390 research outputs found
Charge Carrier Extraction by Linearly Increasing Voltage:Analytic framework and ambipolar transients
Up to now the basic theoretical description of charge extraction by linearly
increasing voltage (CELIV) is solved for a low conductivity approximation only.
Here we present the full analytical solution, thus generalize the theoretical
framework for this method. We compare the analytical solution and the
approximated theory, showing that especially for typical organic solar cell
materials the latter approach has a very limited validity. Photo-CELIV
measurements on poly(3-hexyl thiophene-2,5-diyl):[6,6]-phenyl-C61 butyric acid
methyl ester based solar cells were then evaluated by fitting the current
transients to the analytical solution. We found that the fit results are in a
very good agreement with the experimental observations, if ambipolar transport
is taken into account, the origin of which we will discuss. Furthermore we
present parametric equations for the mobility and the charge carrier density,
which can be applied over the entire experimental range of parameters.Comment: 8 pages, 5 figure
Symmetries of generalized soliton models and submodels on target space
Some physically relevant non-linear models with solitons, which have target
space , are known to have submodels with infinitly many conservation laws
defined by the eikonal equation. Here we calculate all the symmetries of these
models and their submodels by the prolongation method. We find that for some
models, like the Baby Skyrme model, the submodels have additional symmetries,
whereas for others, like the Faddeev--Niemi model, they do not.Comment: 18 pages, one Latex fil
Reduction Operators of Linear Second-Order Parabolic Equations
The reduction operators, i.e., the operators of nonclassical (conditional)
symmetry, of (1+1)-dimensional second order linear parabolic partial
differential equations and all the possible reductions of these equations to
ordinary differential ones are exhaustively described. This problem proves to
be equivalent, in some sense, to solving the initial equations. The ``no-go''
result is extended to the investigation of point transformations (admissible
transformations, equivalence transformations, Lie symmetries) and Lie
reductions of the determining equations for the nonclassical symmetries.
Transformations linearizing the determining equations are obtained in the
general case and under different additional constraints. A nontrivial example
illustrating applications of reduction operators to finding exact solutions of
equations from the class under consideration is presented. An observed
connection between reduction operators and Darboux transformations is
discussed.Comment: 31 pages, minor misprints are correcte
The Inflationary Perturbation Spectrum
Motivated by the prospect of testing inflation from precision cosmic
microwave background observations, we present analytic results for scalar and
tensor perturbations in single-field inflation models based on the application
of uniform approximations. This technique is systematically improvable,
possesses controlled error bounds, and does not rely on assuming the slow-roll
parameters to be constant. We provide closed-form expressions for the power
spectra and the corresponding scalar and tensor spectral indices.Comment: 4 pages, 1 figur
Nonlinear Evolution Equations Invariant Under Schroedinger Group in three-dimensional Space-time
A classification of all possible realizations of the Galilei,
Galilei-similitude and Schroedinger Lie algebras in three-dimensional
space-time in terms of vector fields under the action of the group of local
diffeomorphisms of the space \R^3\times\C is presented. Using this result a
variety of general second order evolution equations invariant under the
corresponding groups are constructed and their physical significance are
discussed
Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
The Chern-Simons lagrangian density in the space of metrics of a
3-dimensional manifold M is not invariant under the action of diffeomorphisms
on M. However, its Euler-Lagrange operator can be identified with the Cotton
tensor, which is invariant under diffeomorphims. As the lagrangian is not
invariant, Noether Theorem cannot be applied to obtain conserved currents. We
show that it is possible to obtain an equivariant conserved current for the
Cotton tensor by using the first equivariant Pontryagin form on the bundle of
metrics. Finally we define a hamiltonian current which gives the contribution
of the Chern-Simons term to the black hole entropy, energy and angular
momentum.Comment: 13 page
Singular reduction modules of differential equations
The notion of singular reduction modules, i.e., of singular modules of
nonclassical (conditional) symmetry, of differential equations is introduced.
It is shown that the derivation of nonclassical symmetries for differential
equations can be improved by an in-depth prior study of the associated singular
modules of vector fields. The form of differential functions and differential
equations possessing parameterized families of singular modules is described up
to point transformations. Singular cases of finding reduction modules are
related to lowering the order of the corresponding reduced equations. As
examples, singular reduction modules of evolution equations and second-order
quasi-linear equations are studied. Reductions of differential equations to
algebraic equations and to first-order ordinary differential equations are
considered in detail within the framework proposed and are related to previous
no-go results on nonclassical symmetries.Comment: 38 pages, advanced version. Extension of results of arXiv:0808.3577
to the case of a greater number of independent variable
The Darboux coordinates for a new family of Hamiltonian operators and linearization of associated evolution equations
A. de Sole, V. G. Kac, and M. Wakimoto (arXiv:1004.5387) have recently
introduced a new family of compatible Hamiltonian operators of the form
, where , ,
is the dependent variable and is the total derivative with respect to
the independent variable. We present a differential substitution that reduces
any linear combination of these operators to an operator with constant
coefficients and linearizes any evolution equation which is bi-Hamiltonian with
respect to a pair of any nontrivial linear combinations of the operators
. We also give the Darboux coordinates for for any odd
.Comment: 6 pages, AMS-LaTeX, extended versio
Ultrafocused electromagnetic field pulses with a hollow cylindrical waveguide
We theoretically show that a dipole externally driven by a pulse with a lower-bounded temporal width, and placed inside a cylindrical hollow waveguide, can generate a train of arbitrarily short and focused electromagnetic pulses. The waveguide encloses vacuum with perfect electric conducting walls. A dipole driven by a single short pulse, which is properly engineered to exploit the linear spectral filtering of the cylindrical hollow waveguide, excites longitudinal waveguide modes that are coherently refocused at some particular instances of time, thereby producing arbitrarily short and focused electromagnetic pulses. We numerically show that such ultrafocused pulses persist outside the cylindrical waveguide at distances comparable to its radius
Conservation laws for multidimensional systems and related linear algebra problems
We consider multidimensional systems of PDEs of generalized evolution form
with t-derivatives of arbitrary order on the left-hand side and with the
right-hand side dependent on lower order t-derivatives and arbitrary space
derivatives. For such systems we find an explicit necessary condition for
existence of higher conservation laws in terms of the system's symbol. For
systems that violate this condition we give an effective upper bound on the
order of conservation laws. Using this result, we completely describe
conservation laws for viscous transonic equations, for the Brusselator model,
and the Belousov-Zhabotinskii system. To achieve this, we solve over an
arbitrary field the matrix equations SA=A^tS and SA=-A^tS for a quadratic
matrix A and its transpose A^t, which may be of independent interest.Comment: 12 pages; proof of Theorem 1 clarified; misprints correcte
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