238 research outputs found
An explicit height bound for the classical modular polynomial
For a prime m, let Phi_m be the classical modular polynomial, and let
h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we
prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we
find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values
is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To
appear in the Ramanujan Journal. 17 pages
Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder
We study the statistics of thermodynamic quantities in two related systems
with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in
a random potential and the 2-dimensional random bond dimer model. The first
system is examined by a replica-symmetric Bethe ansatz (RBA) while the latter
is studied numerically by a polynomial algorithm which circumvents slow glassy
dynamics. We establish a mapping of the two models which allows for a detailed
comparison of RBA predictions and simulations. Over a wide range of disorder
strength, the effective lattice stiffness and cumulants of various
thermodynamic quantities in both approaches are found to agree excellently. Our
comparison provides, for the first time, a detailed quantitative confirmation
of the replica approach and renders the planar line lattice a unique testing
ground for concepts in random systems.Comment: 16 pages, 14 figure
Enhancement of pair correlation in a one-dimensional hybridization model
We propose an integrable model of one-dimensional (1D) interacting electrons
coupled with the local orbitals arrayed periodically in the chain. Since the
local orbitals are introduced in a way that double occupation is forbidden, the
model keeps the main feature of the periodic Anderson model with an interacting
host. For the attractive interaction, it is found that the local orbitals
enhance the effective mass of the Cooper-pair-like singlets and also the pair
correlation in the ground state. However, the persistent current is depressed
in this case. For the repulsive interaction case, the Hamiltonian is
non-Hermitian but allows Cooper pair solutions with small momenta, which are
induced by the hybridization between the extended state and the local orbitals.Comment: 11 page revtex, no figur
Electromagnetic corrections in eta --> 3 pi decays
We re-evaluate the electromagnetic corrections to eta --> 3 pi decays at
next-to-leading order in the chiral expansion, arguing that effects of order
e^2(m_u-m_d) disregarded so far are not negligible compared to other
contributions of order e^2 times a light quark mass. Despite the appearance of
the Coulomb pole in eta --> pi+ pi- pi0 and cusps in eta --> 3 pi0, the overall
corrections remain small.Comment: 21 pages, 11 figures; references updated, version published in EPJ
Can forest management based on natural disturbances maintain ecological resilience?
Given the increasingly global stresses on forests, many ecologists argue that managers must maintain ecological resilience: the capacity of ecosystems to absorb disturbances without undergoing fundamental change. In this review we ask: Can the emerging paradigm of natural-disturbance-based management (NDBM) maintain ecological resilience in managed forests? Applying resilience theory requires careful articulation of the ecosystem state under consideration, the disturbances and stresses that affect the persistence of possible alternative states, and the spatial and temporal scales of management relevance. Implementing NDBM while maintaining resilience means recognizing that (i) biodiversity is important for long-term ecosystem persistence, (ii) natural disturbances play a critical role as a generator of structural and compositional heterogeneity at multiple scales, and (iii) traditional management tends to produce forests more homogeneous than those disturbed naturally and increases the likelihood of unexpected catastrophic change by constraining variation of key environmental processes. NDBM may maintain resilience if silvicultural strategies retain the structures and processes that perpetuate desired states while reducing those that enhance resilience of undesirable states. Such strategies require an understanding of harvesting impacts on slow ecosystem processes, such as seed-bank or nutrient dynamics, which in the long term can lead to ecological surprises by altering the forest's capacity to reorganize after disturbance
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
Neutralizing antibody vaccine for pandemic and pre-emergent coronaviruses
Betacoronaviruses (betaCoVs) caused the severe acute respiratory syndrome (SARS) and Middle East Respiratory Syndrome (MERS) outbreaks, and the SARS-CoV-2 pandemic1–4. Vaccines that elicit protective immunity against SARS-CoV-2 and betaCoVs circulating in animals have the potential to prevent future betaCoV pandemics. Here, we show that macaque immunization with a multimeric SARS-CoV-2 receptor binding domain (RBD) nanoparticle adjuvanted with 3M-052/Alum elicited cross-neutralizing antibody (cross-nAb) responses against batCoVs, SARS-CoV-1, SARS-CoV-2, and SARS-CoV-2 variants B.1.1.7, P.1, and B.1.351. Nanoparticle vaccination resulted in a SARS-CoV-2 reciprocal geometric mean neutralization ID50 titer of 47,216, and protection against SARS-CoV-2 in macaque upper and lower respiratory tracts. Importantly, nucleoside-modified mRNA encoding a stabilized transmembrane spike or monomeric RBD also induced SARS-CoV-1 and batCoV cross-nAbs, albeit at lower titers. These results demonstrate current mRNA vaccines may provide some protection from future zoonotic betaCoV outbreaks, and provide a platform for further development of pan-betaCoV vaccines
Petrophysical, Geochemical, and Hydrological Evidence for Extensive Fracture-Mediated Fluid and Heat Transport in the Alpine Fault's Hanging-Wall Damage Zone
Fault rock assemblages reflect interaction between deformation, stress, temperature, fluid, and chemical regimes on distinct spatial and temporal scales at various positions in the crust. Here we interpret measurements made in the hanging-wall of the Alpine Fault during the second stage of the Deep Fault Drilling Project (DFDP-2). We present observational evidence for extensive fracturing and high hanging-wall hydraulic conductivity (∼10−9 to 10−7 m/s, corresponding to permeability of ∼10−16 to 10−14 m2) extending several hundred meters from the fault's principal slip zone. Mud losses, gas chemistry anomalies, and petrophysical data indicate that a subset of fractures intersected by the borehole are capable of transmitting fluid volumes of several cubic meters on time scales of hours. DFDP-2 observations and other data suggest that this hydrogeologically active portion of the fault zone in the hanging-wall is several kilometers wide in the uppermost crust. This finding is consistent with numerical models of earthquake rupture and off-fault damage. We conclude that the mechanically and hydrogeologically active part of the Alpine Fault is a more dynamic and extensive feature than commonly described in models based on exhumed faults. We propose that the hydrogeologically active damage zone of the Alpine Fault and other large active faults in areas of high topographic relief can be subdivided into an inner zone in which damage is controlled principally by earthquake rupture processes and an outer zone in which damage reflects coseismic shaking, strain accumulation and release on interseismic timescales, and inherited fracturing related to exhumation
De novo design of proteins housing excitonically coupled chlorophyll special pairs
Natural photosystems couple light harvesting to charge separation using a ‘special pair’ of chlorophyll molecules that accepts excitation energy from the antenna and initiates an electron-transfer cascade. To investigate the photophysics of special pairs independently of the complexities of native photosynthetic proteins, and as a first step toward creating synthetic photosystems for new energy conversion technologies, we designed C2-symmetric proteins that hold two chlorophyll molecules in closely juxtaposed arrangements. X-ray crystallography confirmed that one designed protein binds two chlorophylls in the same orientation as native special pairs, whereas a second designed protein positions them in a previously unseen geometry. Spectroscopy revealed that the chlorophylls are excitonically coupled, and fluorescence lifetime imaging demonstrated energy transfer. The cryo-electron microscopy structure of a designed 24-chlorophyll octahedral nanocage with a special pair on each edge closely matched the design model. The results suggest that the de novo design of artificial photosynthetic systems is within reach of current computational methods
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