Bell's Law Research Articles

A Physical Framework to Study the Effect of Magnetic Fields on the Spike-Time Coding.

A temporal neural code reliant on the pattern of spike times rather than spike rates offers a feasible mechanism for encoding information from weak periodic external stimuli, such as static or extremely low-frequency electromagnetic fields. Our model focuses on the influence of magnetic fields on neurotransmitter dynamics near the neuron membrane. Neurotransmitter binding to specific receptor sites on membrane proteins can regulate biochemical reactions. The duration a neurotransmitter spends in the bonded state serves as a metric for the magnetic field's capacity as a chemical regulator. By initiating a physical analysis of ligand-receptor binding, utilizing the alpha function for synaptic conductance, and employing a modified version of Bell's law, we quantified the impact of magnetic fields on the bond half-life time and, consequently, on postsynaptic spike timing.

Investigation of critical parameters in power supplies components failure due to electric pulse

This paper presents an investigation aiming to determine the thresholds that lead to the destruction of power supplies components, such as rectifier bridge and rectifier diode, under differential mode electric pulse injection in the case of High Electromagnetic Pulse (HEMP) scenario. The coupling of HEMP field on long power lines generates high level current and voltage pulse disturbances which can propagate on the power network and flow into power supply input stages such as switch-mode power supplies (SMPS) present on main powered equipment. As a consequence of this injected parasitic, different electrical stresses occur inside the SMPS at electronic components level leading to cascaded destruction events. During a previous study, some internal electrical stresses have been measured and identified as the destruction cause of critical components such as rectifier bridge or rectifier diode. An electrical stress generator made of different capacitor cells is built to reproduce the electric pulses which will be present at the SMPS components terminals during their destruction. Oscilloscope associated to current and differential voltage probes are used to determine the failure moment. The performed tests have shown that rectifier bridge destruction follows a Wunsch and Bell law in current and in power according to the injection pulse duration. Concerning the rectifier diode, its destruction is due to its reverse voltage which has been measured around 135 V. This information will be used, in a future work, to better understand the destruction mechanism observed on complete power supplies and build behavioural models able to predict the destruction of power supplies in the case of HEMP scenario.

The Book Computer Structures: Thoughts After 40 Years

This article discusses the effect of Computer Structures on readers and students. Having a zoo of many computers in one place has been useful to the computer science community for access, comparison, and reference though useful, is not quite enough. The main impact is the understanding that is gained in the writing that went into the subsequent computers, the taxonomy, Bell's law, and the various lines of research it stimulated.

Editor's Column

This final issue of the SSCS News features an extensive new article by Gordon Bell entitled "Bell's Law for the Birth and Death of Computer Classes: A Theory of the Computer's Evolution." We also print two additional articles on the influence of Dr. Eric Vittoz by Joyce Kwong and Anantha Chandrakasan of MIT and by Dr. Erik H. M. Heijne of CERN, plus a classic paper written in 1981 by Dr.Vittoz, who was the Feature Author of our Summer '08 issue.

Bell's law for the birth and death of computer classes

A theory of the computer's evolution.

Bell's Law for the Birth and Death of Computer Classes: A theory of the Computer's Evolution

In 1951 a man could walk inside a computer. By 2010, a computer cluster with millions of processors will have expanded to building size. In this new paper Gordon Bell explains the history of the computing industry, positing a general theory ("Bell's Law) for the creation, evolution, and death of computer classes since 1951. Using the exponential transistor density increases forecast by Moore's Law in 1965 and 1975 as the principal basis for the life cycle of computer classes after the microprocessor was introduced in 1971, he predicts that the powerful microprocessor will be the basis for nearly all computer classes in 2010, from personal computers and servers costing a few thousand dollars to scalable servers costing a few hundred million dollars. Soon afterward, billions of cell phones for personal computing, and tens of billions of wireless sensor nets will unwire and interconnect everything.

Deformations of an elastic, internally constrained material. Part 1: Homogeneous deformations

The nonlinear elastic response of a class of materials for which the deformation is subject to an internal material constraint described in experiments by James F. Bell on the finite deformation of a variety of metals is investigated. The purely kinematical consequences of the Bell constraint are discussed, and restrictions on the full range of compatible deformations are presented in geometrical terms. Then various forms of the constitutive equation relating the stress and stretch tensors for an isotropic elastic Bell material are presented. Inequalities on the mechanical response functions are introduced. The importance of these in applications is demonstrated in several examples throughout the paper. This paper focuses on homogeneous deformations. In a simple illustration of the theory, a generalized form of Bell's empirical rule for uniaxial loading is derived, and some peculiarities in the response under all-around compressive loading are discussed. General formulae for universal relations possible in an isotropic elastic, Bell constrained material are presented. A simple method for the determination of the left stretch tensor for essentially plane problems is illustrated in the solution of the problem of pure shear of a materially uniform rectangular block. A general formula which includes the empirical rule found in pure shear experiments by Bell is derived as a special case. The whole apparatus is then applied in the solution of the general problem of a homogeneous simple shear superimposed on a uniform triaxial stretch; and the great variety of results possible in an isotropic, elastic Bell material is illustrated. The problem of the finite torsion and extension of a thin-walled cylindrical tube is investigated. The results are shown to be consistent with Bell's data for which the rigid body rotation is found to be quite small compared with the gross deformation of the tube. Several universal formulas relating various kinds of stress components to the deformation independently of the material response functions are derived, including a universal rule relating the axial force to the torque. Constitutive equations for hyperelastic Bell materials are derived. The empirical work function studied by Bell is introduced; and a new constitutive equation is derived, which we name Bell's law. On the basis of this law, we then derive exactly Bell's parabolic laws for uniaxial loading and for pure shear. Also, form Bell's law, a simple constitutive equation relating Bell's deviatoric stress tensor to his finite deviatoric strain tensor is obtained. We thereby derive Bell's invariant parabolic law relating the deviatoric stress intensity to the corresponding strain intensity; and, finally, Bell's fundamental law for the work function expressed in these terms is recovered. This rule is the foundation for all of Bell's own theoretical study of the isotropic materials cataloged in his finite strain experiments on metals, all consistent with the internal material constraint studied here.

Bell's law

Charles Bell was born in Edinburgh in 1774 and died in 1842 at Hallow’ near Worcester, where he was buried. Both parents were connected with the episcopal Church of Scotland. Two of his brothers distinguished themselves—-John as an anatomist and surgeon and George as an authority on Scots law. Charles studied medicine at Edinburgh University, without however taking a degree, but qualified as a Fellow of the Edinburgh College of Surgeons in 1799, having already as a student developed a strong interest in anatomy, which continued throughout his life. He was an attractive and imaginative artist, qualities which are particularly in evidence in his Essays on the anatomy of expression (1806) and his Bridgewater Treatise on The hand (1833), of which Sherrington used to speak with admiration.

The role of the dorsal roots in muscle tonus.

It is hard to see why cutting the sensory fibers for a muscle should abolish its tonus since powerful tonic contraction can be induced from the vestibular labyrinth, from the sensory nerves of the opposite limb and from other sources. It would seem as if afferent impulses from these sources should be able to maintain at least a moderate degree of tonus in the absence of those coming from the muscle itself.For this reason Frank1 has suggested that the dorsal roots are important in this connection not so much because they carry sensory fibers from the muscles as because they contain efferent fibers through which tonic impulses are conveyed to the muscles. Such special tonic fibers might be thought of as causing a jellying or increase in viscosity of the contracted muscle thus delaying its relaxation. Frank failed to subject his hypothesis to a thorough experimental test and partly for this reason, and partly because it is in conflict with Bell's law, his theory has received but scant consideration.The resul...

A Sketch of the History of Reflex Action. II. Bell's Law

A Sketch of the History of Reflex Action. II. Bell's Law