1,851 research outputs found
A remark on zeta functions of finite graphs via quantum walks
From the viewpoint of quantum walks, the Ihara zeta function of a finite
graph can be said to be closely related to its evolution matrix. In this note
we introduce another kind of zeta function of a graph, which is closely related
to, as to say, the square of the evolution matrix of a quantum walk. Then we
give to such a function two types of determinant expressions and derive from it
some geometric properties of a finite graph. As an application, we illustrate
the distribution of poles of this function comparing with those of the usual
Ihara zeta function.Comment: 14 pages, 1 figur
Giant dispersion of critical currents in superconductor with fractal clusters of a normal phase
The influence of fractal clusters of a normal phase on the dynamics of a
magnetic flux trapped in a percolative superconductor is considered. The
critical current distribution and the current-voltage characteristics of
fractal superconducting structures in the resistive state are obtained for an
arbitrary fractal dimension of the cluster boundaries. The range of fractal
dimensions, where the dispersion of critical currents becomes infinite, is
found. It is revealed that the fractality of clusters depresses of the electric
field caused by the magnetic flux motion thus increasing the critical current
value. It is expected that the maximum current-carrying capability of a
superconductor can be achieved in the region of giant dispersion of critical
currents.Comment: 7 pages with 3 figure
Multipod structures of lamellae-forming diblock copolymers in three-dimensional confinement spaces: experimental observation and computer simulation
The three-dimensional (3D) confinement effect on the microphase-separated structure of a diblock copolymer was investigated both experimentally and computationally. Block copolymer nanoparticles were prepared by adding a poor solvent into a block copolymer solution and subsequently evaporating the good solvent. The 3D structures of the nanoparticles were quantitatively determined with transmission electron microtomography (TEMT). TEMT observations revealed that various complex structures, including tennis-ball, mushroom-like, and multipod structures, were formed in the 3D confinement. Detailed structural analysis, showed that one block of the diblock copolymer slightly prefers to segregate into the particle surface compared with the other block. The observed structures were further elaborated using cell dynamics computer simulatio
Engineered Nanogel Particles Enhance the Photoautotrophic Biosynthesis of Polyhydroxyalkanoate in Marine Photosynthetic Bacteria
Improving polyhydroxyalkanoate (PHA, a biodegradable plastic) production under photoautotrophic cultivation is challenging for sustainable bioproduction. In this study, we demonstrated the use of engineered nanogel particles to enhance PHA accumulation in the marine photosynthetic bacterium Rhodovulum sulfidophilum under photoautotrophic culture. We screened the effect of 13 engineered nanogel particles on the cell growth and PHA accumulation of R. sulfidophilum. The addition of anionic nanogel particles significantly enhanced PHA accumulation in R. sulfidophilum up to 157-fold compared to that without nanogel particles. By performing ÂčÂłC tracer experiments and gas chromatographyâmass spectrometry analysis, we confirmed that HCOââ» was assimilated throughout the central carbon metabolism and that the accumulated PHA was indeed incorporated from HCOââ». Our results indicate successful PHA production with the supplementation of engineered nanogel particles under photoautotrophic cultivation in R. sulfidophilum. Furthermore, the strategy of using engineered nanoparticles demonstrated in this study may be applicable to other microbial cell factories to produce other commodity metabolites
Resistive state of superconducting structures with fractal clusters of a normal phase
The effect of morphologic factors on magnetic flux dynamics and critical
currents in percolative superconducting structures is considered. The
superconductor contains the fractal clusters of a normal phase, which act as
pinning centers. The properties of these clusters are analyzed in the general
case of gamma-distribution of their areas. The statistical characteristics of
the normal phase clusters are studied, the critical current distribution is
derived, and the dependencies of the main statistical parameters on the fractal
dimension are found. The effect of fractal clusters of a normal phase on the
electric field induced by the motion of the magnetic flux after the vortices
have been broken away from pinning centers is considered. The voltage-current
characteristics of fractal superconducting structures in a resistive state for
an arbitrary fractal dimension are obtained. It is found that the fractality of
the boundaries of normal phase clusters intensifies magnetic flux trapping and
thereby increases the current-carrying capability of the superconductor.Comment: 15 pages with 8 figures, revtex3, alternative e-mail of author is
[email protected]
A Remark on the Renormalization Group Equation for the Penner Model
It is possible to extract values for critical couplings and gamma_string in
matrix models by deriving a renormalization group equation for the variation of
the of the free energy as the size N of the matrices in the theory is varied.
In this paper we derive a ``renormalization group equation'' for the Penner
model by direct differentiation of the partition function and show that it
reproduces the correct values of the critical coupling and gamma_string and is
consistent with the logarithmic corrections present for g=0,1.Comment: LaTeX, 5 pages, LPTHE-Orsay-94-5
Rapid acceleration of electrons in the magnetosphere by fast-mode MHD waves
During major megnetic storms, enhanced flux of relativistic electrons in the
inner magnetosphere have been observed to correleated with ULF waves. The
enhancements can take place over a period of several hours. In order to account
for such a rapid generation of relativistic electrons, we examine the mechanism
of transit-time acceleration of electrons by low-frequency fast-mode MHD waves,
here the assumed form of ULF waves. Calcaulations of the acceleration
timescales in the model show that fast-mode waves in the Pc4 to Pc5 frequency
range, with typically observed wave amplitudes 10--20 nT, can accelerate the
seed electrons to energies of order MeV in a period of a few hours.Comment: 9 pages, 3 figures, Accepted to J. Geophys. Re
The packing of two species of polygons on the square lattice
We decorate the square lattice with two species of polygons under the
constraint that every lattice edge is covered by only one polygon and every
vertex is visited by both types of polygons. We end up with a 24 vertex model
which is known in the literature as the fully packed double loop model. In the
particular case in which the fugacities of the polygons are the same, the model
admits an exact solution. The solution is obtained using coordinate Bethe
ansatz and provides a closed expression for the free energy. In particular we
find the free energy of the four colorings model and the double Hamiltonian
walk and recover the known entropy of the Ice model. When both fugacities are
set equal to two the model undergoes an infinite order phase transition.Comment: 21 pages, 4 figure
SurfaceâReactive Patchy Nanoparticles and Nanodiscs Prepared by Tandem Nanoprecipitation and Internal Phase Separation
Nanoparticles with structural or chemical anisotropy are promising materials in domains as diverse as cellular delivery, photonic materials, or interfacial engineering. The surface chemistry may play a major role in some of these contexts. Introducing reactivity into such polymeric nanomaterials is thus of great potential, yet is still a concept in its infancy. In the current contribution, a simple nanoprecipitation technique leads to nanoparticles with diameters as low as 150 nm and wellâdefined reactive surface patches of less than 30 nm in width, as well as surfaceâreactive flat, discâlike nanoparticles with corresponding dimensions, via an additional crosslinking/delamination sequence. To this aim, chemically doped block copolymers (BCPs) are employed. Control over morphology is attained by tuning preparation conditions, such as polymer concentration, solvent mixture composition, and blending with nonâfunctional BCP. Surface reactivity is demonstrated using a modular ligation method for the siteâselective immobilization of thiol molecules. The current approach constitutes a straightforward methodology requiring minimal engineering to produce nanoparticles with confined surface reactivity and/or shape anisotropy.Nanoparticles with surfaceâexpressed reactive patches and corresponding nanodiscs are prepared by a simple nanoprecipitation technique with functional block copolymers. The surface pattern formation is controlled by preparation conditions (concentration, solvent, and functionality). Spatially confined functionalization is demonstrated by grafting model thiol compounds. These nanomaterials are structurally approaching biological particles and are interesting building blocks for colloidal assemblies.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146386/1/adfm201800846_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146386/2/adfm201800846.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146386/3/adfm201800846-sup-0001-S1.pd
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