11,608 research outputs found
Isomonodromic deformatiion with an irregular singularity and hyperelliptic curve
In this paper, we extend the result of Kitaev and Korotkin to the case where
a monodromy-preserving deformation has an irregular singularity. For the
monodromy-preserving deformation, we obtain the -function whose
deformation parameters are the positions of regular singularities and the
parameter of an irregular singularity. Furthermore, the -function is
expressed by the hyperelliptic function moving the argument \z and
the period \B, where and the positions of regular singularities move
and \B, respectively.Comment: 23 pages, 2 figure
Trees and the urban environment - weighing risks and benefits
The presence of mature, broad-leafed trees in urban areas is increasingly evidenced as being beneficial for public health, mental well-being and the environment. Consequently, any loss of such trees should be regarded as increasing risk, potentially with significant consequences. Currently, austerity measures and fragmented policies are tending to miss out on the opportunities presented by a greener environment, and some policies connected with, for example, road safety and highway engineering have the potential to reduce tree presence if disproportionately applied, as does fear of litigation
Ultradiscretization of the solution of periodic Toda equation
A periodic box-ball system (pBBS) is obtained by ultradiscretizing the
periodic discrete Toda equation (pd Toda eq.). We show the relation between a
Young diagram of the pBBS and a spectral curve of the pd Toda eq.. The formula
for the fundamental cycle of the pBBS is obtained as a colloraly.Comment: 41 pages; 7 figure
Effect of spin orbit scattering on the magnetic and superconducting properties of nearly ferromagnetic metals: application to granular Pt
We calculate the effect of scattering on the static, exchange enhanced, spin
susceptibility and show that in particular spin orbit scattering leads to a
reduction of the giant moments and spin glass freezing temperature due to
dilute magnetic impurities. The harmful spin fluctuation contribution to the
intra-grain pairing interaction is strongly reduced opening the way for BCS
superconductivity. We are thus able to explain the superconducting and magnetic
properties recently observed in granular Pt as due to scattering effects in
single small grains.Comment: 9 pages 3 figures, accepted for publication in Phys. Rev. Letter
Discreteness and the transmission of light from distant sources
We model the classical transmission of a massless scalar field from a source
to a detector on a background causal set. The predictions do not differ
significantly from those of the continuum. Thus, introducing an intrinsic
inexactitude to lengths and durations - or more specifically, replacing the
Lorentzian manifold with an underlying discrete structure - need not disrupt
the usual dynamics of propagation.Comment: 16 pages, 1 figure. Version 2: reference adde
Dynamical study of the hyperextended scalar-tensor theory in the empty Bianchi type I model
The dynamics of the hyperextended scalar-tensor theory in the empty Bianchi
type I model is investigated. We describe a method giving the sign of the first
and second derivatives of the metric functions whatever the coupling function.
Hence, we can predict if a theory gives birth to expanding, contracting,
bouncing or inflationary cosmology. The dynamics of a string inspired theory
without antisymetric field strength is analysed. Some exact solutions are
found.Comment: 18 pages, 3 figure
Dynamical study of the empty Bianchi type I model in generalised scalar-tensor theory
A dynamical study of the generalised scalar-tensor theory in the empty
Bianchi type I model is made. We use a method from which we derive the sign of
the first and second derivatives of the metric functions and examine three
different theories that can all tend towards relativistic behaviours at late
time. We determine conditions so that the dynamic be in expansion and
decelerated at late time.Comment: 18 pages, 3 figures, to appear in General Relativity and Gravitatio
Energy-momentum diffusion from spacetime discreteness
We study potentially observable consequences of spatiotemporal discreteness
for the motion of massive and massless particles. First we describe some simple
intrinsic models for the motion of a massive point particle in a fixed causal
set background. At large scales, the microscopic swerves induced by the
underlying atomicity manifest themselves as a Lorentz invariant diffusion in
energy-momentum governed by a single phenomenological parameter, and we derive
in full the corresponding diffusion equation. Inspired by the simplicity of the
result, we then derive the most general Lorentz invariant diffusion equation
for a massless particle, which turns out to contain two phenomenological
parameters describing, respectively, diffusion and drift in the particle's
energy. The particles do not leave the light cone however: their worldlines
continue to be null geodesics. Finally, we deduce bounds on the drift and
diffusion constants for photons from the blackbody nature of the spectrum of
the cosmic microwave background radiation.Comment: 13 pages, 4 figures, corrected minor typos and updated to match
published versio
Specific heat and thermal conductivity in the mixed state of MgB2
The specific heat C and the electronic and phononic thermal conductivities
kappa_e and kappa_{ph} are calculated in the mixed state for magnetic fields H
near H_{c2}. The effects of supercurrent flow and Andreev scattering of the
Abrikosov vortex lattice on the quasiparticles are taken into account. The
resulting function C(H) is nearly linear while kappa_e(H) exhibits an upward
curvature near H_{c2}. The slopes decrease with impurity scattering which
improves the agreement with the data on MgB_2. The ratio of phonon relaxation
times tau_n/tau_s = g(omega_0,H) for phonon energy omega_0, which is nearly a
step function at omega_0 = 2Delta for the BCS state, is smeared out and tends
to one for increasing H. This leads to a rapid reduction of kappa_{ph}(H) in
MgB_2 for relatively small fields due to the rapid suppression of the smaller
energy gap.Comment: 8 pages, 4 figures, accepted for publication in Phys. Rev. Letter
Functional representation of the Volterra hierarchy
In this paper I study the functional representation of the Volterra hierarchy
(VH). Using the Miwa's shifts I rewrite the infinite set of Volterra equations
as one functional equation. This result is used to derive a formal solution of
the associated linear problem, a generating function for the conservation laws
and to obtain a new form of the Miura and Backlund transformations. I also
discuss some relations between the VH and KP hierarchy.Comment: 17 pages, submitted to Journal of Nonlinear Mathematical Physic
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