200 research outputs found
Edge-Orders
Canonical orderings and their relatives such as st-numberings have been used
as a key tool in algorithmic graph theory for the last decades. Recently, a
unifying concept behind all these orders has been shown: they can be described
by a graph decomposition into parts that have a prescribed vertex-connectivity.
Despite extensive interest in canonical orderings, no analogue of this
unifying concept is known for edge-connectivity. In this paper, we establish
such a concept named edge-orders and show how to compute (1,1)-edge-orders of
2-edge-connected graphs as well as (2,1)-edge-orders of 3-edge-connected graphs
in linear time, respectively. While the former can be seen as the edge-variants
of st-numberings, the latter are the edge-variants of Mondshein sequences and
non-separating ear decompositions. The methods that we use for obtaining such
edge-orders differ considerably in almost all details from the ones used for
their vertex-counterparts, as different graph-theoretic constructions are used
in the inductive proof and standard reductions from edge- to
vertex-connectivity are bound to fail.
As a first application, we consider the famous Edge-Independent Spanning Tree
Conjecture, which asserts that every k-edge-connected graph contains k rooted
spanning trees that are pairwise edge-independent. We illustrate the impact of
the above edge-orders by deducing algorithms that construct 2- and 3-edge
independent spanning trees of 2- and 3-edge-connected graphs, the latter of
which improves the best known running time from O(n^2) to linear time
BIOMOLECULE LOCALIZATION AND SURFACE ENGINEERING WITHIN SIZE TUNABLE NANOPOROUS SILICA PARTICLES
Mesoporous silica materials are versatile platforms for biological catalysis, isolation of small molecules for detection and separation applications. The design of mesoporous silica supports for tailored protein and biomolecule interactions has been limited by the techniques to demonstrate biomolecule location and functionality as a function of pore size. This work examines the interaction of proteins and lipid bilayers with engineered porous silica surfaces using spherical silica particles with tunable pore diameters (3 – 12 nm) in the range relevant to biomolecule uptake in the pores, and large particle sizes (5 - 15 µm) amenable to microscopy imaging
The differentiation of protein location between the external surface and within the pore, important to applications requiring protein protection or catalytic activity in pores, is demonstrated. A protease / fluorescent protein system is used to investigate protein location and protection as a function of pore size, indicating a narrow pore size range capable of protein protection, slightly larger than the protein of interest and approaching the protease dimensions. Selective functionalization, in this case exterior-only surface functionalization of mesoporous particles with amines, is extended to larger pore silica materials. A reaction time dependent functionalization approach is demonstrated as the first visually confirmed, selective amine functionalization method in protein accessible supports.
Mesoporous silica nanoparticles are effective supports for lipid bilayer membranes and membrane associated proteins for separations and therapeutic delivery, although the role of support porosity on membrane fluidity is unknown. Transport properties of bilayers in lipid filled nanoparticles as a function of pore diameter and location in the particle are measured for the first time. Bilayer diffusivity increases with increasing pore size and is independent of bilayer location within the core, mid or cap of the particle, suggesting uniform long range bilayer mobility in lipid filled pores. Application of lipid bilayers on mesoporous silica was examined for membrane associated proteins A unique method to adhere functional proteins in lipid bilayers on mesoporous silica particles is established using vesicles derived from cell plasma membranes and their associated proteins. This method of membrane protein investigation retains proteins within native lipid membranes, stabilizing proteins for investigation on supports
Non-perturbative approaches to magnetism in strongly correlated electron systems
The microscopic basis for the stability of itinerant ferromagnetism in
correlated electron systems is examined. To this end several routes to
ferromagnetism are explored, using both rigorous methods valid in arbitrary
spatial dimensions, as well as Quantum Monte Carlo investigations in the limit
of infinite dimensions (dynamical mean-field theory). In particular we discuss
the qualitative and quantitative importance of (i) the direct Heisenberg
exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a
high spectral density near the band edges caused by an appropriate lattice
structure and/or kinetic energy of the electrons. We furnish evidence of the
stability of itinerant ferromagnetism in the pure Hubbard model for appropriate
lattices at electronic densities not too close to half-filling and large enough
. Already a weak direct exchange interaction, as well as band degeneracy, is
found to reduce the critical value of above which ferromagnetism becomes
stable considerably. Using similar numerical techniques the Hubbard model with
an easy axis is studied to explain metamagnetism in strongly anisotropic
antiferromagnets from a unifying microscopic point of view.Comment: 11 pages, Latex, and 6 postscript figures; Z. Phys. B, in pres
Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules
We report a scalable Fortran implementation of the phaseless auxiliary-field
quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and
beneficial scaling with respect to system size. Furthermore, we investigate
modifications of the phaseless approximation that can help to reduce the
overcorrelation problems common to the ph-AFQMC. We apply the method to the 26
molecules in the HEAT set, the benzene molecule, and water clusters. We observe
a mean absolute deviation of the total energy of 1.15 kcal/mol for the
molecules in the HEAT set; close to chemical accuracy. For the benzene
molecule, the modified algorithm despite using a single-Slater-determinant
trial wavefunction yields the same accuracy as the original phaseless scheme
with 400 Slater determinants. Despite these improvements, we find systematic
errors for the CN, CO, and O molecules that need to be addressed with
more accurate trial wavefunctions. For water clusters, we find that the
ph-AFQMC yields excellent binding energies that differ from CCSD(T) by
typically less than 0.5 kcal/mol.Comment: 13 pages, 7 figure
Coexistence of solutions in dynamical mean-field theory of the Mott transition
In this paper, I discuss the finite-temperature metal-insulator transition of
the paramagnetic Hubbard model within dynamical mean-field theory. I show that
coexisting solutions, the hallmark of such a transition, can be obtained in a
consistent way both from Quantum Monte Carlo (QMC) simulations and from the
Exact Diagonalization method. I pay special attention to discretization errors
within QMC. These errors explain why it is difficult to obtain the solutions by
QMC close to the boundaries of the coexistence region.Comment: 3 pages, 2 figures, RevTe
Quantum Monte Carlo calculation of the finite temperature Mott-Hubbard transition
We present clear numerical evidence for the coexistence of metallic and
insulating dynamical mean field theory(DMFT) solutions in a half-filled
single-band Hubbard model with bare semicircular density of states at finite
temperatures. Quantum Monte Carlo(QMC) method is used to solve the DMFT
equations. We discuss important technical aspects of the DMFT-QMC which need to
be taken into account in order to obtain the reliable results near the
coexistence region. Among them are the critical slowing down of the iterative
solutions near phase boundaries, the convergence criteria for the DMFT
iterations, the interpolation of the discretized Green's function and the
reduction of QMC statistical and systematic errors. Comparison of our results
with those of other numerical methods is presented in a phase diagram.Comment: 4 pages, 5 figure
Landau Theory of the Finite Temperature Mott Transition
In the context of the dynamical mean-field theory of the Hubbard model, we
identify microscopically an order parameter for the finite temperature Mott
endpoint. We derive a Landau functional of the order parameter. We then use the
order parameter theory to elucidate the singular behavior of various physical
quantities which are experimentally accessible.Comment: 4 pages, 2 figure
Surface Instabilities and Magnetic Soft Matter
We report on the formation of surface instabilities in a layer of
thermoreversible ferrogel when exposed to a vertical magnetic field. Both
static and time dependent magnetic fields are employed. Under variations of
temperature, the viscoelastic properties of our soft magnetic matter can be
tuned. Stress relaxation experiments unveil a stretched exponential scaling of
the shear modulus, with an exponent of beta=1/3. The resulting magnetic
threshold for the formation of Rosensweig-cusps is measured for different
temperatures, and compared with theoretical predictions by Bohlius et. al. in
J. Phys.: Condens. Matter., 2006, 18, 2671-2684.Comment: accepted to Soft Matte
Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons
A general expansion scheme based on the concept of linked cluster expansion
from the theory of classical spin systems is constructed for models of
interacting electrons. It is shown that with a suitable variational formulation
of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling
the expansion represents a universal and comprehensive tool for systematic
improvements of static mean-field theories. As an example of the general
formalism we investigate in detail an analytically tractable series of ring
diagrams that correctly capture dynamical fluctuations at weak coupling. We
introduce renormalizations of the diagrammatic expansion at various levels and
show how the resultant theories are related to other approximations of similar
origin. We demonstrate that only fully self-consistent approximations produce
global and thermodynamically consistent extensions of static mean field
theories. A fully self-consistent theory for the ring diagrams is reached by
summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file
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