4,847 research outputs found
Harper operators, Fermi curves, and Picard-Fuchs equations
This paper is a continuation of the work on the spectral problem of Harper
operator using algebraic geometry. We continue to discuss the local monodromy
of algebraic Fermi curves based on Picard-Lefschetz formula. The density of
states over approximating components of Fermi curves satisfies a Picard-Fuchs
equation. By the property of Landen transformation, the density of states has a
Lambert series as the quarter period. A -expansion of the energy level can
be derived from a mirror map as in the B-model.Comment: v2, 13 pages, minor changes have been mad
Catastrophic vs Gradual Collapse of Thin-Walled Nanocrystalline Ni Hollow Cylinders As Building Blocks of Microlattice Structures
Lightweight yet stiff and strong lattice structures are attractive for various engineering applications, such as cores of sandwich shells and components designed for impact mitigation. Recent breakthroughs in manufacturing enable efficient fabrication of hierarchically architected microlattices, with dimensional control spanning seven orders of magnitude in length scale. These materials have the potential to exploit desirable nanoscale-size effects in a macroscopic structure, as long as their mechanical behavior at each appropriate scale – nano, micro, and macro levels – is properly understood. In this letter, we report the nanomechanical response of individual microlattice members. We show that hollow nanocrystalline Ni cylinders differing only in wall thicknesses, 500 and 150 nm, exhibit strikingly different collapse modes: the 500 nm sample collapses in a brittle manner, via a single strain burst, while the 150 nm sample shows a gradual collapse, via a series of small and discrete strain bursts. Further, compressive strength in 150 nm sample is 99.2% lower than predicted by shell buckling theory, likely due to localized buckling and fracture events observed during in situ compression experiments. We attribute this difference to the size-induced transition in deformation behavior, unique to nanoscale, and discuss it in the framework of “size effects” in crystalline strength
Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
We present a proof of the mirror conjecture of Aganagic-Vafa
[arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk
enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric
Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary
framing. In particular, we recover previous results on the conjecture for (i)
an inner brane at zero framing in the total space of the canonical line bundle
of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer
brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]),
and (iii) an outer brane at zero framing in the total space of the canonical
line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure
Scale-invariant magnetoresistance in a cuprate superconductor
The anomalous metallic state in high-temperature superconducting cuprates is
masked by the onset of superconductivity near a quantum critical point. Use of
high magnetic fields to suppress superconductivity has enabled a detailed study
of the ground state in these systems. Yet, the direct effect of strong magnetic
fields on the metallic behavior at low temperatures is poorly understood,
especially near critical doping, . Here we report a high-field
magnetoresistance study of thin films of \LSCO cuprates in close vicinity to
critical doping, . We find that the metallic state
exposed by suppressing superconductivity is characterized by a
magnetoresistance that is linear in magnetic field up to the highest measured
fields of T. The slope of the linear-in-field resistivity is
temperature-independent at very high fields. It mirrors the magnitude and
doping evolution of the linear-in-temperature resistivity that has been
ascribed to Planckian dissipation near a quantum critical point. This
establishes true scale-invariant conductivity as the signature of the strange
metal state in the high-temperature superconducting cuprates.Comment: 10 pages, 3 figure
Trace initial interaction from final state observable in relativistic heavy ion collisions
In order to trace the initial interaction in ultra-relativistic heavy ion
collision in all azimuthal directions, two azimuthal multiplicity-correlation
patterns -- neighboring and fixed-to-arbitrary angular-bin correlation patterns
-- are suggested. From the simulation of Au + Au collisions at 200 GeV by using
the Monte Carlo models RQMD with hadron re-scattering and AMPT with and without
string melting, we observe that the correlation patterns change gradually from
out-of-plane preferential one to in-plane preferential one when the centrality
of collision shifts from central to peripheral, meanwhile the anisotropic
collective flow v_2 keeps positive in all cases. This regularity is found to be
model and collision energy independent. The physics behind the two opposite
trends of correlation patterns, in particular, the presence of out-of-plane
correlation patterns at RHIC energy, are discussed.Comment: 5pages, 4figure
Classical Scattering in Dimensional String Theory
We find the general solution to Polchinski's classical scattering equations
for dimensional string theory. This allows efficient computation of
scattering amplitudes in the standard Liouville background.
Moreover, the solution leads to a mapping from a large class of time-dependent
collective field theory backgrounds to corresponding nonlinear sigma models.
Finally, we derive recursion relations between tachyon amplitudes. These may be
summarized by an infinite set of nonlinear PDE's for the partition function in
an arbitrary time-dependent background.Comment: 15 p
Resonance and frequency-locking phenomena in spatially extended phytoplankton-zooplankton system with additive noise and periodic forces
In this paper, we present a spatial version of phytoplankton-zooplankton
model that includes some important factors such as external periodic forces,
noise, and diffusion processes. The spatially extended
phytoplankton-zooplankton system is from the original study by Scheffer [M
Scheffer, Fish and nutrients interplay determines algal biomass: a minimal
model, Oikos \textbf{62} (1991) 271-282]. Our results show that the spatially
extended system exhibit a resonant patterns and frequency-locking phenomena.
The system also shows that the noise and the external periodic forces play a
constructive role in the Scheffer's model: first, the noise can enhance the
oscillation of phytoplankton species' density and format a large clusters in
the space when the noise intensity is within certain interval. Second, the
external periodic forces can induce 4:1 and 1:1 frequency-locking and spatially
homogeneous oscillation phenomena to appear. Finally, the resonant patterns are
observed in the system when the spatial noises and external periodic forces are
both turned on. Moreover, we found that the 4:1 frequency-locking transform
into 1:1 frequency-locking when the noise intensity increased. In addition to
elucidating our results outside the domain of Turing instability, we provide
further analysis of Turing linear stability with the help of the numerical
calculation by using the Maple software. Significantly, oscillations are
enhanced in the system when the noise term presents. These results indicate
that the oceanic plankton bloom may partly due to interplay between the
stochastic factors and external forces instead of deterministic factors. These
results also may help us to understand the effects arising from undeniable
subject to random fluctuations in oceanic plankton bloom.Comment: Some typos errors are proof, and some strong relate references are
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On touching random surfaces, two-dimensional quantum gravity and non-critical string theory
A set of physical operators which are responsible for touching interactions
in the framework of c<1 unitary conformal matter coupled to 2D quantum gravity
is found. As a special case the non-critical bosonic strings are considered.
Some analogies with four dimensional quantum gravity are also discussed, e.g.
creation-annihilation operators for baby universes, Coleman mechanism for the
cosmological constant.Comment: 22 pages, Latex2e, 3 figure
The structure of the Kac-Wang-Yan algebra
The Lie algebra of regular differential operators on the circle
has a universal central extension . The invariant subalgebra
under an involution preserving the principal gradation
was introduced by Kac, Wang, and Yan. The vacuum -module
with central charge , and its irreducible quotient
, possess vertex algebra structures, and has a
nontrivial structure if and only if . We show that
for each integer , and are
-algebras of types and
, respectively. These results are formal
consequences of Weyl's first and second fundamental theorems of invariant
theory for the orthogonal group and the symplectic group
, respectively. Based on Sergeev's theorems on the invariant
theory of we conjecture that is of
type , and we prove this for . As an
application, we show that invariant subalgebras of -systems and
free fermion algebras under arbitrary reductive group actions are strongly
finitely generated.Comment: Final versio
Perturbation Theory in Two Dimensional Open String Field Theory
In this paper we develop the covariant string field theory approach to open
2d strings. Upon constructing the vertices, we apply the formalism to calculate
the lowest order contributions to the 4- and 5- point tachyon--tachyon tree
amplitudes. Our results are shown to match the `bulk' amplitude calculations of
Bershadsky and Kutasov. In the present approach the pole structure of the
amplitudes becomes manifest and their origin as coming from the higher string
modes transparent.Comment: 26 page
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