I. Liu - Academia.edu (original) (raw)

Papers by I. Liu

Research paper thumbnail of Relativistic thermodynamics of gases

Research paper thumbnail of The influence of temperature on the formation of salt domes

The study of salt tectonics arouses interest in the oil industry, being relevant for the understa... more The study of salt tectonics arouses interest in the oil industry, being relevant for the understanding of the mechanisms and dynamics of such deformations. The study and the simulation of the mechanical aspects of the salt migration represent useful results in understanding this phenomenon. However, it is supposed that temperature effects are also important for the formation of oil basins. This work aims to study the influence of temperature on the formation of the salt dome. To this end, it is considered the temperature influence on the geophysical properties of the materials and a mathematical model called Sucessive Linear Approximation Method (SLA) is used, which allows, in a unified manner, the simulation of the motion of salt and the sediment layers. This method was shown to be very efficient in several simulations for large deformations of nearly-incompressible bodies to which are simulated the deformations of sediment and salt layers. Results will be presented illustrating the effect of temperature on the formation of oil basins, as well as the efficiency of method ALI for simulating large deformations with temperature influence.

Research paper thumbnail of Shock structure in viscoelasticity of relaxation type

Nonlinear Analysis: Theory, Methods & Applications, 2006

We are concerned with the shock structure in viscoelasticity of rate type. The existence of a sho... more We are concerned with the shock structure in viscoelasticity of rate type. The existence of a shock profile, which in the vanishing relaxation limit becomes an elastic shock, is demonstrated by an explicit construction of the solution of viscoelastic equations provided that the equilibrium stress-strain relation is governed by a parabolic law. For a more general stress-strain law which does not differ substantially from a parabolic one, the solution is obtained from a perturbation expansion.

Research paper thumbnail of Numerical simulation of salt migration--Large deformation in viscoelastic solid bodies

Research paper thumbnail of Extended thermodynamics of classical and degenerate ideal gases

Archive for Rational Mechanics and Analysis, 1983

ABSTRACT Details of the theoretical basis of the field theory of extended thermodynamics for dete... more ABSTRACT Details of the theoretical basis of the field theory of extended thermodynamics for determining the thirteen fields of mass, momentum, and energy densities, the stress deviator, and the heat flux are presented. The kinetic theory of gases is reviewed, together with analytical considerations of thermodynamic processes, the entropy principle, and hyperbolicity. The principle of material frame indifference is examined, and an evaluation is made of entropy inequality. Aspects of the concept of absolute temperature are explored, and the theory is applied to classical and degenerate gases. Mention is also made of small amplitude plane harmonic waves and techniques for performing a transition from extended thermodynamics to ordinary thermodynamics.

Research paper thumbnail of Oscillation waves in Riemann problems for phase transitions

Research paper thumbnail of Relativistic thermodynamics of gases

Annals of Physics, 1986

Relativistic thermodynamics of degenerate gases is presented here as a field theory of the 14 lie... more Relativistic thermodynamics of degenerate gases is presented here as a field theory of the 14 lields of particle density -particle flux, and stress-energy -momentum.

Research paper thumbnail of I-Shih Liu · Rubens Sampaio Remarks on material frame-indifference controversy

Regarding a frame of reference as an observer, the notion of frame-indifference (also referred to... more Regarding a frame of reference as an observer, the notion of frame-indifference (also referred to as objectivity) concerns the transformation properties of physical quantities under change of observer. For kinematic quantities, they can usually be derived from the deformation/motion, while for non-kinematic quantities, such as force and stress, A frame-indifference property must be postulated. frame-indifference postulate for the stress, sometimes unsuitably called the principle of frame-indifference, is a universal assumption, which has nothing to do with material properties. This has caused some confusions in the interpretation of "material" frame-indifference in the literature. Material frame-indifference deals with the constitutive functions, which characterize intrinsic properties of the material under different observers. We shall carefully render these concepts mathematically and deduce the well-known condition of material objectivity as a consequence of the frame-indifference postulate and the principle of material frame-indifference. We shall also emphasize and remark on some persistent controversy and some misleading statements found in recent literature.

Research paper thumbnail of Relativistic thermodynamics of gases

Research paper thumbnail of The influence of temperature on the formation of salt domes

The study of salt tectonics arouses interest in the oil industry, being relevant for the understa... more The study of salt tectonics arouses interest in the oil industry, being relevant for the understanding of the mechanisms and dynamics of such deformations. The study and the simulation of the mechanical aspects of the salt migration represent useful results in understanding this phenomenon. However, it is supposed that temperature effects are also important for the formation of oil basins. This work aims to study the influence of temperature on the formation of the salt dome. To this end, it is considered the temperature influence on the geophysical properties of the materials and a mathematical model called Sucessive Linear Approximation Method (SLA) is used, which allows, in a unified manner, the simulation of the motion of salt and the sediment layers. This method was shown to be very efficient in several simulations for large deformations of nearly-incompressible bodies to which are simulated the deformations of sediment and salt layers. Results will be presented illustrating the effect of temperature on the formation of oil basins, as well as the efficiency of method ALI for simulating large deformations with temperature influence.

Research paper thumbnail of Shock structure in viscoelasticity of relaxation type

Nonlinear Analysis: Theory, Methods & Applications, 2006

We are concerned with the shock structure in viscoelasticity of rate type. The existence of a sho... more We are concerned with the shock structure in viscoelasticity of rate type. The existence of a shock profile, which in the vanishing relaxation limit becomes an elastic shock, is demonstrated by an explicit construction of the solution of viscoelastic equations provided that the equilibrium stress-strain relation is governed by a parabolic law. For a more general stress-strain law which does not differ substantially from a parabolic one, the solution is obtained from a perturbation expansion.

Research paper thumbnail of Numerical simulation of salt migration--Large deformation in viscoelastic solid bodies

Research paper thumbnail of Extended thermodynamics of classical and degenerate ideal gases

Archive for Rational Mechanics and Analysis, 1983

ABSTRACT Details of the theoretical basis of the field theory of extended thermodynamics for dete... more ABSTRACT Details of the theoretical basis of the field theory of extended thermodynamics for determining the thirteen fields of mass, momentum, and energy densities, the stress deviator, and the heat flux are presented. The kinetic theory of gases is reviewed, together with analytical considerations of thermodynamic processes, the entropy principle, and hyperbolicity. The principle of material frame indifference is examined, and an evaluation is made of entropy inequality. Aspects of the concept of absolute temperature are explored, and the theory is applied to classical and degenerate gases. Mention is also made of small amplitude plane harmonic waves and techniques for performing a transition from extended thermodynamics to ordinary thermodynamics.

Research paper thumbnail of Oscillation waves in Riemann problems for phase transitions

Research paper thumbnail of Relativistic thermodynamics of gases

Annals of Physics, 1986

Relativistic thermodynamics of degenerate gases is presented here as a field theory of the 14 lie... more Relativistic thermodynamics of degenerate gases is presented here as a field theory of the 14 lields of particle density -particle flux, and stress-energy -momentum.

Research paper thumbnail of I-Shih Liu · Rubens Sampaio Remarks on material frame-indifference controversy

Regarding a frame of reference as an observer, the notion of frame-indifference (also referred to... more Regarding a frame of reference as an observer, the notion of frame-indifference (also referred to as objectivity) concerns the transformation properties of physical quantities under change of observer. For kinematic quantities, they can usually be derived from the deformation/motion, while for non-kinematic quantities, such as force and stress, A frame-indifference property must be postulated. frame-indifference postulate for the stress, sometimes unsuitably called the principle of frame-indifference, is a universal assumption, which has nothing to do with material properties. This has caused some confusions in the interpretation of "material" frame-indifference in the literature. Material frame-indifference deals with the constitutive functions, which characterize intrinsic properties of the material under different observers. We shall carefully render these concepts mathematically and deduce the well-known condition of material objectivity as a consequence of the frame-indifference postulate and the principle of material frame-indifference. We shall also emphasize and remark on some persistent controversy and some misleading statements found in recent literature.