4,510 research outputs found
Weakly nonlocal irreversible thermodynamics - the Guyer-Krumhansl and the Cahn-Hilliard equations
Examples of irreversible thermodynamic theory of nonlocal phenomena are
given, based on generalized entropy current. Thermodynamic currents and forces
are identified to derive the Guyer-Krumhansl and Cahn-Hilliard equations. In
the latter case Gurtin's rate dependent additional term is received through the
thermodynamic approach.Comment: revise
Constant Froude number in a circular hydraulic jump and its implication on the jump radius selection
The properties of a standard hydraulic jump depend critically on a Froude
number Fr defined as the ratio of the flow velocity to the gravity waves speed.
In the case of a horizontal circular jump, the question of the Froude number is
not well documented. Our experiments show that Fr measured just after the jump
is locked on a constant value that does not depend on flow rate Q, kinematic
viscosity {\nu} and surface tension {\gamma}. Combining this result to a
lubrication description of the outer flow yields, under appropriate conditions,
a new and simple law ruling the jump radius RJ : , in excellent agreement
with our experimental data. This unexpected RJ result asks an unsolved question
to all available models.Comment: 5 pages, 3 figure
Convective instabilities in two superposed horizontal liquid layers heated laterally
This work is devoted to the theoretical study of the stability of two
superposed horizontal liquid layers bounded by two solid planes and subjected
to a horizontal temperature gradient.
The liquids are supposed to be immiscible with a nondeformable interface.
The forces acting on the system are buoyancy and interfacial tension. Four
different flow patterns and temperature profiles are found for the basic state.
A linear perturbative analysis with respect to two and three dimensional
perturbations reveals the existence of three kind of patterns. Depending on the
relative height of both liquids several situations are predicted: either wave
propagation from cold to the hot regions, or waves propagating in the opposite
direction or still stationary longitudinal rolls. The behavior of three
different pairs of liquids which have been used in experiments on bilayers
under vertical gradient by other authors have been examined. The instability
mechanisms are discussed and a qualitative interpretation of the different
behaviors exhibited by the system is provided. In some configurations it is
possible to find a codimension-two point created by the interaction of two Hopf
modes with different frequencies and wavenumbers. These results suggest to
consider two liquid layers as an interesting prototype for the study of
propagation and interaction of waves in the context of the B\'enard-Marangoni
problem.Comment: 21 pages, 9 figures, 2 tables;accepted to be published in PR
A multi-level interface model for damaged masonry
The aim of the present work is to propose a new micro-mechanical model in the context of the deductive approach used to derive interface models. This model, based on a previous study introduced previously by A. Rekik and F. Lebon, is used to reproduce the damage in masonry by combining structural analysis and homogenization methods. The focal point of this method is to assume the existence of a third material, called interphase, which is a mixture of the two principal constituents of masonry, brick and mortar, and that is the interface between them. This new element presents a low thickness, a low stiffness and a given damage ratio. The mechanical problem of masonry, initially a 3D problem, is solved numerically as a 2D problem using finite element methods. The properties of the interface brick-mortar material are obtained using three essentials steps. First of all, an exact homogenisation of a laminates is used to define a first homogeneous equivalent medium named HEM-1. After, the assumption of damaged material is taken into account by using the general framework given by M. Kachanov to evaluate the global behaviour of the damaged HEM-1 defining thus a second equivalent homogeneous medium noted HEM-2. The last step consists in using an asymptotic analysis technique which is performed to model HEM-2 as an interface or a joint. The properties of this joint are deduced from those of the HEM-2 material as proposed in former papers. Particularly, through the second homogenization are taken into account the variability of microcracks oriented family and simultaneously the opening-closure effects (unilateral behaviour). Numerically this interface is modelled with connector finite elements. Numerical results are compared to experimental ones available in the literature
Tsallis statistics generalization of non-equilibrium work relations
We use third constraint formulation of Tsallis statistics and derive the
-statistics generalization of non-equilibrium work relations such as the
Jarzynski equality and the Crooks fluctuation theorem which relate the free
energy differences between two equilibrium states and the work distribution of
the non-equilibrium processes.Comment: 5 page
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