Time-independent Steady State Research Articles

Shedding (Incoherent) Light on Quantum Effects in Light-Induced Biological Processes.

Light-induced processes that occur in nature, such as photosynthesis and photoisomerization in the first steps in vision, are often studied in the laboratory using coherent pulsed laser sources, which induce time-dependent coherent wavepacket molecule dynamics. Nature, however, uses stationary incoherent thermal radiation, such as sunlight, leading to a totally different molecular response, the time-independent steady state. It is vital to appreciate this difference in order to assess the role of quantum coherence effects in biological systems. Developments in this area are discussed in detail.

Flow Patterns Induced by the Thermocapillary Effect and Resultant Structures of Suspended Particles in a Hanging Droplet.

We focus on the flow patterns and resultant structures of suspended solid particles in a hanging droplet caused by the thermocapillary effect. A droplet is hung on a heated cylindrical rod facing downward, and another cooled rod is placed just beneath the droplet to create the temperature difference between both ends of the droplet. As the temperature difference increases, the induced flow exhibits transitions from an axisymmetric time-independent steady state to three-dimensional time-dependent oscillatory states. These flow states are judged through detecting spatiotemporal correlations between the behaviors of the particles and the variation of the temperature over the droplet surface. We find that the particle accumulation structures are realized in this geometry and that their structures vary as a function of the intensity of the thermocapillary effect.

Mapping current fluctuations of stochastic pumps to nonequilibrium steady states.

We show that current fluctuations in a stochastic pump can be robustly mapped to fluctuations in a corresponding time-independent nonequilibrium steady state. We thus refine a recently proposed mapping so that it ensures equivalence of not only the averages, but also optimal representation of fluctuations in currents and density. Our mapping leads to a natural decomposition of the entropy production in stochastic pumps similar to the "housekeeping" heat. As a consequence of the decomposition of entropy production, the current fluctuations in weakly perturbed stochastic pumps are shown to satisfy a universal bound determined by the steady state entropy production.

Equilibration of isolated many-body quantum systems with respect to general distinguishability measures.

We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are unimaginably rare in time. Measuring the distinguishability in terms of quantum mechanical expectation values, results of this type have been previously established under increasingly weak assumptions about the initial disequilibrium, the many-body Hamiltonian, and the considered observables. Here, we further extend these results with respect to generalized distinguishability measures which fully take into account the fact that the actually observed, primary data are not expectation values but rather the probabilistic occurrence of different possible measurement outcomes.

Quantum quench in two dimensions using the variational Baeriswyl wave function

By combining the Baeriswyl wavefunction with equilibrium and time-dependent variational principles, we develop a non-equilibrium formalism to study quantum quenches for two dimensional spinless fermions with nearest-neighbour hopping and repulsion. The variational ground state energy and the short time dynamics agree convincingly with the results of numerically exact simulations. We find that depending on the initial and final interaction strength, the quenched system either exhibits undamped oscillations or relaxes to a time independent steady state. The time averaged expectation value of the CDW order parameter rises sharply when crossing from the steady state regime to the oscillating regime, indicating that the system, being non-integrable, shows signs of thermalization with an effective temperature above or below the equilibrium critical temperature, respectively.

Numerical study of the effects of permeability heterogeneity on density-driven convective mixing during CO2 dissolution storage

Permanence and security of carbon dioxide (CO2) in geologic formations requires dissolution of CO2 into brine, which slightly increases the brine density. Previous studies have shown that this small increase in brine density induces convective currents, which greatly enhances the mixing efficiency and thus CO2 storage capacity and rate in the brine. Density-driven convection, in turn, is known to be largely dominated by permeability heterogeneity. This study explores the relationship between the process of density-driven convection and the permeability heterogeneity of an aquifer during CO2 dissolution storage, using high-resolution numerical simulations. While the porosity is kept constant, the heterogeneity of the aquifer is introduced through a spatially varying permeability field, characterized by the Dykstra-Parsons coefficient and the correlation length. Depending on the concentration profile of dissolved CO2, we classify the convective finger patterns as dispersive, preferential, and unbiased fingering. Our results indicate that the transition between unbiased and both preferential and dispersive fingering is mainly governed by the Dykstra-Parsons coefficient, whereas the transition between preferential and dispersive fingering is controlled by the permeability correlation length. Furthermore, we find that the CO2 dissolution flux at the top boundary will reach a time-independent steady state. Although this flux strongly correlates with permeability distribution, it generally increases with the permeability heterogeneity when the correlation length is less than the system size.

An analysis of ion channels in time-varying fields by the generalized Poisson-Nernst-Planck theory

An analysis is given in the article for the study of ion channel behavior in time-varying fields based on the generalized Poisson-Nernst-Planck theory, in which possible effects of the polarization relaxation and the effects of coupling among ion species, their diffusive fluxes and polarization in the mixture of ions can be evaluated. Analytical expressions for ion currents and voltages of the ion channel across a membrane are derived for the one-dimensional configuration both in time-independent steady state and in time-varying fields. While the results recover the classical Goldman-Hodgkin-Katz current and voltage equations in the time-independent steady state, it is shown that in time-varying fields, both the ionic current and the displacement current contribute to the total current in the ion channel, which depends not only on the equilibrium susceptibility of the mixture of the ions, but also on the dissipative polarization relaxation as well as the effect of coupling between the polarization and diffusive fluxes of the ions in the mixture. At the linear approximation, dissipative admittances that may characterize effectively the frequency responses of the ion channel in time-harmonic fields are also derived analytically for the one-dimensional case.

Transition to zero resistance in a two-dimensional electron gas driven with microwaves

High-mobility 2D electron systems in a perpendicular magnetic field exhibit zero resistance states (ZRS) when driven with microwave radiation. We study the nonequilibrium phase transition into this ZRS using phenomenological equations of motion to describe the current and density fluctuations. We focus on two models for the transition into a time-independent steady state. Model-I assumes rotational invariance, density conservation, and symmetry under shifting the density globally by a constant. This model is argued to describe physics on small length scales where the density does not vary appreciably from its mean. The ordered state that arises in this case breaks rotational invariance and consists of a uniform current and transverse Hall field. We discuss some properties of this state, such as stability to fluctuations and the appearance of a Goldstone mode associated with the continuous symmetry breaking. Using dynamical renormalization group techniques, we find that with short-range interactions this model can admit a continuous transition described by mean-field theory, whereas with long-range interactions the transition is driven first-order. Model-II, which assumes only rotational invariance and density conservation and is argued to be appropriate on longer length scales, is shown to predict a first-order transition with either short- or long-range interactions. We discuss implications for experiments, including scaling relations and a possible way to detect the Goldstone mode in the case of a continuous transition into the ZRS, as well as possible signatures of a first-order transition in larger samples. We also point out the connection of our work to the well-studied phenomenon of `flocking'.

Closure as a scientific concept and its application to ecosystem ecology and the science of the biosphere

Closure is a key concept in the physical sciences that has infrequently been used in ecology. The paper reviews closure to the flow of matter and energy (adiabatic walls) and closure to the flow of matter (diathermal walls). A system with rigid adiabatic walls will degrade eventually to chemical equilibrium, a state of maximum entropy. A third type of closure involves semi-permeable walls permitting the flow of one or more types of chemicals. These closure concepts were important to the development of classical thermodynamics and statistical mechanics in the 19th and 20th centuries. “Equilibrium” is often used to describe a time independent steady state. This usage leads to confusion, because equilibrium has such a precise meaning in thermal physics. All living systems are far-from-equilibrium and life cannot persist without the flow of energy. The Earth is an almost materially closed system. Only a small amount of cosmic matter is captured by the Earth’s gravitational field and only a small fraction of lighter elements escape that field. The Earth receives photon flux from the sun and generates thermal energy from the planetary decay of radioisotopes. A hypothesis can be advanced that the planetary biosphere exists in part because of material closure due to gravitation. In the science of ecology partial material closure has been introduced in limnology and island ecology. This has advanced biogeographical theory and systems ecology. The development in the past half century of first balanced aquaria and terrariums, and then partially materially closed microcosms and mesocosms has also greatly aided the development of ecology as an experimental rather than merely descriptive science. All the above systems are open atmospherically, and often have some water and nutrient inputs. The development of truly materially closed man-made systems offers further scope for the development of experimental ecology. The paper reviews and defines the various types of closed ecological systems: Class 1: natural planetary biospheres (like the Earth’s); and Class 2: man-made systems which range from laboratory microbial ecospheres to ones capable of human life support: Controlled Environmental Life Support Systems (CELSS such as are being developed by NASA and the European Space Agency), Closed Ecological Systems (such as Bios-3 at the Institute of Biophysics in Krasnoyarsk, Russia and the Biosphere 2 Test Module) to mini-biospheric systems with a complexity of internal ecosystems (e.g., Biosphere 2 and the Closed Ecology Experimental Facility, CEEF, in Japan).

Large-scale simulations of Ostwald ripening in elastically stressed solids. II. Coarsening kinetics and particle size distribution

Ostwald ripening of misfitting second-phase particles in an elastically anisotropic solid is studied by large-scale simulations. The coarsening kinetics for the average particle size are described by a t 1/3 power law with a rate constant equal to its stress-free value when the particles are fourfold symmetric. However, the rate constant increases when the elastic stress is sufficient to induce a large number of twofold-symmetric particles. We find that interparticle elastic interactions at a 10% area fraction of particles do not affect the overall coarsening kinetics. A mean-field approach was used to develop a theory of Ostwald ripening in the presence of elastic stress. The simulation results on the coarsening kinetics agree well with the theoretical predictions. The particle size distribution scaled by the average particle size is not time invariant, but widens slightly with an increasing ratio of elastic to interfacial energies. No time-independent steady state under scaling is found, but a unique time-dependent state exists that is characterized by the ratio of elastic energy to interfacial energy.

A definition of internal constancy and homeostasis in the context of non-equilibrium thermodynamics.

The constancy of the internal environment, internal homeostasis, and its stability are necessary conditions for the survival of a biological system within its environment. These have never been clearly defined. For this purpose nonequilibrium thermodynamics is taken as a reference, and the essential principles of equilibrium, reversibility, stationary steady state and stability (Lyapounov, asymptotic, local and global), are briefly illustrated. On this basis, internal homeostasis describes a stationary state of nonequilibrium, the actual state of rest, X(t), resulting from the relation X(t) = Xs + x(t), between a time-independent steady state of reference (Xs), and time-dependent fluctuations of the state variables, x(t). In humans, two resting spontaneous homeostatic states are: (1) the conscious state of quiet wakefulness, during which time-dependent variables display bounded oscillations around the mean time-independent steady state level, this conscious state being thus stable in the sense of Lyapounov, and (2) the unconscious stable state of non-rapid eye movement sleep, in which the time-dependent variables would approach the lowest spontaneously attainable time-independent state asymptotically, sleep becoming a globally stable and attractive state. Exercise may be described as a non-resting, unstable active state far away from equilibrium and hibernation is a resting, time-independent steady state very near equilibrium. The range between sleep and exercise is neurohumorally regulated. For spontaneously stable states to occur, slowing of the metabolic rate, withdrawal of the sympathetic drive and reinforcement of the vagal tone to the heart and circulation are required, thus confirming that the parasympathetic division of the autonomic nervous system is the main controller of homeostasis.

The application of reverse flow reactors to endothermic reactions

The concept of the reverse flow reactor traditionally used for mildly exothermic reactions has been extended to endothermic reactions and applied to the dehydrogenation of ethylbenzene. Periodic alternation of a reactant and a regenerating medium countercurrently over a fixed bed of catalyst in endothermic processes can be shown to result in higher conversions than traditional non-periodic systems. With this configuration several new process parameters are introduced such as total cycle time and the ratio of countercurrent flows. By judicious choice of operating conditions the hottest point of the reactor can be placed at the exit of the reactant stream allowing for much more favourable equilibriums and outlet conversions than if it were the coldest spot in the reactor as is common in steady-state processes. Two types of modeling are utilized. The first employs a technique which assumes that the switching is so rapid that the temperature distribution in the catalyst is in time independent steady-state. This high switching frequency model is compared against a more complicated time dependent dynamic model which traditionally is employed in reverse flow systems. Results for the first model are shown to be the limiting case of the dynamic model with fast switching. The models show significant conversion improvement with respect to existing steady state processes.

Phase resetting and bifurcation in the ventricular myocardium

With the dynamic differential equations of Beeler, G. W., and H. Reuter (1977, J. Physiol. [Lond.]. 268:177-210), we have studied the oscillatory behavior of the ventricular muscle fiber stimulated by a depolarizing applied current I app. The dynamic solutions of BR equations revealed that as I app increases, a periodic repetitive spiking mode appears above the subthreshold I app, which transforms to a periodic spiking-bursting mode of oscillations, and finally to chaos near the suprathreshold I app (i.e., near the termination of the periodic state). Phase resetting and annihilation of repetitive firing in the ventricular myocardium were demonstrated by a brief current pulse of the proper magnitude applied at the proper phase. These phenomena were further examined by a bifurcation analysis. A bifurcation diagram constructed as a function of I app revealed the existence of a stable periodic solution for a certain range of current values. Two Hopf bifurcation points exist in the solution, one just above the lower periodic limit point and the other substantially below the upper periodic limit point. Between each periodic limit point and the Hopf bifurcation, the cell exhibited the coexistence of two different stable modes of operation; the oscillatory repetitive firing state and the time-independent steady state. As in the Hodgkin-Huxley case, there was a low amplitude unstable periodic state, which separates the domain of the stable periodic state from the stable steady state. Thus, in support of the dynamic perturbation methods, the bifurcation diagram of the BR equation predicts the region where instantaneous perturbations, such as brief current pulses, can send the stable repetitive rhythmic state into the stable steady state.

KQ Mon and the Nature of the UX Ursa Majoris Nova-Like Variables

ABSTRACTKQ Mon, a new UX UMa type nova-like variable discovered by H.E. Bond, exhibits optical spectra, UBV and high speed photometric characteristics strongly similar to other members of the UX Ursa Majoris subset. However its ultraviolet spectra when compared with other UX UMa stars shed considerable light on the nature of these objects. Its spectrum is dominated by strong broad highly ionized absorption lines including the NV, SiIV and CIV UV resonance doublets. No emission lines or P Cygni type features are evident and the velocity displacements are smaller suggesting the absence of a hot high velocity wind characterizing other UX UMa stars. A physical interpretation of the UV absorption spectra and optical spectra and their observed temporal variations is presented. Based upon (1) high mass accretion rates derived by fitting the observations with theoretical continuum fluxes from steady accretion disk models by R.E. Williams, (2) the presence of outflowing winds with the determination of corresponding mass loss rates and properties of the theoretical wind models by Cassinelli, Olson and Stalio, and (3) new time independent steady state disk structure computations, a model is suggested to explain the observed properties of the UX UMa stars and their lack of major outbursts.

Control of repetitive firing in squid axon membrane as a model for a neuroneoscillator.

1. Repetitive firing in space-clamped squid axons bathed in low Ca and stimulated by a just suprathreshold step of current can be annihilated by a brief depolarizing or hyperpolarizing pulse of the proper magnitude applied at the proper phase. 2. In response to such perturbations, membrane potential and ionic currents show damped oscillations toward a steady state. 3. For other, non-annihilating, perturbations repetitive firing resumes with unaltered frequency but with phase resetting. 4. Experimental findings are compared with calculations for the space-and current-clamped Hodgkin-Huxley equations. Annihilation of repetitive firing to a steady state corresponds to a solution trajectory perturbed off a stable limit cycle and into the domain of attraction of a coexistent stable singular point. 5. Experimentally and theoretically the nerve exhibits hysteresis with two different stable modes of operation for a just suprathreshold range of bias current: the oscillatory repetitive firing state and the time-independent steady state. 6. Analogy is made to a brief synaptic input (excitatory or inhibitory) which may start or stop a biological pace-maker.

Solutions of the Fokker-Planck equation for the early time when the diffusive modes are not yet valid

The transport of energetic charged particles in fluctuating magnetic fields is analysed by means of the Fokker-Planck equation for the early time, when the diffusive modes are not yet valid. Exact solutions are found for the particle fluxes integrated over space; after these have reached a time-independent final steady state, the usually considered diffusive modes of the velocity-integrated density become valid. The time for that is finite. The analysis is done both for a constant and a divergent mean magnetic field.