There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The partition of unity finite element method: Basic theory and applications

Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

This paper presents the theory of dissipative systems in the context of finite dimensional stationary linear systems with quadratic supply rates. A necessary and sufficient frequency domain condition for dissipativeness is derived. This is followed by the evaluation of the available storage and the required supply and of a time-domain criterion for dissipativeness involving certain matrix inequalities. The quadratic storage functions and the dissipation functions are then examined. The discussion then turns to reciprocal systems and it is shown that external reciprocity and dissipativeness imply the existence of a state space realization which is also internally reciprocal and dissipative. The paper proceeds with an examination of reversible systems and of relaxation systems. In particular, it is shown how a unique internal storage function may be defined for relaxation systems. These results are applied to the synthesis of electrical networks and the theory of linear viscoelastic materials.

Dissipative dynamical systems Part II: Linear systems with quadratic supply rates

Oil exploration and production actively began 100 years ago, from the present day. What we see now, known as primary production by natural flowing of oil by pumped wells. This covers 15% of oil recovery from reservoir. Later 25% of oil is recovered by water flooding is activated which is termed as secondary production. There is still significant oil left in the reservoir, if there is no proper employment of commercial valuable techniques for the production, the oilwell would simply be abandoned. But as the demand for oil kept raising new techniques emerged, eventually from those EOR was a successful in artificial up lifting of oil from the reservoir by providing enough pressure to the trapped oil to flow out of well. It is a tertiary production. EOR is different because it works from microscopic levels as well as by injecting the substances like gases, special liquid (polymers) and stream in the form of injection through injecting wells for oil recovery, which is termed as Enhanced Oil Recovery (EOR). The flooding in EOR, categorized as chemical flooding (by chemicals), stream or thermal injection (by stream) and miscible gas drive (CO2, N2 and LPG). These flooding will alter the physical and chemical properties of reservoirs for the flow of oil out of the well. EOR can unlock a percentage of 30-45% of trapped oil. After naming as successful technique in onshore for tertiary production, research is still going to implement EOR in offshore, to improve tertiary production and exploit hidden billion barrels of oil.

Enhanced Oil Recovery

An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation

Slightly nonlinear materials and structures with purely hysteretic damping, subjected to harmonic disturbances, are examined. It is shown that a load-deformation or stress-strain relation, on first loading, supplemented by a rule to obtain the curves on unloading and reloading, leads to a behavior similar to that of a linear viscoelastic material, but the equivalent damping ratio does not depend on frequency or amplitude. The relations between stress and strain in unloading and reloading can be obtained from a relation for first loading. It is contended that some materials that are considered viscoelastic actually possess this type of hysteretic behavior. Expressions are included for equivalent viscous damping and for the period of free vibration.

Ismael Herrera

Papers

Enhanced Oil Recovery

An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation

On a Kind of Hysteretic Damping

Waves in materials with memory: I. The velocity of one-dimensional shock and acceleration waves

Boundary methods : an algebraic theory