Studies of Mental “Noise”

Successive tests of subjects' performance in reaction time tasks were treated as time series and submitted to spectrum analysis. Rather than revealing the white noise expected by the view that variability is due to random error (equivalent power across frequency), the power spectra revealed colored noise. The slopes of the power spectra did not vary much for tasks differing in memory requirements. Spectrum analysis of time series from the logistic map also showed colored noise in regions on the edge of chaos, showing that the presence of colored noise in cognitive data need not oblige a theoretical account based on a complex, high-dimensional, system.     

Versuche zu einem „shear-rate-blockage“-Effekt am Protoplasma zentrifugierter Gewebe

Ohne ZusammenfassungI thank Mr.Scott Blair for his answer reserving the term dilatancy for cases of real dilatation. Now it's only to wish that this terminology is used according to his Report on the principles of rheological nomenclature (Amsterdam 1949).     

Group Classification of Equations of the Form y″ = f(x,y)

The problem of classification of ordinary differential equations of the form y = f(x,y) by admissible local Lie groups of transformations is solved. Standard equations are listed on the basis of the equivalence concept. The classes of equations admitting a oneparameter group and obtained from the standard equations by invariant extension are described.     

Mathematics and Rheology

Summary The great advances made in Rheology during the last forty years owe much to the application of mathematics. But in some cases, there have been misunderstandings. As a result, rheologists have sometimes been unnecessarily restricted. Mathematics is limited only by self-consistency: Rheology deals with the physical world.In particular, three terms are discussed: infinity, zero and negative, all of which have at least two meanings which have been confused. Rheological phenomena cannot be explained merely by mathematical formulation. Unnecessary mathematics should be avoided but professional rheologists must not shirk mathematics.This paper was read in an abbreviated form, at aConference of the British Society of Rheology in April 1971 The Proceedings were not published.     

Exact Solutions of the Hydrodynamic Equations Derived from Partially Invariant Solutions

The paper proposes a heuristic approach to constructing exact solutions of the hydrodynamic equations based on the specificity of these equations. A number of systems of hydrodynamic equations possess the following structure: they contain a reduced system of n equations and an additional equation for an extra function w. In this case, the reduced system, in which w = 0, admits a Lie group G. Taking a certain partially invariant solution of the reduced system with respect to this group as a seed:rdquo; solution, we can find a solution of the entire system, in which the functional dependence of the invariant part of the seed solution on the invariants of the group G has the previous form. Implementation of the algorithm proposed is exemplified by constructing new exact solutions of the equations of rotationally symmetric motion of an ideal incompressible liquid and the equations of concentrational convection in a plane boundary layer and thermal convection in a rotating layer of a viscous liquid.     

The problems of nonlinear bending for orthotropic rectangular plate with four clamped edges

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On the sensitive dynamical system and the transition from the apparently deterministic process to the completely random process

The detailed analysis of the dynamical process of coin tossing is made. Through calculations, it is illustrated how and why the result is extremely sensitive to the initial conditions. It is also shown that, as the initial height of the mass center of the coin increases, the final configuration, i.e. head or tail, becomes more and more sensitive to the initial parameters (the initial velocity angular velocity, and the initial orientation), the coefficient of the air drag, and the energy absorption factor of the surface on which the coin bounces. If we keep the head upward initially but allow a small range for the change of some other initial parameters, the frequency that the final configuration is head, would be 1 if the initial height h of the mass center is sufficiently small, and would be clo to 1/2 if h is sufficiently large. An interesting question is how this frequency changes continuously from 1 to 1/2 as h increases. Detailed calculations show that such a transition is very similar to the transition from laminar to turbulent flows. A basic difference between the transition stage and the completely random stage is indicated: In the completely random stage, the deterministic process of the individual case is extremely sensitive to the initial conditions and the dynamical parameters, out the statistical properties of the ensemble are insensitive to the small changes of the initial conditions and the dynamical parameters. On the contrary, in the transition stage, both the deterministic process of the individual case and the statistical properties of the ensemble are sensitive to the initial conditions and the dynamical parameters. The mechanism for this feature of the transition stage is the existence of the long-train structure in the parameter space. The illuminations of this analysis on some other random phenomena are discussed.     

Investigation of a “hanging” shock wave near a generating point

The hodograph method is used to plot a hanging shock wave in the plane nonequilibrium supersonic flow of an ideal gas. This paper considers the general case of an analytical solution in the plane of the hodograph at the point of generation of the shock wave. A type of limiting line is established which makes it possible to plot a shock wave (it is found that the shock wave may not extend over the whole flow, with a convolution in the physical plane).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 30–37, November–December, 1971.     

Direct derivation of the two-shaft system balance conditions for the second order reciprocal inertia forces on the V-type eight cylinders internal combustion engines with a plane crankshaft

By employing the four shafts balance concept paper [1] has reported a balance regime for the second order reciprocal inertia forces on the V-type eight cylinder internal combustion engines with a plane crankshaft. Thereafter, paper [2] has acquired a two-shafts balance regime, but through a rather tedious roudabout degenerating manipulation. The present article has, but starting out directly from the two-shafts balance concept, successfully acquired the same results as those in paper [2]. In addition, we propose, herein, a third balance system which might be, in general, called the slipper balance regime.     

Entropy and causality as criteria for the existence of shock waves in low temperature heat conduction

A set of symmetric hyberbolic field equations, describing heat conduction in dielectric solids at low temperatures, is studied with respect to the propagation of temperature shock waves. The field equations have been derived from the Boltzmann-Peierls equation and include the phenomenon of second sound, a special form of wavelike energy transport occuring in some crystals in a temperature range close to absolute zero.Two physical criteria, an entropy shock condition and the Lax condition, which is based on a causality argument, are applied to study the existence of so called hot and cold shocks. These are characterized by a temperature rise or fall across the shock respectively, and it turns out that the only possible solution to the problem is a hot shock, predicted by either one of the criteria.In the recent literature, however, a similar case was treated revealing a partial contradiction between the two criteria. Regarding the fact that there exists a proof of equivalence for small shocks, we were thus led to investigate this equivalence in the general case, which is illustrated by means of a simple example.     

On universal solutions in initially stressed bodies

A saddle point (or maximum-minimum) principle is set up for the quasi-static boundary-value problem in linear viscoelasticity. The appropriate class of convolution-type functionals for it is taken in terms of bilinear forms with a weight function involving the Fourier transform. The minimax property is shown to hold as a direct consequence of thermodynamic restrictions on the relaxation function. This approach can be extended to further linear evolution problems where initial data are not prescribed.     

Whose Thoughts Are They, Anyway? Dimensionally Exploding Bion's “Double-Headed Arrow” into Coadapting, Transitional Space

The physics and biology that found psychoanalysis account for discontinuous experience only in the presence of nonmeasurable, metaphysical operators; these include the ego and its subsystems as well as biological experience inherited through Lamarckian principles. Complex, self-organizing systems, however, can link biology to experience without metaphysics. They can also account for psychoanalytically relevant behaviors without appealing to stable internal representations. These behaviors include what W. R. Bion called transformation in O and its corollary, the appearance of the selected fact. By dimensionally exploding the double-headed arrow that he used to link the states Ps and D in his model for thinking (Ps D), we can generate a space that is, at once, psychoanalytically imaginal and dynamically coadapting. Isomorphic to D. W. Winnicott's transitional space, it is self-organizing. It is describable according to dynamics formulated by W J. Freeman, S. Kauffman and C. Langton and it can generate instantaneous conscious contents by way of a selective process analogous to spatio-temporal binding. As a whole, this model supports a clinical stance advanced by D. W. Winnicott as play, within transitional space.     

Almost analytic solutions and their tests of the horizontal diffusion equation for the movement of water in unsaturated soil

Itisalwaysdifficulttofindthesolutionsoftheequationforthemovementofwaterinunsaturatedsoi1.Theprimar}'reasonisthatthehydraulicconductivityK(T)orthediffusivityofsoiIwaterD(o)isfunctionofwaterpotential(W)orwatercontent'(o)'Atpresent,thegeneralwaystofindthesol…     

A particle transport problem with a quadratic nonlinearity and general boundary conditions: The stationary solution

Summary We study a stationary, nonlinear, particle transport problem in slab geometry with general boundary conditions. The existence and uniqueness of the solution is proved by means of fixed point techniques, provided that the source term is sufficiently small.

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Sommario Si studia un problema stazionario nonlineare di particelle in geometria piana con condizioni al contorno generali. L'esistenza e unicitá della soluzione è dimostrata con tecniche di punto fisso purchè il termine di sorgente sia sufficientemente piccolo.

     

Das erweiterte Korrespondenzgesetz für die dynamische Idealviskosität und die Idealwärmeleitfähigkeit reiner Stoffe

Zusammenfassung Zur Berechnung der dynamischen Idealviskosität Ideal (T) und der Idealwärmeleitfähigkeit ideal (T) benötigt man die kritische TemperaturT _kr, das kritische spezifische Volum _kr, die MolmasseM, den kritischen Parameter _kr und die molare isochore WärmekapazitätC _v(T). Sowohl das theoretisch, als auch das empirisch abgeleitete erweiterte Korrespondenzgesetz ergeben eine für praktische Zwecke ausreichende Genauigkeit für die Meßwertwiedergabe, die bei den assoziierenden Stoffen und den Quantenstoffen jedoch geringer ist als bei den Normalstoffen.

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The extended correspondence law for the ideal dynamic viscosity and the ideal thermal conductivity of pure substances

For the calculation of the ideal dynamic viscosity Ideal (T) and the ideal thermal conductivity ideal (T) the critical temperatureT _kr, the critical specific volumev _kr, the molecular massM, the critical parameter _kr, and the molar isochoric heat capacityC _v(T) is needed. Not only the theoretically determined but also the empirically determined extended correspondence law gives for practical use a good representation of the measured data, which for the associating substances and the quantum substances is not so good as for the normal substances.

     

Über die Übertragungseinheiten und ein „Vierfelderdiagramm” zur Berechnung von Wärmeübertragern

Zusammenfassung Es wird dargelegt, wie man nach Einführung des bekannten Begriffes Übertragungseinheit und mit Hilfe eines Vierfelderdiagramms zu einer relativ einfachen und durchsichtigen Berechnung von Gleich- und Gegenstrom-Wärmeübertragern gelangt.

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On transfer units and a four-quadrant-diagram for the calculation of heat exchangers

It is shown that the introduction of the known concept of a transfer unit and the use of a four-quadrant diagram leads to a relatively simple and clear computation method for co-current and counter-current heat exchangers.

     

The problem of the neutron diffusion: A survey

Summary This paper expounds researches done by the author and others on the theory of the diffusion of neutrons in a moderating medium from the point of view of phenomenological theory and of transport integro-differential equations.In particular the transformational methods with a rigorous analysis for the case of slab-geometry are considered.

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Sommario In questo lavoro si espongono ricerche dell'autore e di altri concernenti il problema della diffusione dei neutroni in un mezzo moderatore, sia dal punto di vista fenomenologico, sia dal punto di vista della teoria del trasporto.Si rivolge particolare attenzione ai metodi trasformazionali e ad una analisi rigorosa nel caso della lastra infinitamente estesa.

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Here we do not consider the kinetics of the nuclear reactor or related problems.     

Axioms and fundamental equations of image processing

Image-processing transforms must satisfy a list of formal requirements. We discuss these requirements and classify them into three categories: architectural requirements like locality, recursivity and causality in the scale space, stability requirements like the comparison principle and morphological requirements, which correspond to shape-preserving properties (rotation invariance, scale invariance, etc.). A complete classification is given of all image multiscale transforms satisfying these requirements. This classification yields a characterization of all classical models and includes new ones, which all are partial differential equations. The new models we introduce have more invariance properties than all the previously known models and in particular have a projection invariance essential for shape recognition. Numerical experiments are presented and compared. The same method is applied to the multiscale analysis of movies. By introducing a property of Galilean invariance, we find a single multiscale morphological model for movie analysis.     

Some aspects of dilute suspension theory

A theory proposed by the author as representative of the flow of a general suspension contains three interaction forces, f, S and N. For a quasi-concentrated suspension and for a dilute suspension, N and S, N are omitted, respectively. For the latter special case, we treat diffusion of a fluid through an elastic solid. For a quasi-concentrated suspension, we show that F and S depend on the gradient of the motion gradient. We demonstrate the existence of interesting phenomena: non-simple behavior, dissipative effects, generalized lift and drag forces.Presented at the second conference Recent Developments in Structured Continua, May 23 – 25, 1990, in Sherbrooke, Québec, Canada.     

On linear versus nonlinear flow rules in strain localization analysis

Summary This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear comparison material is critically reviewed and compared to the criterion resulting from actual nonlinear plastic flow laws.

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Sommario Si svolgono alcune considerazioni sui fenomeni di biforcazione in solidi elastoplastici in regime di piccole deformazioni (di linearità geometrica) e precisamente sul manifestarsi di localizzazioni intese come discontinuità nel campo delle deformazioni incrementali. Si considerano leggi nonassociate. Vengono così inclusi nella trattazione modelli costitutivi frequentemente adottati per descrivere il comportamento di materiali ad attrito interno e soggetti a danneggiamento (nel senso di degrado di rigidezze elastiche in seguito a deformazioni anelastiche), oltre che soggetti a manifestazioni di instabilità per incrudimento negativo (softening). Si esamina criticamente il criterio, frequentemente adottato in letteratura, di localizzazione fondato su materiale di confronto incrementalmente lineare e si fornisce, corredato da osservazioni comparative, il criterio che risulta dall'assunzione del modello di materiale incrementale non lineare