Mark H. Holmes

Bio: Mark H. Holmes is an academic researcher from Rensselaer Polytechnic Institute. The author has contributed to research in topics: Basilar membrane & Differential equation. The author has an hindex of 21, co-authored 77 publications receiving 4228 citations. Previous affiliations of Mark H. Holmes include Duke University & University of California, Los Angeles.

Introduction to Perturbation Methods

Abstract: Preface.- Preface to Second Edition.- Introduction to Asymptotic Approximations.- Matched Asymptotic Expansions.- Multiple Scales.- The WKB and Related Methods.- The Method of Homogenization- Introduction to Bifurcation and Stability.- References.- Index.

Boundary Conditions at the Cartilage-Synovial Fluid Interface for Joint Lubrication and Theoretical Verifications

Abstract: The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A "pseudo-no-slip" kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.

Principles of Neural Science

Abstract: I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Some asymptotic methods for strongly nonlinear equations

Abstract: This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modied perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this eld in China so the references, therefore, are not exhaustive.

The basic science of articular cartilage: structure, composition, and function

Abstract: Articular cartilage is the highly specialized connective tissue of diarthrodial joints. Its principal function is to provide a smooth, lubricated surface for articulation and to facilitate the transmission of loads with a low frictional coefficient (Figure 1). Articular cartilage is devoid of blood vessels, lymphatics, and nerves and is subject to a harsh biomechanical environment. Most important, articular cartilage has a limited capacity for intrinsic healing and repair. In this regard, the preservation and health of articular cartilage are paramount to joint health. Figure 1. Gross photograph of healthy articular cartilage in an adult human knee. Injury to articular cartilage is recognized as a cause of significant musculoskeletal morbidity. The unique and complex structure of articular cartilage makes treatment and repair or restoration of the defects challenging for the patient, the surgeon, and the physical therapist. The preservation of articular cartilage is highly dependent on maintaining its organized architecture.

Skeletal Tissue Mechanics

Abstract: Forces in Joints, Skeletal Biology, Analysis of Bone Remodeling, Mechanical Properties of Bone, Fatigue and Fracture Resistance of Bone, Mechanical Adaptation of the Skeleton, Synovial Joint Mechanics, Mechanical Properties of Ligament and Tendon