4,596 research outputs found
The natural capital framework for sustainable, efficient and equitable decision making
The concept of ânatural capitalâ is gaining traction internationally as recognition grows of the central role of the natural environment in sustaining economic and social well-being. It is therefore encouraging to see the first signs of a ânatural capital approachâ to decision making being accepted within government policy processes and the private sector. However, there are multiple different understandings of this âapproachâ, many of which misuse or omit key features of its foundations in natural science and economics. To address this, we present a framework for natural capital analysis and decision making that links ecological and economic perspectives
Analytical solutions of the Schr\"{o}dinger equation with the Woods-Saxon potential for arbitrary state
In this work, the analytical solution of the radial Schr\"{o}dinger equation
for the Woods-Saxon potential is presented. In our calculations, we have
applied the Nikiforov-Uvarov method by using the Pekeris approximation to the
centrifugal potential for arbitrary states. The bound state energy
eigenvalues and corresponding eigenfunctions are obtained for various values of
and quantum numbers.Comment: 14 page
Structural frequency functions for an impulsive, distributed forcing function
The response of a penetrator structure to a spatially distributed mechanical impulse with a magnitude approaching field test force levels (1-2 Mlb) were measured. The frequency response function calculated from the response to this unique forcing function is compared to frequency response functions calculated from response to point forces of about 2000 pounds. The results show that the strain gages installed on the penetrator case respond similiarly to a point, axial force and to a spatially distributed, axial force. This result suggests that the distributed axial force generated in a penetration event may be reconstructed as a point axial force when the penetrator behaves in linear manner
On the rationality of the moduli space of L\"uroth quartics
We prove that the moduli space M_L of L"uroth quartics in P^2, i.e. the space
of quartics which can be circumscribed around a complete pentagon of lines
modulo the action of PGL_3(CC) is rational, as is the related moduli space of
Bateman seven-tuples of points in P^2.Comment: 7 page
Any l-state analytical solutions of the Klein-Gordon equation for the Woods-Saxon potential
The radial part of the Klein-Gordon equation for the Woods-Saxon potential is
solved. In our calculations, we have applied the Nikiforov-Uvarov method by
using the Pekeris approximation to the centrifugal potential for any
states. The exact bound state energy eigenvalues and the corresponding
eigenfunctions are obtained on the various values of the quantum numbers
and . The non-relativistic limit of the bound state energy spectrum was also
found.Comment: 15 pages, 1 tabl
Electromagnetic vortex lines riding atop null solutions of the Maxwell equations
New method of introducing vortex lines of the electromagnetic field is
outlined. The vortex lines arise when a complex Riemann-Silberstein vector
is multiplied by a complex scalar function
. Such a multiplication may lead to new solutions of the Maxwell
equations only when the electromagnetic field is null, i.e. when both
relativistic invariants vanish. In general, zeroes of the function give
rise to electromagnetic vortices. The description of these vortices benefits
from the ideas of Penrose, Robinson and Trautman developed in general
relativity.Comment: NATO Workshop on Singular Optics 2003 To appear in Journal of Optics
Relativistic ideal Fermi gas at zero temperature and preferred frame
We discuss the limit T->0 of the relativistic ideal Fermi gas of luxons
(particles moving with the speed of light) and tachyons (hypothetical particles
faster than light) based on observations of our recent paper: K. Kowalski, J.
Rembielinski and K.A. Smolinski, Phys. Rev. D, 76, 045018 (2007). For bradyons
this limit is in fact the nonrelativistic one and therefore it is not studied
herein
High orders of Weyl series for the heat content
This article concerns the Weyl series of spectral functions associated with
the Dirichlet Laplacian in a -dimensional domain with a smooth boundary. In
the case of the heat kernel, Berry and Howls predicted the asymptotic form of
the Weyl series characterized by a set of parameters. Here, we concentrate on
another spectral function, the (normalized) heat content. We show on several
exactly solvable examples that, for even , the same asymptotic formula is
valid with different values of the parameters. The considered domains are
-dimensional balls and two limiting cases of the elliptic domain with
eccentricity : A slightly deformed disk () and an
extremely prolonged ellipse (). These cases include 2D domains
with circular symmetry and those with only one shortest periodic orbit for the
classical billiard. We analyse also the heat content for the balls in odd
dimensions for which the asymptotic form of the Weyl series changes
significantly.Comment: 20 pages, 1 figur
Universal low-energy properties of three two-dimensional particles
Universal low-energy properties are studied for three identical bosons
confined in two dimensions. The short-range pair-wise interaction in the
low-energy limit is described by means of the boundary condition model. The
wave function is expanded in a set of eigenfunctions on the hypersphere and the
system of hyper-radial equations is used to obtain analytical and numerical
results. Within the framework of this method, exact analytical expressions are
derived for the eigenpotentials and the coupling terms of hyper-radial
equations. The derivation of the coupling terms is generally applicable to a
variety of three-body problems provided the interaction is described by the
boundary condition model. The asymptotic form of the total wave function at a
small and a large hyper-radius is studied and the universal logarithmic
dependence in the vicinity of the triple-collision point is
derived. Precise three-body binding energies and the scattering length
are calculated.Comment: 30 pages with 13 figure
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