924 research outputs found
Stress dependent thermal pressurization of a fluid-saturated rock
Temperature increase in saturated porous materials under undrained conditions
leads to thermal pressurization of the pore fluid due to the discrepancy
between the thermal expansion coefficients of the pore fluid and of the solid
matrix. This increase in the pore fluid pressure induces a reduction of the
effective mean stress and can lead to shear failure or hydraulic fracturing.
The equations governing the phenomenon of thermal pressurization are presented
and this phenomenon is studied experimentally for a saturated granular rock in
an undrained heating test under constant isotropic stress. Careful analysis of
the effect of mechanical and thermal deformation of the drainage and pressure
measurement system is performed and a correction of the measured pore pressure
is introduced. The test results are modelled using a non-linear
thermo-poro-elastic constitutive model of the granular rock with emphasis on
the stress-dependent character of the rock compressibility. The effects of
stress and temperature on thermal pressurization observed in the tests are
correctly reproduced by the model
Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains
We analyze the 1D focusing nonlinear Schr\"{o}dinger equation in a finite
interval with homogeneous Dirichlet or Neumann boundary conditions. There are
two main dynamics, the collapse which is very fast and a slow cascade of
Fourier modes. For the cubic nonlinearity the calculations show no long term
energy exchange between Fourier modes as opposed to higher nonlinearities. This
slow dynamics is explained by fairly simple amplitude equations for the
resonant Fourier modes. Their solutions are well behaved so filtering high
frequencies prevents collapse. Finally these equations elucidate the unique
role of the zero mode for the Neumann boundary conditions
Scaling Properties of Weak Chaos in Nonlinear Disordered Lattices
The Discrete Nonlinear Schroedinger Equation with a random potential in one
dimension is studied as a dynamical system. It is characterized by the length,
the strength of the random potential and by the field density that determines
the effect of nonlinearity. The probability of the system to be regular is
established numerically and found to be a scaling function. This property is
used to calculate the asymptotic properties of the system in regimes beyond our
computational power.Comment: 4 pages, 5 figure
Dissipative solitons which cannot be trapped
In this paper we study the behavior of dissipative solitons in systems with
high order nonlinear dissipation and show how they cannot survive under the
effect of trapping potentials both of rigid wall type or asymptotically
increasing ones. This provides an striking example of a soliton which cannot be
trapped and only survives to the action of a weak potential
Finite time collapse of N classical fields described by coupled nonlinear Schrodinger equations
We prove the finite-time collapse of a system of N classical fields, which
are described by N coupled nonlinear Schrodinger equations. We derive the
conditions under which all of the fields experiences this finite-time collapse.
Finally, for two-dimensional systems, we derive constraints on the number of
particles associated with each field that are necessary to prevent collapse.Comment: v2: corrected typo on equation
Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
Motivated by recent experimental studies of matter-waves and optical beams in
double well potentials, we study the solutions of the nonlinear Schr\"{o}dinger
equation in such a context. Using a Galerkin-type approach, we obtain a
detailed handle on the nonlinear solution branches of the problem, starting
from the corresponding linear ones and predict the relevant bifurcations of
solutions for both attractive and repulsive nonlinearities. The results
illustrate the nontrivial differences that arise between the steady
states/bifurcations emerging in symmetric and asymmetric double wells
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