83,249 research outputs found
Some remarks on the model of rigid heat conductor with memory: unbounded heat relaxation function
The model of rigid linear heat conductor with memory is reconsidered
focussing the interest on the heat relaxation function. Thus, the definitions
of heat flux and thermal work are revised to understand where changes are
required when the heat flux relaxation function is assumed to be unbounded
at the initial time . That is, it is represented by a regular integrable
function, namely , but its time derivative is not integrable,
that is . Notably, also under these relaxed assumptions
on , whenever the heat flux is the same also the related thermal work is the
same. Thus, also in the case under investigation, the notion of equivalence is
introduced and its physical relevance is pointed out
Some remarks on the model of rigid heat conductor with memory: unbounded heat relaxation function
The model of rigid linear heat conductor with memory is reconsidered
focussing the interest on the heat relaxation function. Thus, the definitions
of heat flux and thermal work are revised to understand where changes are
required when the heat flux relaxation function is assumed to be unbounded
at the initial time . That is, it is represented by a regular integrable
function, namely , but its time derivative is not integrable,
that is . Notably, also under these relaxed assumptions
on , whenever the heat flux is the same also the related thermal work is the
same. Thus, also in the case under investigation, the notion of equivalence is
introduced and its physical relevance is pointed out
Singular Kernel Problems in Materials with Memory
In recent years the interest on devising and study new materials is growing since they are widely used in different applications which go from rheology to bio-materials or aerospace applications. In this framework, there is also a growing interest in understanding the behaviour of materials with memory, here considered. The name of the model aims to emphasize that the behaviour of such materials crucially depends on time not only through the present time but also through the past history. Under the analytical point of view, this corresponds to model problems represented by integro-differential equations which exhibit a kernel non local in time. This is the case of rigid thermodynamics with memory as well as of isothermal viscoelasticity; in the two different models the kernel represents, in turn, the heat flux relaxation function and the relaxation modulus. In dealing with classical materials with memory these kernels are regular function of both the present time as well as the past history. Aiming to study new materials integro-differential problems admitting singular kernels are compared. Specifically, on one side the temperature evolution in a rigid heat conductor with memory characterized by a heat flux relaxation function singular at the origin, and, on the other, the displacement evolution within a viscoelastic model characterized by a relaxation modulus which is unbounded at the origin, are considered. One dimensional problems are examined; indeed, even if the results are valid also in three dimensional general cases, here the attention is focussed on pointing out analogies between the two different materials with memory under investigation. Notably, the method adopted has a wider interest since it can be applied in the cases of other evolution problems which are modeled by analogue integro-differential equations. An initial boundary value problem with homogeneneous Neumann boundary conditions is studied.In recent years the interest on devising and study
new materials is growing since they are widely used in different applications
which go from rheology to bio-materials or aerospace applications.
In this framework,
there is also a growing interest in understanding the behaviour of materials with memory, here
considered. The name
of the model aims to emphasize that the behaviour of
such materials crucially depends on time not only
through the present time but also through the past history. Under the
analytical point of view, this corresponds to model problems represented by
integro-differential
equations which exhibit a kernel non local in time. This is the case of rigid
thermodynamics with memory as well as of isothermal viscoelasticity; in the two different
models the kernel represents, in turn, the heat flux relaxation function and
the relaxation modulus. In dealing with
classical materials with memory these kernels are regular function of both the present
time as wel
Effect of surface tension on nanotube nanofluids
This letter presents heat transfer results that single-walled carbon nanotube (CNT) suspensions in a boiling environment can extend the saturated boiling regime and postpone catastrophic failure of the material even further than previously reported if the surface tension of the nanofluid is carefully controlled. The maximum enhancement in the critical heat flux is nearly four times for a surfactant to CNT concentration ratio of 1:5. The experimental results show that the material burnout is a strong function of the relaxation of the nanofluid surface tension with the base fluid
A minimum principle for the quasi-static problem in linear viscoelasticity
A minimum principle is set up for the quasi-static
boundary-value problem (QSP) in linear viscoelasticity.
A linear homogeneous and isotropic viscoelastic solid under unidimensional displacements is considered along with the complete set of thermodynamic restrictions on the relaxation function. It is assumed that boundary conditions are of Dirichlet type and initial history data are not given. The variational formulation of QSP is set up through a convex functional based on a "weighted" inner product as the bilinear form and is strictly related to the thermodynamic restrictions on the relaxation function. As an aside, the same technique is proved to be applicable to analogous physical problems such as the quasi-static heat flux equation
Decoherence and Relaxation of a Quantum Bit in the Presence of Rabi Oscillations
Dissipative dynamics of a quantum bit driven by a strong resonant field and
interacting with a heat bath is investigated. We derive generalized Bloch
equations and find modifications of the qubit's damping rates caused by Rabi
oscillations. Nonequilibrium decoherence of a phase qubit inductively coupled
to a LC-circuit is considered as an illustration of the general results. It is
argued that recent experimental results give a clear evidence of effective
suppression of decoherence in a strongly driven flux qubit.Comment: 14 pages; misprints correcte
- …