An Analytical Solution for Unsteady Flow in a Phreatic Aquifer in the Case of Continuous Rise

In this study, we examine the classical problem of unsteady flow in a phreatic aquifer, induced by continuous rise of the water flux and head on its boundary. A closed-form analytical solution for the governing Boussinesq equation is derived for a semi-infinite aquifer.     

Some aspects of the protein folding problem examined in one-dimensional systems

Some concepts, such as energy landscape, Gibbs energy landscape, and cooperativity, frequently used in the theory of protein folding, are examined exactly in one-dimensional systems. It is shown that much of the confusion that exists regarding these, and other concepts arise from the misinterpretation of Anfinsen's thermodynamic hypothesis.     

A fast and simple algorithm for the computation of Legendre coefficients

We present an O(N log N){\mathcal{O}({N\,{\rm log}\,N})} algorithm for the calculation of the first N coefficients in an expansion of an analytic function in Legendre polynomials. In essence, the algorithm consists of an integration of a suitably weighted function along an ellipse, a task which can be accomplished with Fast Fourier Transform, followed by some post-processing. The mathematical underpinning of this algorithm is an old formula that expresses expansion coefficients [^(f)]_m{\hat{f}_m} as infinite linear combinations of derivatives. We evaluate the latter with the Cauchy theorem, thereby expressing each [^(f)]_m{\hat{f}_m} as a scaled integral of f(z)j_m(z)/z^m+1{f(z)\varphi_m(z)/z^{m+1}} along an appropriate contour, where j_m{\varphi_m} is a slowly converging hypergeometric function. Next, we transform j_m{\varphi_m} into another hypergeometric function which converges rapidly. Once we replace the latter function by its truncated Taylor expansion and choose an appropriate elliptic contour, we obtain an expression for the [^(f)]_m{\hat{f}_m}s which is amenable to rapid computation.     

Trivalent antigens for degranulation of mast cells

Degranulation of basophils and mast cells plays a central role in allergic reactions. Degranulation is a response to cell surface receptor aggregation caused by association of receptors with antibodies bound to multivalent antigens. Tools used in studying this process have included small-molecule divalent antigens, but they suffer from weak signaling apparently due to small aggregate size. We have prepared trivalent antigens that allow formation of larger aggregates and potent responses from mast cells.     

Oil Plume Distribution in an Aquifer near an Impermeable Barrier

The saturation distribution of an oil contaminant, in the vicinity of an infinite impermeable barrier within an aquifer, is modeled by a two-dimensional, nonlinear diffusion-convection equation. A closed form self-similar solution is obtained for the steady-state saturation distribution. The obtained solution may be used to determine the length of the barrier used to block the spreading of the contaminant in the aquifer.     

Prechemistry barriers and checkpoints do not contribute to fidelity and catalysis as long as they are not rate limiting

In the preceding article, “Perspective: Pre-chemistry conformational changes in DNA polymerase mechanisms” contributed by Schlick and coworkers as well as previous studies of these workers (Schlick et al. in Theor Chem Acc 131:1287, 2012; Radhakrishnan and Schlick in J Am Chem Soc 127:13245–13252, 2005; Radhakrishnan and Schlick in Biochem Biophys Res Commun 350:521–529, 2006; Radhakrishnan et al. in Biochemistry 45:15142–15156, 2006; Radhakrishnan and Schlick in Proc Natl Acad Sci USA 101:5970–5975, 2004) have argued that the conformational changes preceding the chemical step contribute to DNA synthesis and to the fidelity of DNA polymerases. In one of our previous investigations (Ram Prasad and Warshel in Proteins 79:2900–2919, 2011), we argued and showed that as long as the free energy barriers associated with any of the prechemistry steps are not rate limiting, they could not contribute to the catalysis and then to the fidelity. Though all our arguments are based on exact and well-defined scientific logics, Schlick and coworkers seem to overlook some of the clear conditions in these arguments and in particular the requirement that the chemical step is rate limiting in their arguments that the prechemistry barriers contribute to the catalysis. In fact, as long as the prechemistry steps are not rate limiting, we have shown that the enzymes cannot carry the memory of the previous steps. We also address other potential misunderstandings about several key issues; First, we clarify that it is misleading to relate the prechemistry proposal to the clear fact that the substrate-induced conformational changes determine the final preorganization (the issue is the height of the barrier of the enzyme substrate system and not the trivial fact that the enzyme has to change its structure when the substrate binds). Second, we address the presumed role of dynamical effects in enzyme catalysis and the assumption that any observable should be explored in studies of biological function even if they are not relevant to the given effect. Third, we clarify that the fidelity cannot be explained or quantified by invoking the induced fit or conformational selection effects but by evaluating the free energy contributions to the rate-limiting steps from the structures of the corresponding systems (that of course can reflect the induce fit structural changes). Overall, we put a major emphasis on clarifying what is the prechemistry proposal and thus on trying to force the reader to focus on the only real controversy. We of course dismiss any implication that our studies cannot explore mutational effects as we actually pioneered such computational studies and we clarify that in studies of chemical rates, the focus must be placed on evaluating the chemical barriers, rather than on irrelevant factors, but that the calculations of the chemical barriers must consider all the factors that determine this barrier (including metal ions) and also examine if needed different problematic proposals such as dynamical effects, tunneling, and prechemistry.     

Radial Oil–Water Transport Toward an Extraction Well

We apply steady-state capillary-controlled upscaling in heterogeneous environments. A phase may fail to form a connected path across a given domain at capillary equilibrium. Moreover, even if a continuous saturation path exists, some regions of the domain may produce disconnected clusters that do not contribute to the overall connectivity of the system. In such cases, conventional upscaling processes might not be accurate since identification and removal of these isolated clusters are extremely important to the global connectivity of the system and the stability of the numerical solvers. In this study, we address the impact of percolation during capillary-controlled displacements in heterogeneous porous media and present a comprehensive investigation using random absolute permeability fields, for water-wet, oil-wet and mixed-wet systems, where J-function scaling is used to relate capillary pressure, porosity and absolute permeabilities in each grid cell. Important information is revealed about the average connectivity of the phases and trapping at the Darcy scale due to capillary forces. We show that in oil-wet and mixed-wet media, large-scale trapping of oil controlled by variations in local capillary pressure may be more significant than the local trapping, controlled by pore-scale displacement.     

Ranking asymmetric auctions

We compare the expected revenue in first- and second-price auctions with asymmetric bidders. We consider “close to uniform” distributions with identical supports and show that in the case of identical supports the expected revenue in second-price auctions may exceed that in first-price auctions. We also show that asymmetry over lower valuations has a stronger negative impact on the expected revenue in first-price auctions than in second-price auctions. However, asymmetry over high valuations always increases the revenue in first-price auctions.     

On the Discretization of Double-Bracket Flows

This paper extends the method of Magnus series to Lie-algebraic equations originating in double-bracket flows. We show that the solution of the isospectral flow Y'=[[Y,N],Y] , Y(0)=Y ₀ ∈\Sym(n) , can be represented in the form Y(t)=e ^Ω(t) Y ₀ e ^-Ω(t) , where the Taylor expansion of Ω can be constructed explicitly, term-by-term, identifying individual expansion terms with certain rooted trees with bicolor leaves. This approach is extended to other Lie-algebraic equations that can be appropriately expressed in terms of a finite ``alphabet.'     

Asymptotic solvers for ordinary differential equations with multiple frequencies

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question.Numerical examples illustrate the effectiveness of the method.