585 research outputs found
On the ternary complex analysis and its applications
Previouly a possible extension of the complex number, together with its
connected trigonometry was introduced. In this paper we focuss on the simplest
case of ternary complex numbers. Then, some types of holomorphicity adapted to
the ternary complex numbers and the corresponding results upon integration of
differential forms are given. Several physical applications are given, and in
particuler one type of holomorphic function gives rise to a new form of
stationary magnetic field. The movement of a monopole type object in this field
is then studied and shown to be integrable. The monopole scattering in the
ternary field is finally studied.Comment: LaTeX 28 page
On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere
Single variable hypergeometric functions pFq arise in connection with the
power series solution of the Schrodinger equation or in the summation of
perturbation expansions in quantum mechanics. For these applications, it is of
interest to obtain analytic expressions, and we present the reduction of a
number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related
series have additional applications in quantum and statistical physics and
chemistry.Comment: 17 pages, no figure
Multi-Dimensional Hermite Polynomials in Quantum Optics
We study a class of optical circuits with vacuum input states consisting of
Gaussian sources without coherent displacements such as down-converters and
squeezers, together with detectors and passive interferometry (beam-splitters,
polarisation rotations, phase-shifters etc.). We show that the outgoing state
leaving the optical circuit can be expressed in terms of so-called
multi-dimensional Hermite polynomials and give their recursion and
orthogonality relations. We show how quantum teleportation of photon
polarisation can be modelled using this description.Comment: 10 pages, submitted to J. Phys. A, removed spurious fil
Controlling Effect of Geometrically Defined Local Structural Changes on Chaotic Hamiltonian Systems
An effective characterization of chaotic conservative Hamiltonian systems in
terms of the curvature associated with a Riemannian metric tensor derived from
the structure of the Hamiltonian has been extended to a wide class of potential
models of standard form through definition of a conformal metric. The geodesic
equations reproduce the Hamilton equations of the original potential model
through an inverse map in the tangent space. The second covariant derivative of
the geodesic deviation in this space generates a dynamical curvature, resulting
in (energy dependent) criteria for unstable behavior different from the usual
Lyapunov criteria. We show here that this criterion can be constructively used
to modify locally the potential of a chaotic Hamiltonian model in such a way
that stable motion is achieved. Since our criterion for instability is local in
coordinate space, these results provide a new and minimal method for achieving
control of a chaotic system
A massive Feynman integral and some reduction relations for Appell functions
New explicit expressions are derived for the one-loop two-point Feynman
integral with arbitrary external momentum and masses and in D
dimensions. The results are given in terms of Appell functions, manifestly
symmetric with respect to the masses . Equating our expressions with
previously known results in terms of Gauss hypergeometric functions yields
reduction relations for the involved Appell functions that are apparently new
mathematical results.Comment: 19 pages. To appear in Journal of Mathematical Physic
New solutions of Heun general equation
We show that in four particular cases the derivative of the solution of Heun
general equation can be expressed in terms of a solution to another Heun
equation. Starting from this property, we use the Gauss hypergeometric
functions to construct series solutions to Heun equation for the mentioned
cases. Each of the hypergeometric functions involved has correct singular
behavior at only one of the singular points of the equation; the sum, however,
has correct behavior
On Virtual Displacement and Virtual Work in Lagrangian Dynamics
The confusion and ambiguity encountered by students, in understanding virtual
displacement and virtual work, is discussed in this article. A definition of
virtual displacement is presented that allows one to express them explicitly
for holonomic (velocity independent), non-holonomic (velocity dependent),
scleronomous (time independent) and rheonomous (time dependent) constraints. It
is observed that for holonomic, scleronomous constraints, the virtual
displacements are the displacements allowed by the constraints. However, this
is not so for a general class of constraints. For simple physical systems, it
is shown that, the work done by the constraint forces on virtual displacements
is zero. This motivates Lagrange's extension of d'Alembert's principle to
system of particles in constrained motion. However a similar zero work
principle does not hold for the allowed displacements. It is also demonstrated
that d'Alembert's principle of zero virtual work is necessary for the
solvability of a constrained mechanical problem. We identify this special class
of constraints, physically realized and solvable, as {\it the ideal
constraints}. The concept of virtual displacement and the principle of zero
virtual work by constraint forces are central to both Lagrange's method of
undetermined multipliers, and Lagrange's equations in generalized coordinates.Comment: 12 pages, 10 figures. This article is based on an earlier article
physics/0410123. It includes new figures, equations and logical conten
Geodesics around Weyl-Bach's Ring Solution
We explore some of the gravitational features of a uniform ring both in the
Newtonian potential theory and in General Relativity. We use a spacetime
associated to a Weyl static solution of the vacuum Einstein's equations with
ring like singularity. The Newtonian motion for a test particle in the
gravitational field of the ring is studied and compared with the corresponding
geodesic motion in the given spacetime. We have found a relativistic peculiar
attraction: free falling particle geodesics are lead to the inner rim but never
hit the ring.Comment: 8 figures, 14 pages. LaTeX w/ subfigure, graphic
Projective dynamics and first integrals
We present the theory of tensors with Young tableau symmetry as an efficient
computational tool in dealing with the polynomial first integrals of a natural
system in classical mechanics. We relate a special kind of such first
integrals, already studied by Lundmark, to Beltrami's theorem about
projectively flat Riemannian manifolds. We set the ground for a new and simple
theory of the integrable systems having only quadratic first integrals. This
theory begins with two centered quadrics related by central projection, each
quadric being a model of a space of constant curvature. Finally, we present an
extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure
Morning versus Afternoon Body Mass in Free-Living or Controlled Euhydration
The standard protocol to assess hydration status is by measuring body mass in the early morning without controlling fluid intake. However, obtaining first-morning body mass is not necessarily feasible for many situations, for example, most physical activities take place in the afternoon. Thus, first-morning body mass might not be practical to assess hydration status. PURPOSE: To investigate first-morning body mass versus afternoon body mass in free- living and controlled euhydration. METHODS: 9 males (age: 21 ± 2; mass: 79.7 ± 17.8 kg) and 5 females (age: 22 ± 2; mass: 60.5 ± 13.6 kg) visited the laboratory in the morning (7:00-9:00am) and afternoon (2:00-4:00pm) for six days to measure their nude body mass and urine specific gravity (USG). Participants were in the free-living (FL) condition for the first three consecutive days, and then in a euhydrated (EUH) state (USGRESULTS: There were no interactions between FL and EUH with morning and afternoon in USG (Morning-FL, 1.017±0.005; Afternoon-FL, 1.012±0.006; Morning-EUH, 1.011±0.004; Afternoon-EUH, 1.007±0.004; p=0.390). No statistically significant differences were found between morning and afternoon in both FL and EUH controlled (Morning-FL, 72.7±18.3 kg; Afternoon-FL, 72.0±18.1 kg; Morning-EUH, 72.9±18.1 kg; Afternoon-EUH, 73.1±18.1 kg, p=0.661). CONCLUSION: There is no difference between morning and afternoon body mass, regardless of the hydration status. This means that first morning body mass is no more, or less, accurate than afternoon
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