Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation

The extended finite element method (X-FEM) is a numerical method for modeling strong (displacement) as well as weak (strain) discontinuities within a standard finite element framework. In the X-FEM, special functions are added to the finite element approximation using the framework of partition of unity. For crack modeling in isotropic linear elasticity, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are used to account for the crack. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence quasi-static crack propagation simulations can be carried out without remeshing. In this paper, we discuss some of the key issues in the X-FEM and describe its implementation within a general-purpose finite element code. The finite element program Dynaflow™ is considered in this study and the implementation for modeling 2-d cracks in isotropic and bimaterial media is described. In particular, the array-allocation for enriched degrees of freedom, use of geometric-based queries for carrying out nodal enrichment and mesh partitioning, and the assembly procedure for the discrete equations are presented. We place particular emphasis on the design of a computer code to enable the modeling of discontinuous phenomena within a finite element framework.     

Donor-Acceptor Complexes in Copolymerization. XXXVII. Alternating Diene-Dienophile Copolymers. 5. Formation of Conjugated Diene-Maleic Anhydride Copolymers through Retrograde Dissociation of Furan-Maleic Anhydride Diels-Alder Adduct

Abstract

The equimolar, alternating copolymer of isoprene, as well as other conjugated dienes, and maleic anhydride is formed by the radical catalyzed reaction of the conjugated diene with maleic anhydride in the presence of furan as well as with the furan-maleic anhydride Diels-Alder adduct. The retrograde dissociation of the cyclic adduct above 60°C regenerates furan and maleic anhydride which in the presence of isoprene forms the isoprene-maleic anhydride ground state complex. The latter yields the corresponding cyclic adduct in the absence of a radical catalyst and undergoes excitation and homopolymerization in the presence of a catalyst.     

Donor-Acceptor Complexes in Copolymerization. XXXVI. Alternating Diene-Dienophile Copolymers. 4. Copolymerization of Furan and 2-Methylfuran with Maleic Anhydride

Abstract

The copolymerization of furan and 2-methylfuran with maleic anhydride in the presence of a radical catalyst yields equimolar, alternating copolymers in which the furan units have a 2,5-linkage (NMR and IR). The copolymerization appears to have a floor temperature of about 40°C. The furan-maleic anhydride Diels-Alder adduct polymerizes in solution in the presence of a radical catalyst at temperatures above 60°C to yield the identical copolymer as is obtained from the monomers. The adduct undergoes a retrograde reaction above 60°C to regenerate the monomers which then copolymerize through excitation of the ground state comonomer charge transfer complex.     

Synthesis and Properties of a New Polyesterimide from a Forest Product

Polyesterimide offers a class of resin which combines the advantage of high temperature stability with ease of process-ability. Gum rosin, the exudate of pine trees, has been developed as the raw material for preparation of polyesterimide. Abietic acid of rosin reacts readily with maleic anhydride to form the Diels-Alder adduct, which reacts with p-amino benzoic acid to produce a dicarboxylic acid containing an internal imide group. The dicarboxylic acid reacts with diethylene glycol under melt polycondensation at higher temperature (260–300°C)to produce polyesterimide. The polymer is found to be soluble in highly polar solvents. The polymer is amorphous and of low molecular weight. Thermal stability of the polymer has been characterized, and the polymer was found to be thermostable.     

Numerical study of the vortex-induced electroosmotic mixing of non-Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.     

Remarks on some zero-sum problems

Let Z denote the ring of integers and for a prime p and positive integers r and d, let f_r(P, d) denote the smallest positive integer such that given any sequence of f_r(p, d) elements in (Z/pZ(^d, there exists a subsequence of (rp) elements whose sum is zero in (Z/pZ(^d. That f₁(p, 1) = 2p − 1, is a classical result due to Erdős, Ginzburg and Ziv. Whereas the determination of the exact value of f₁(p, 2) has resisted the attacks of many well known mathematicians, we shall see that exact values of f_r(p, 1) for r ≥ 1 can be easily obtained from the above mentioned theorem of Erdős, Ginzburg and Ziv and those of f_r(p, 2) for r ≥ 2 can be established by the existing techniques developed by Alon, Dubiner and Rónyai in connection with obtaining good upper bounds for f₁(p, 2). We shall also take this opportunity to describe some of the early results in the introduction.     

Current trends in virtual high throughput screening using ligand-based and structure-based methods

High throughput in silico methods have offered the tantalizing potential to drastically accelerate the drug discovery process. Yet despite significant efforts expended by academia, national labs and industry over the years, many of these methods have not lived up to their initial promise of reducing the time and costs associated with the drug discovery enterprise, a process that can typically take over a decade and cost hundreds of millions of dollars from conception to final approval and marketing of a drug. Nevertheless structure-based modeling has become a mainstay of computational biology and medicinal chemistry, helping to leverage our knowledge of the biological target and the chemistry of protein-ligand interactions. While ligand-based methods utilize the chemistry of molecules that are known to bind to the biological target, structure-based drug design methods rely on knowledge of the three-dimensional structure of the target, as obtained through crystallographic, spectroscopic or bioinformatics techniques. Here we review recent developments in the methodology and applications of structure-based and ligand-based methods and target-based chemogenomics in Virtual High Throughput Screening (VHTS), highlighting some case studies of recent applications, as well as current research in further development of these methods. The limitations of these approaches will also be discussed, to give the reader an indication of what might be expected in years to come.     

Discovery of a Potent GLUT Inhibitor from a Library of Rapafucins by Using 3D Microarrays

Glucose transporters play an essential role in cancer cell proliferation and survival and have been pursued as promising cancer drug targets. Using microarrays of a library of new macrocycles known as rapafucins, which were inspired by the natural product rapamycin, we screened for new inhibitors of GLUT1. We identified multiple hits from the rapafucin 3D microarray and confirmed one hit as a bona fide GLUT1 ligand, which we named rapaglutin A (RgA). We demonstrate that RgA is a potent inhibitor of GLUT1 as well as GLUT3 and GLUT4, with an IC₅₀ value of low nanomolar for GLUT1. RgA was found to inhibit glucose uptake, leading to a decrease in cellular ATP synthesis, activation of AMP‐dependent kinase, inhibition of mTOR signaling, and induction of cell‐cycle arrest and apoptosis in cancer cells. Moreover, RgA was capable of inhibiting tumor xenografts in vivo without obvious side effects. RgA could thus be a new chemical tool to study GLUT function and a promising lead for developing anticancer drugs.     

An Alternative Approach to Predicting Reservoir Performance in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Coalbed methane (CBM) reservoirs contain gas molecules in adsorbed state into the solid matrix of coal. The pressure depletion in CBM reservoir causes the matrix gas to desorb into the cleat system which leads to matrix shrinkage. The pore volume of the cleat network changes as coal matrix shrinks. Consequently, cleat porosity and permeability of reservoir change as reservoir pressure depletes. The change in cleat porosity and permeability due to shrinkage of coal matrix with depletion of reservoir pressure invalidates the underlying assumptions made in the derivation of diffusivity equation. Under the conditions of changing porosity and permeability, the utility of the standard method of inflow performance relationship (IPR), paired with \(\frac{P}{Z^{*}}\) method suggested by King (in: SPE Annual Technical Conference and Exhibition, New Orleans, 1990), for performance prediction diminishes. In this paper, an effort has been made to predict reservoir performance of such CBM reservoirs with an alternative approach. The method suggested by Upadhyay and Laik (Transp Porous Media, 2017. doi: 10.1007/s11242-016-0816-6) has been leveraged to describe pseudo-steady-state flow in the form of a new equation that relates stress-dependent pseudo-pressure function with time. The analytical equation derived in this paper is useful in predicting reservoir pressure and flowing bottom hole pressure of a CBM well under the situation when coal matrix shrinks below desorption pressure. The paper aims to predict production performance of CBM reservoirs producing under the influence of matrix shrinkage effect with an approach alternative to conventional IPR approach paired with \(\frac{P}{Z^{*}}\) method. The results of this analytical solution have been validated with the help of numerical simulator CMG–GEM as well as in-field production data. The equations and workflow suggested in this paper can be easily implemented in spreadsheet applications like Microsoft Excel tools.