+\alpha}p(t,x,y)$ in terms of the Martin boundary of $\Omega$ at infinity, where $\alpha>0$ depends on the geometry of $\Omega$. We next derive an analogous result for $t^{\kappa/2}\mathbb{P}_x(T >t)$, with $\kappa = 1+\alpha - n/2$, where $T$ is the exit time form $\Omega$. Lastly, we deduce the renormalized Yaglom limit for the process conditioned on survival.Comment: 31 page

A sustainable approach for tungsten carbide synthesis using renewable biopolymers

Here we present a sustainable, environment-friendly and energy-efficient approach for synthesis of porous tungsten carbide (WC). A biopolymer-metal oxide composite featuring iota-carrageenan, chitin and tungsten trioxide (WO3) was used as the precursor material. The reaction mechanism for the synthesis of WC was estimated using the results from X-ray diffraction characterization (XRD). A synthesis temperature of 1300 °C and dwell time of 3 h were found to be the optimum process parameters to obtain WC\u3e98% pure. The grain size, porosity and Brunauer–Emmett–Teller (BET) surface area of the synthesized WC were characterized using field emission scanning electron microscopy, high resolution transmission electron microscopy and nitrogen adsorption-desorption. A mesoporous WC was synthesized here with a grain size around 20 nm and BET surface area of 67.03 m2/g. Gel casting was used to demonstrate the manufacturing capability of the proposed precursor material. The WC obtained after heat treatment preserved the original shape albeit significant shrinkage. The WC synthesized here has potential applications in high temperature filters, catalysis, fuel cells and batteries

Synthesis of Tungsten Carbide from Bacterial Cellulose

Here we present preliminary experiments for the synthesis of carbide material using bacterial cellulose as carbon source. We used bacteria cellulose available as Nata de Coco and infiltrated it with tungsten trioxide (WO3) nanoparticles. This composite was heat treated at 1300 °C in nitrogen atmosphere. The XRD pattern confirms the synthesis of tungsten carbide (WC) in the carbonaceous material, though a significant amount of metallic tungsten remained unreacted. SEM images shows that WC particles are present only at the surface of the carbon, which may be a consequence of improper infiltration or collapse of carbon matrix during heat treatment

Additive Manufacturing of Carbides using Renewable resources

We present preliminary experiments leading to novel additive manufacturing of carbides using a biopolymer-metal oxide composite as the precursor material. Renewable biopolymers replace petroleum-based ones as carbon source; and the temperature needed for carbide formation is drastically reduced due the colloidal proximity of the reactants. Additive manufacturing of a precursor gel composite could enable complex shapes, especially those currently challenging for powder pressing or machining of bulk carbides. To this end, we characterized water-based gels featuring iota-carrageenan (IC) as matrix; cellulose or chitin as fillers; and silica nanoparticles. Composite synthesis featured addition of a mixture of iota-carrageenan and chitin or cellulose to a silica nanoparticle dispersion. . Different 3D shapes were made with the composites by manual extrusion using a syringe. After heat treatment at 1300 °C in a nitrogen environment, carbonaceous 3D shapes were obtained. SEM-EDX, BET and XRD analysis were performed on the carbonaceous samples towards characterizing their composition and geometry. These results reveal a highly porous and amorphous material. Ongoing work is optimizing the heat treatment protocol and implementing a linear motion stage to enable additive manufacturing

Enrichment of diluted cell populations from large sample volumes using 3D Carbon-electrode Dielectrophoresis

Here, we report on an enrichment protocol using carbon electrodedielectrophoresis to isolate and purify a targeted cell population from sample volumes up to 4 ml. We aim at trapping, washing, and recovering an enriched cell fraction that will facilitate downstream analysis. We used an increasingly diluted sample of yeast, 106–102 cells/ml, to demonstrate the isolation and enrichment of few cells at increasing flow rates. A maximum average enrichment of 154.2 ± 23.7 times was achieved when the sample flow rate was 10 μl/min and yeast cells were suspended in low electrically conductive media that maximizes dielectrophoresis trapping. A COMSOL Multiphysics model allowed for the comparison between experimental and simulation results. Discussion is conducted on the discrepancies between such results and how the model can be further improved

Carbon cone electrodes for Selection, Manipulation and Lysis of Single cells

Here we present initial experiments towards an integrated platform for single cell selection, manipulation and lysis. An array of polarized conical carbon electrodes can be dipped in a cell culture, trap cells of interest using dielectrophoresis and transport them to specific locations where they can be lyzed electrically to extract intracellular components from targeted particles over specific locations. What we contribute in this work is modeling of the electric field and its gradient around carbon cones, as well as initial cone fabrication results. Ongoing work is on demonstrating cell trapping and lysis using these conical electrodes by only varying the magnitude and frequency of their polarizing AC signal. Here we use conical carbon electrode to trap volumes to keep a single particle in place and yields strong enough electric fields for lysing once the cell is on top of a specific location. Electric Gradient of the range of 1015 m*kq2 /(s6*A2 )can be used to trap single cell. COMSOL Modeling dictate the use of structures (height 30 um) with tip of 45 degrees to obtain a 10 um3-volume to allow for manipulation and lysis of a single yeast cell

Molecular dynamics simulation of the elliptical vibration assisted machining (EVAM) of pure iron

It is well known that diamond wears out rapidly (within several metres of cutting length) when machining low carbon ferrous alloys and pure iron. The past few years have seen a growing interest in the field of elliptical vibration-assisted machining (EVAM) due to it being successful in the micromachining of difficult-to-cut materials including steel. During EVAM, a cutting tool is prescribed an oscillatory motion perpendicular to the direction of cutting, thereby causing the tool to be relieved intermittently from chemical and physical contact with the workpiece. This phenomenon serves as a guideline to develop the simulation test bed for studying EVAM in this work to compare it with conventional cutting. The pilot implementation of the EVAM came as a quasi-3-dimensional (Q3D) elliptical cutting model of body-centred cubic (BCC) iron with a diamond cutting tool using molecular dynamics (MD) simulation. The developed MD model supplemented by the advanced visualization techniques was used to probe the material removal behaviour, the development of the peak stress in the workpiece and the way the cutting force evolves during the cutting process. One of the key observations was that the cutting chips of BCC iron during conventional cutting underwent crystal twinning and became polycrystalline, while EVAM resulted in cutting chips becoming highly disordered, leading to better viscous flow compared to conventional cutting

3D Carbon-Electrode Dielectrophoresis for Enrichment of a Small Cell Population from a Large Sample Volume

Isolation and enrichment of cells from a diluted sample is necessary for different clinical applications. Here we have demonstrated the use of 3D carbon electrode dielectrophoresis (DEP) to process a diluted yeast sample featuring concentration as low as 102 cells/ml. The yeast cells in the sample were first trapped on carbon electrodes by implementing positive DEP force and then released and concentrated in a small volume of clean buffer. The maximum limit of the cell trapping for our device was found to be around 4000 cells. Using 10 µl/min, an enrichment of 154.2 ± 23.7 folds was achieved, where sample of 102 cells/ml concentration was enriched up to 4 X 104 cells/ml. Upon increasing the flow rate up to 30 µl/min, the enrichment dropped down to 18.4 ± 4 folds due to the increase of drag force, though the enriched concentration around 104 cells/ml was still achieved