The potential and flux landscape theory of evolution

We established the potential and flux landscape theory for evolution. We found explicitly the conventional Wright's gradient adaptive landscape based on the mean fitness is inadequate to describe the general evolutionary dynamics. We show the intrinsic potential as being Lyapunov function(monotonically decreasing in time) does exist and can define the adaptive landscape for general evolution dynamics for studying global stability. The driving force determining the dynamics can be decomposed into gradient of potential landscape and curl probability flux. Non-zero flux causes detailed balance breaking and measures how far the evolution from equilibrium state. The gradient of intrinsic potential and curl flux are perpendicular to each other in zero fluctuation limit resembling electric and magnetic forces on electrons. We quantified intrinsic energy, entropy and free energy of evolution and constructed non-equilibrium thermodynamics. The intrinsic non-equilibrium free energy is a Lyapunov function. Both intrinsic potential and free energy can be used to quantify the global stability and robustness of evolution. We investigated an example of three allele evolutionary dynamics with frequency dependent selection (detailed balance broken). We uncovered the underlying single, triple, and limit cycle attractor landscapes. We found quantitative criterions for stability through landscape topography. We also quantified evolution pathways and found paths do not follow potential gradient and are irreversible due to non-zero flux. We generalized the original Fisher's fundamental theorem to the general (i.e., frequency dependent selection) regime of evolution by linking the adaptive rate with not only genetic variance related to the potential but also the flux. We show there is an optimum potential where curl flux resulting from biotic interactions of individuals within a species or between species can sustain an endless evolution even if the physical environment is unchanged. We offer a theoretical basis for explaining the corresponding Red Queen hypothesis proposed by Van Valen. Our work provides a theoretical foundation for evolutionary dynamics.     

Kinetics of matrix polymerization of divinylbenzene in the mesoporous molecular sieve SBA-15

We have used IR spectroscopy for a comparative study of matrix and bulk polymerization of divinylbenzene in an SBA-15 silica mesoporous molecular sieve. We have shown that the initiation rate is practically independent of the synthesis method. The overall rate of matrix polymerization is 2 orders of magnitude slower than the rate of the bulk process, except for bulk polymerization (in contrast to matrix polymerization) there is typically an initial induction period. We provide a rationale for the change in the polymerization rate constants in each of the intermediate steps and show the effect of these constants on the change in the overall rate of the process. We have shown that it is possible to use IR spectroscopy for qualitative and quantitative study of the matrix polymerization process.     

Effect of the Nature of the Template on Formation of the Spatial Structure of Germanium Dioxide under Sol–Gel Synthesis Conditions

We have synthesized for the first time novel forms of germanium dioxide, templated by micellar structures, with hexagonal and/or lamellar spatial structure. We used an original method for detemplating the synthesized materials. We show that it is possible to use these as the basis for obtaining mesophase sorbents, including mesoporous molecular sieves (MMSs). We note that in each specific case, in synthesis of new nanoperiodic and mesoporous materials, including semiconductors, the determining factor is the correct choice of certain template/framework former systems that match with respect to chemical structure and reactivity.     

The eigenvalue problem in phase space

We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c‐function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi‐representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc.     

Adsorption of xenon on purified HiPco single walled carbon nanotubes

We have measured adsorption of xenon on purified HiPco single-walled carbon nanotubes (SWNTs) for coverages in the first layer. We compare the results on this substrate to those our group obtained in earlier measurements on lower purity arc-discharge produced nanotubes. To obtain an estimate for the binding energy of Xe, we measured five low-coverage isotherms for temperatures between 220 and 260 K. We determined a value of 256 meV for the binding energy; this value is 9% lower than the value we found for arc discharge nanotubes and is 1.59 times the value found for this quantity on planar graphite. We have measured five full monolayer isotherms between 150 and 175 K. We have used these data to obtain the coverage dependence of the isosteric heat. The experimental values obtained are compared with previously published computer simulation results for this quantity.     

Interface motion of capillary-driven flow in rectangular microchannel

In microchannel flow, gas-liquid interface behavior is important for developing a wide range of microfluidic applications, especially in passive microfluidic systems. This paper presents a discussion of interface motion driven by capillary action in a microchannel. We have extended the theory beyond the previous theory of capillary rise problem for a circular tube, to a rectangular microchannel. The same formula for the relation between nondimensional time and interface position is obtained as for a circular tube. We examined rectangular microchannels with several sizes (about 50 to 100 microm square) of glass capillaries and 85 x 68 microm and 75 x 45 microm polydimethylsiloxane (PDMS) microchannels fabricated by photolithography technique, respectively. We observed movement of the gas-liquid interface position and compared it to the dimensionless relation. We obtained the value of a dimensionless variable of driving force that is related to dynamic contact angles for glass-water, glass-ethanol, and PDMS-ethanol. Using this variable, interface motion can be predicted for any size of rectangular channels.     

Interplay between shear flow and elastic deformations in liquid crystals

We study shear flow in liquid crystal cells with elastic deformations using a lattice Boltzmann scheme that solves the full, three-dimensional Beris-Edwards equations of hydrodynamics. We consider first twisted and hybrid aligned nematic cells, in which the deformation is imposed by conflicting anchoring at the boundaries. We find that backflow renders the velocity profile non Newtonian, and that the director profile divides into two regions characterized by different director orientations. We next consider a cholesteric liquid crystal, in which a twist deformation is naturally present. We confirm the presence of secondary flow for small shear rates, and are able to follow the dynamical pathway of shear-induced unwinding, for higher shear rates. Finally, we analyze how the coupling between shear and elastic deformation can affect shear banding in an initially isotropic phase. We find that for a nematic liquid crystal, elastic distortions may cause an asymmetry in the dynamics of band formation, whereas for a cholesteric, shear can induce twist in an initially isotropic sample.     

Exact solution of a model of condensed-phase electron transfer with non-Condon effects

Non-Condon effects are important in the analysis of electron transfer in many systems coupled to a condensed-phase environment. We detail a novel condensed-phase electron transfer Hamiltonian that extends the spin-boson model to account for non-Condon effects. We show that the relevant reduced system density matrix dynamics can be calculated exactly for a particular class of bath Hamiltonians and system-bath couplings. An explicit formula for the long-time behavior of these systems is derived. We show that they exhibit non-Boltzmann long-time behavior that is independent of temperature, and depends on the system Hamiltonian and the initial system density matrix.     

Diagrammatic kinetic theory for a lattice model of a liquid. I. Theory

We present a diagrammatic formalism for the time correlation functions of density fluctuations for an excluded volume lattice gas on a simple d-dimensional hypercubic lattice. We consider a multicomponent system in which particles of different species can have different transition rates. Our theoretical approach uses a Hilbert space formalism for the time dependent dynamical variables of a stochastic process that satisfies the detailed balance condition. We construct a Liouville matrix consistent with the dynamics of the model to calculate both the equation of motion for multipoint densities in configuration space and the interactions in the diagrammatic theory. A Boley basis of fluctuation vectors for the Hilbert space is used to develop two formally exact diagrammatic series for the time correlation functions. These theoretical techniques are generalizations of methods previously used for spin systems and atomic liquids, and they are generalizable to more complex lattice models of liquids such as a lattice gas with attractive interactions or polymer models. We use our formalism to construct approximate kinetic theories for the van Hove correlation and self-correlation function. The most simple approximation is the mean field approximation, which is exact for the van Hove correlation function of a one component system but an approximation for the self-correlation function. We use our first diagrammatic series to derive a two site multiple scattering approximation that gives a simple analytic expression for the spatial Fourier transform of the self-correlation function. We employ our second diagrammatic series to derive a simple mode coupling type approximation that provides a system of equations that can be solved for the self-correlation function.     

Quantum sieving in single-walled carbon nanotubes: effect of interaction potential and rotational-translational coupling

The selective adsorption of heavy isotopes in narrow nanotubes, known as quantum sieving, is studied using a simple approximate theory for several different potential models. We address the reasons for wide disagreement among previously published results for quantum sieving. We analyze the sensitivity of quantum sieving to perturbations in the potential parameters used in the calculations. The selectivities are very sensitive to changes in the atomic diameter parameter and less sensitive to changes in the potential well depth. We present an approximate method for accounting for rotational-translational coupling that is computationally efficient and accurate for the narrowest nanotubes. For wide nanotubes, the estimation of rotational-translational coupling becomes inaccurate because of neglect of the effect of rotational states on the translational degrees of freedom.     

The effect of salt stoichiometry on protein-salt interactions determined by ternary diffusion in aqueous solutions

We report the four diffusion coefficients for the lysozyme-MgCl2-water ternary system at 25 degrees C and pH 4.5. The comparison with previous results for the lysozyme-NaCl-water ternary system is used to examine the effect of salt stoichiometry on the transport properties of lysozyme-salt aqueous mixtures. We find that the two cross-diffusion coefficients are very sensitive to salt stoichiometry. One of the cross-diffusion coefficients is examined in terms of common-ion, excluded-volume, and protein-preferential hydration effects. We use the four ternary diffusion coefficients to extract chemical-potential cross-derivatives and protein-preferential interaction coefficients. These thermodynamic data characterize the protein-salt thermodynamic interactions. We demonstrate the presence of the common-ion effect (Donnan effect) by analyzing the dependence of the preferential-interaction coefficient not only with respect to salt concentration but also with respect to salt stoichiometry. We conclude that the common-ion effect and the protein-preferential hydration are both important for describing the lysozyme-MgCl2 thermodynamic interaction.     

Thermodynamic integration from classical to quantum mechanics

We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.     

Structural properties and energetics of diffuse 87Rb clusters in three-dimension

A correlated two-body basis function is used to describe the three-dimensional bosonic clusters interacting via two-body van der Waals potential. We calculate the ground state and the zero orbital angular momentum excited states for Rb(N) clusters with up to N = 40. We solve the many-particle Schro?dinger equation by potential harmonics expansion method, which keeps all possible two-body correlations in the calculation and determines the lowest effective many-body potential. We study energetics and structural properties for such diffuse clusters both at dimer and tuned scattering length. The motivation of the present study is to investigate the possibility of formation of N-body clusters interacting through the van der Waals interaction. We also compare the system with the well studied He, Ne, and Ar clusters. We also calculate correlation properties and observe the generalised Tjon line for large cluster. We test the validity of the shape-independent potential in the calculation of the ground state energy of such diffuse cluster. These are the first such calculations reported for Rb clusters.     

Dynamic scaling in phase separation kinetics for quasi-two-dimensional membranes

We consider the dynamics of phase separation in lipid bilayer membranes, modeled as flat two-dimensional liquid sheets within a bulk fluid, both in the creeping flow approximation. We present scaling arguments that suggest asymptotic coarsening in these systems is characterized by a length scale R(t) ~ t(1/2) for critical (bicontinuous) phase separation and R(t) ~t(1/3) for off-critical concentrations (droplet morphology). In this limit, the bulk fluid is the primary source of dissipation. We also address these questions with continuum stochastic hydrodynamic simulations. We see evidence of scaling violation in critical phase separation, where isolated circular domains coarsen slower than elongated ones. However, we also find a region of apparent scaling where R(t) ~ t(1/2) is observed. This appears to be due to the competition of thermal and hydrodynamic effects. We argue that the diversity of scaling exponents measured in experiment and prior simulations can in part be attributed to certain measurements lying outside the asymptotic long-length-scale regime, and provide a framework to help understand these results. We also discuss a few simple generalizations to confined membranes and membranes in which inertia is relevant.     

A novel approach to combinatorial library design

We address the problem of designing a general-purpose combinatorial library to screen for pharmaceutical leads. Conventional approaches focus on diversity as the primary factor in designing such libraries. We suggest making screening libraries out of a set of pharmaceutically relevant scaffolds, with multiple analogs per scaffold. The rationale for this rests on the fact that even though the hit-rate in active series is much higher than in the database as a whole, often a large fraction of the compounds in active series are inactive. This is especially true when the series has not been optimized for the target under study. We introduce the concept of hit-rate within a series and use historic screening data to arrive at a crude estimate for it. We then use simple probability arguments to show that 50-100 compounds are required in each series in order to be nearly certain of finding at least one active compound in each true active series for any given target.     

Away from generalized gradient approximation: orbital-dependent exchange-correlation functionals

The local-density approximation of density functional theory (DFT) is remarkably accurate, for instance, for geometries and frequencies, and the generalized gradient approximations have also made bond energies quite reliable. Sometimes, however, one meets with failure in individual cases. One of the possible routes towards better functionals would be the incorporation of orbital dependence (which is an implicit density dependency) in the functionals. We discuss this approach both for energies and for response properties. One possibility is the use of the Hartree-Fock-type exchange energy expression as orbital-dependent functional. We will argue that in spite of the increasing popularity of this approach, it does not offer any advantage over Hartree-Fock for energies. We will advocate not to apply the separation of exchange and correlation, which is so ingrained in quantum chemistry, but to model both simultaneously. For response properties the energies and shapes of the virtual orbitals are crucial. We will discuss the benefits that Kohn-Sham potentials can offer which are derived from either an orbital-dependent energy functional, including the exact-exchange functional, or which can be obtained directly as orbital-dependent functional. We highlight the similarity of the Hartree-Fock and Kohn-Sham occupied orbitals and orbital energies, and the essentially different meanings the virtual orbitals and orbital energies have in these two models. We will show that these differences are beneficial for DFT in the case of localized excitations (in a small molecule or in a fragment), but are detrimental for charge-transfer excitations. Again, orbital dependency, in this case in the exchange-correlation kernel, offers a solution.     

Nanoparticles in electrochemical sensors for environmental monitoring

We review the state-of-the-art application of nanoparticles (NPs) in electrochemical analysis of environmental pollutants. We summarize methods for preparing NPs and modifying electrode surfaces with NPs. We describe several examples of applications in environmental electrochemical sensors and performance in terms of sensitivity and selectivity for both metal and metal-oxide NPs. We present recent trends in the beneficial use of NPs in constructing electrochemical sensors for environmental monitoring and discuss future challenges.NPs have promising potential to increase competitiveness of electrochemical sensors in environmental monitoring, though research has focused mainly on development of methodology for fabricating new sensors, and the number of studies for optimizing the performance of sensors and the applicability to real samples is still limited.     

Potential-functional embedding theory for molecules and materials

We introduce a potential-functional embedding theory by reformulating a recently proposed density-based embedding theory in terms of functionals of the embedding potential. This potential-functional based theory completes the dual problem in the context of embedding theory for which density-functional embedding theory has existed for two decades. With this potential-functional formalism, it is straightforward to solve for the unique embedding potential shared by all subsystems. We consider charge transfer between subsystems and discuss how to treat fractional numbers of electrons in subsystems. We show that one is able to employ different energy functionals for different subsystems in order to treat different regions with theories of different levels of accuracy, if desired. The embedding potential is solved for by directly minimizing the total energy functional, and we discuss how to efficiently calculate the gradient of the total energy functional with respect to the embedding potential. Forces are also derived, thereby making it possible to optimize structures and account for nuclear dynamics. We also extend the theory to spin-polarized cases. Numerical examples of the theory are given for some homo- and hetero-nuclear diatomic molecules and a more complicated test of a six-hydrogen-atom chain. We also test our theory in a periodic bulk environment with calculations of basic properties of bulk NaCl, by treating each atom as a subsystem. Finally, we demonstrate the theory for water adsorption on the MgO(001)surface.     

Comparison of self-consistent field convergence acceleration techniques

The recently proposed ADIIS and LIST methods for accelerating self-consistent field (SCF) convergence are compared to the previously proposed energy-DIIS (EDIIS) + DIIS technique. We here show mathematically that the ADIIS functional is identical to EDIIS for Hartree-Fock wavefunctions. Convergence failures of EDIIS + DIIS reported in the literature are not reproduced with our codes. We also show that when correctly implemented, the EDIIS + DIIS method is generally better than the LIST methods, at least for the cases previously examined in the literature. We conclude that, among the family of DIIS methods, EDIIS + DIIS remains the method of choice for SCF convergence acceleration.