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A cost-effect, “black” liquid, flat-plate solar collector has been designed, and prototypes have been built and tested. In these collectors a highly absorbent “black” liquid flows in transparent channels and directly absorbs solar energy. The liquid is the hottest substance in the collector, and no metals are required anywhere in the design. The collector differs in the following ways from conventional flat-plate collectors: 1. 1. Solar radiation is absorbed directly by the black liquid without the need to heat any other structures within the collector. 2. 2. Lower heat losses are possible since energy is absorbed directly by the working fluid, and the flow pattern can be arranged so that the hottest spot is in the center of the collector away from all edges. As the fluid moves progressively inward toward the exit, which is located at the center of the collector, it will pick up some of the heat loss along the radial direction. 3. 3. Lower cost may be possible since no metal is required in construction and only glass and/or plastic need be used in addition to the insulation and frame. The absence of metal should eliminate all corrosion problems. 4. 4. New avenues of research are opened up by the use of black liquids: an entirely new class of materials are available which may aid in finding inexpensive, durable absorbers. 5. 5. New configurational arrangements are possible with the absence of metal absorbers. Experimental performance data for the black liquid collector is presented which compares favorably with other conventional flat-plate collectors.

The effects of the electric breakdown limitation on the power output of an electrofluid dynamic generator operating with colloids are studied. The study is performed for both an axisymmetric cylinder of charge and a two-dimensional (Cartesian) slab of charge between infinite, plane, parallel electrodes. The ratio of radius to length or width to length varies from zero to infinity, thus both the so-called slender channels (reference [9]) and broad channels (reference [2]) as well as the intermediate geometries are studied. Normalized power (the value of which is basically limited by electric breakdown) is presented as a function of normalized gas velocity and normalized applied voltage. Also presented is a normalized power per unit mass flow rate as a function of the normalized velocity and voltage. A single chart is sufficient to cover all geometries because the normalized power includes a geometric factor which can be determined from an auxiliary curve to account for the particular geometry.

We show that any probabilistically interpretable quantum theory using a Hilbert space of indefinite metric is equivalent to a quantum theory using a Hilbert space of positive definite metric. However, in general a formally local theory is transformed in this way into a theory that is no longer local: the formally local quantities cannot be measured. We give general criteria which permit to decide whether a theory may be probabilistically interpreted or not. When applied to the scattering of two θ on one N particle in the Lee model, these criteria lead to the result that the probabilistic interpretation is possible not only in the case of the dipole ghost, but also in the case of the complex conjugate energy eigenvalues of the interacting V particle. We also conclude that in both cases, however, the probabilistic interpretation of more complicated scattering problems is only possible provided that new discrete energy eigenstates of negative norm do not appear.

In view of the fact that physical measurements represent transmission of information, a general definition based on the measure of “lack of knowledge” in information theory can be introduced for different entropies each of them corresponding to one particular kind of measurement. By means of this entropy concept the problem of the consistency of microscopic reversibility and macroscopic irreversibility is studied. Under certain conditions it can be shown that the reversible microscopic equation of motion leads to the result that all entropies corresponding to “reduced” quantities, i.e. to quantities which do not determine the microscopic state of the system completely, can never decrease. However, it is to be noted that this behaviour is symmetric in time, in the classical as well as in the quantum mechanical case. Irreversibility is so related on the one hand to incomplete description of a system, but on the other also to the fact that theoretical statements can be verified by experiments in the future only. The validity of the results obtained within the framework of ensemble theory for a single physical system is discussed. As applications of the general ideas a system of free particles and the BOLTZMANN gas are treated.

For pt. I see ibid., vol. 14, no. 5, 427. The statistical model developed in Part I is applied to the discussion of the stability of inhomogeneous Vlasov equilibria. The existence of instability is expressed by the general condition integral I(x)( theta (x)- phi 0)dV>0 provided a certain class of variations compatible with the physical constraints imposed on the system does exist. In this criterion I(x) is the information variable depending on the physical system under consideration, phi (x) the corresponding potential, and phi 0 its spatial average. When I(x) is the charge density the criterion can be applied in order to show the instability of the Bernstein, Greene and Kruskal solutions. It is also shown, by means of the entropy principle, that the isolated inhomogeneous collisionless systems evolve towards more homogeneous equilibria, associated with a higher entropy, by transforming their collective energy into the energy of the random individual fluctuations. Moreover, nearly homogeneous but electrostatically unstable collisionless plasmas prove to evolve towards the marginal state of the stable equilibrium (which is a state of maximum entropy for the collisionless systems), while an electrostatic quasi-static marginally unstable mode with long wavelength appears in the system.

The penetration of an externally applied electric field into a collisionless plasma in a box is generally studied by means of Vlasov’s equation in the stationary case. The following property is shown to hold in the linear as well as in the nonlinear domain provided that the plasma is not too inhomogeneous : if the plasma is electrostatically stable it shields an external electric field, and a plasma showing no such shielding is microinstable. Nevertheless shielded situations can also appear for microinstable plasmas. In particular, the plasma is always instable when a maximum of the modulus of the electric field exists within the box.

Recently Caplan (1) applied the concepts of irreversible thermodynamics and cybernetics to contracting muscle and derived Hill's force-velocity relation. Wilkie and Woledge (2) then compared Caplan's theory to chemical rates inferred from heat data and concluded that the theory was not consistent with the data. Caplan defended his theory in later papers (3, 4) but without any direct experimental verifications. As Wilkie and Woledge (2) point out, the rate of phosphorylcreatine (PC) breakdown during steady states of shortening has not been observed because of technical difficulties. In this paper it is shown that the rate equations may be directly integrated with time to obtain relations among actual quantities instead of rates. The validity of this integration is based on experimental evidence which indicates that certain combinations of the transport coefficients are constant with muscle length. These equations are then directly compared to experimental data of Cain, Infante, and Davies (5) with the following conclusions: (a) The measured variations of DeltaPC for isotonic contractions are almost exactly as predicted by Caplan's theory. (b) The value of the chemical rate ratio, nu(m)/nu(o), obtained from these data was 3.53 which is close to the value of 3 suggested by Caplan (3). (c) The maximum value of the chemical affinity for PC splitting was found to be 10.6 k cal/mole which is as expected from in vitro measurements (2). Because of the excellent agreement between theory and experiment, we conclude that Caplan's theory definitely warrants further investigation.

The free energy and entropy functionals describing the equilibrium of a collisionless low β plasma in a general adiabatic magnetic field are constructed following the rules described in previous articles. The close connection between the conditions insuring the minimum entropy of a given equilibrium configuration and the negative energy variation in a general class of interchanges involving the magnetic energy is discussed. These conditions are expressed in a form which is invariant with respect to transformations between all possible curvilinear coordinate systems defined by the given external magnetic field. The conditions in the invariant form can be used for the calculation of the regions of minimum entropy, where the plasma should be expected to be unstable.

The connection is discussed between the extremum properties of the free energy and information functionals previously defined for characterizing collisionless (in general nonthermal) plasma equilibria and the stability of these equilibria described by means of the dynamical equations. For a given equilibrium many information functionals can be defined, each one being associated with a special class of excitation modes. These modes are selected by a special choice of the information variables, that is the variables depending linearly on one current component or on the charge density, through which the information density depends on space. A different choice of the coefficients of the linear dependence selects the excitation modes which are related to interchanges involving different kinds of energy, as for instance (in the low β case) the part of the magnetic energy related either to the magnetization current or the guiding center drift current, or also the gravitational energy, the azimuthal kinetic energy, and so on. The condition for a minimum of the proper information is necessary and sufficient for the instability of the associated modes in an infinite plasma. This is proved for a certain class of low frequency non-MHD modes (near a marginal frequency ω = 0) by showing that the condition for a minimum of the information is the same as the condition for the existence of associated zero-frequency modes which are marginally unstable as a result of a general stability analysis based on a lagrangian formulation. In the case of low β MHD interchanges or of the gravitational instability it is shown that the minimum of the information, constructed by taking the drift current as information variable, implies a negative plasma energy variation during an interchange. So through the proper definition of the information variables and of the related interchange energy and information functional, a point of view is reached in which physically different instabilities can be seen in the frame of the same general formalism. It is hoped that, by means of a proper choice of the information variables, which can be suggested by physical considerations, other modes can be taken into account and that one can look for new possible unstable modes by examining the extremum properties of the related information functional.

It is shown that the equilibria and the stability of non-Maxwellian inhomogeneous plasma can be described by a theory with a thermodynamical structure, provided that, in the linearly unstable cases, the perturbation modes under consideration are not too far from marginal stability. On the one hand, variational functionals prove to exist which can characterize the equilibrium and its stability by means of their extremum properties; on the other hand, a statistical model is proposed from which the same functionals can be derived in an independent way. In this model the plasma is considered as a statistical assembly of identifiable volume elements Delta V which are functions of relevant random variables (called information variables) that describe the plasma configuration (e.g. the charge or the current density). Two independent constraints are introduced in the statistical system in such a way that it is characterized by the given values of two quantities, viz. the mean square deviation of the information variable which is essentially connected with individual fluctuations inside each Delta V (namely fluctuations of non-interacting particles), and a collective energy related to the inhomogeneous equilibrium defined by means of the Vlasov model.

The definition of the entropy functional introduced in preceding articles and the related variational techniques are extended and applied in the present paper to the characterization of the equilibrium and stability properties of many plasma configurations of practical interest. The entropy functional is minimum at equilibrium with respect to a large class of unstable modes, that is low frequency modes or high frequency nearly electrostatic modes which are initially zero at the boundaries of the plasma. Moreover, the minimum of the entropy can be connected with a negative variation of the electric and magnetic energy in a special class of interchanges. Known sufficient instability conditions prove to be the same as minimum conditions for the entropy. This is explicitly shown for the purely electrostatic micro-instabilities, the flutes, the shear instability, and the unstable mirror-type modes in plane or cylindrical geometry. Finally the conditions for a maximum entropy of a low β plasma equilibrium in a general adiabatic magnetic field configuration are discussed. A nonzero minimum- B configuration can satisfy these conditions, but for a plasma with a low but nonzero β other restrictions have to be imposed on the plasma pressure and on the magnetic field as functions of space.

A fundamental theory of the elementary particles is presented assuming a dependence of the function describing a particle on two space-time variables and symmetry of the fundamental equations between them. All masses, with the exception of charged pions and muons, but including the electron mass of purely electro-magnetic origin, are predicted with a remarkable accuracy introducing a universal length as the only adjustable parameter. The strangeness and the Gell-Mann-Nishijima scheme find a simple interpretation; the isobaric spins of the different masses arise as an automatic consequence of the formalism. It is shown that the theory implies an indefinite metric. The existence of a pion with zeron isobaric spin is predicted by the theory. In the appendix an attempt is presented to explain the existence of the pions with isobaric spin T = 1 and of the muons.

The equations describing the electric and magnetic fields of a collisionless one-dimensional plasma at stationary equilibrium in a box (with B parallel to the walls and E perpendicular to B) can be derived by assuming that their solutions give an extremum value to a certain functional which describes the information necessary for completely fixing the electric and magnetic properties of the physical system for a fixed value of the electric and magnetic energy. According to information theory this functional can be assumed as a definition of an entropy which describes the irreversible behaviour of the collisionless plasma, also when situations very far from the statistical equilibrium are considered. Moreover, it can be shown, using this definition of the entropy, that a functional exists which characterizes the plasma equilibrium with the same formal properties as the Helmholtz function. When the absolute value of all field components has a minimum in the box, the entropy is maximum at equilibrium with respect to any perturbation, for a given electric and magnetic energy. In the special case when only an electric field exists, and for not too inhomogeneous plasmas, it is possible to establish in general, using Penrose's stability criterion, that a minimum value for the entropy in an equilibrium configuration (with fixed electrostatic energy) constitutes a sufficient condition for instability. Examples with magnetic field as the plane sheet pinch or the inhomogeneous plasma in uniform gravitational field with B = ezB0(1 + ϵχ) are also considered. In these examples the instability of the equilibrium is associated with a minimum of the corresponding entropy. It is also shown that the equilibrium of a neutral polytropic isothermal gas sphere confined by its own central gravitational field is associated with a maximum of the here defined entropy.

All solutions describing the electric field of a collisionless Maxwellian or not-Maxwellian onedimensional plasma at stationary equilibrium in a box can be obtained from the requirement that the electrostatic energy has an extremum value under the constraint that I = − ∑i∫δξiGi(n) dx be given, where the Gi(n) are any functions of the density n(x), each Gi(n(x)) being defined for x in the interval Δxi delimited by the zeros of dn/dx or by the walls of the box. The functions Gi may be chosen in an arbitrary way, which is in agreement with the occurrence of an arbitrary function in the most general solution of the relevant mathematical equations. The quantity I describes the “information” which is necessary for a complete description of the electric properties of the physical system. Moreover, it satisfies the following remarkable properties: 1. a) it takes an extremum value at equilibrium with respect to arbitrary variations of the electric field, which, however, should be fixed at the boundaries of each Δxi, under the constraint that the electrostatic energy has a given value; 2. b) in the limit in which thr Penrose stability criterion holds everywhere in the box (linear theory) or can be considered to hold as a local criterion (not too inhomogeneous plasmas) this extremum value is a maximum when the plasma is stable, while if I is minimum the plasma is unstable; 3. c) the extremum value of I with respect to arbitrary variations of n(x), under the constraint that the total number of particles is fixed, corresponds to a completely homogeneous plasma and is connected to the stability problem in the same way as in b). On the ground of these results and according to information theory the quantity I can be assumed as a definition of an entropy which describes the irreversible behaviour of the collisionless plasma, also when situations very far from the statistical equilibrium are considered. Moreover, using this definition of the entropy a quantity F can be introduced the extremum values of which for a fixed volume of the box and fixed kinetic energy of the plasma characterize the equilibrium configurations and which plays formally the same role as the Helmholtz free energy in thermodynamics.

A phenomenological theory for contracting muscle based on irreversible thermodynamics and the sliding filament theory is developed. The individual cross bridges, considered as subunits, are viewed as linear energy converters with constant transport coefficients. With this view of the subunits, phenomenological equations applicable to the whole muscle are obtained. The transport coefficients are shown to be a function of a single parameter which is the number of activated cross bridges at any instant. By requiring Hill's force-velocity relation (1) to be satisfied, the response of the muscle is related to the number of activated cross bridges. The resulting theory differs significantly from the theory developed by Caplan (2) and a comparison of the theories is presented. The theory is shown to correlate well with the heat data of Woledge (3) for a tortoise muscle and gives a value of Y (ratio of chemical affinity to enthalpy of reaction) equal to 0.945. The comparison of the theory with Hill's frog muscle data (1) and (4) is also encouraging. In part II of this series, length variations are considered and the resulting theoretical predictions are shown to be consistent with experimental data.

The effects of the presence of shielding electrodes on the electric fields in electrofluid dynamic (EFD) generator channels are studied. For each case studied, the magnitude of the field distortion is found as the ratio of the maximum electric field to the undisturbed maximum field. The electric-field magnification is derived as a function of both the relative size and sharpness of the protruding electrode and the relative size of the charge cloud. A charge-density attenuation coefficient is defined as the inverse of the electric-field magnification.