Pattern formation in the ferrocyanide-iodate-sulfite reaction: the control of space scale separation

We revisit the conditions for the development of reaction-diffusion patterns in the ferrocyanide-iodate-sulfite bistable and oscillatory reaction. This hydrogen ion autoactivated reaction is the only example known to produce sustained stationary lamellar patterns and a wealth of other spatio-temporal phenomena including self-replication and localized oscillatory domain of spots, due to repulsive front interactions and to a parity-breaking front bifurcation (nonequilibrium Ising-Bloch bifurcation). We show experimentally that the space scale separation necessary for the observation of stationary patterns is mediated by the presence of low mobility weak acid functional groups. The presence of such groups was overlooked in the original observations made with hydrolyzable polyacrylamide gels. This missing information made the original observations difficult to reproduce and frustrated further experimental exploitation of the fantastic potentialities of this system. Using one-side-fed spatial reactors filled with agarose gel, we can reproduce all the previous pattern observations, in particular the stationary labyrinthine patterns, by introducing, above a critical concentration, well controlled amounts of polyacrylate chains in the gel network. We use two different geometries of spatial reactors (annular and disk shapes) to provide complementary information on the actual three-dimensional character of spatial patterns. We also reinvestigate the role of other feed parameters and show that the system exhibits both a domain of spatial bistability and of large-amplitude pH oscillations associated in a typical cross-shape diagram. The experimental method presented here can be adapted to produce patterns in the large number of oscillatory and bistable reactions, since the iodate-sulfite-ferrocynide reaction is a prototype of these systems.     

Laser saturation grating phenomena

Spatial hole burning of population differences by standing waves is considered in terms of Bragg-like gratings. This philosophy is used to explain increased saturation in two-mirror, single-mode laser operation with stationary active systems, modified mode coupling in the corresponding two-mode operation, an intensity dip that might occur in flowed standing wave lasers, bistable unidirectional ring laser operation, and increased saturation in distributed feedback lasers. The analysis is developed for both stationary media and for those moving with respect to the standing wave. The latter treatment is used to interpret washout of grating contributions in Doppler broadened media, and to determine level decay constants in stationary media. This last application constitutes a stationary system analog to the Doppler medium's Lamb dip spectroscopy and can be called saturation grating spectroscopy. Knowledge of the decay constants is particularly important in laser studies involving coherent mode couplings such as due to saturation grating scattering and population pulsations. It is further shown that the same equations result for probe and saturating waves propagating in the same direction. One then obtains a signal absorption with a heterodyne advantage. Inasmuch as diffusion affects the two methods quite differently, this phenomenon should be easily examined. Work supported in part by a U.S. Senior Scientist Award (administered by the Alexander von Humboldt Stiftung) and in part by the Space and Missile Systems Organization, Los Angeles, California.     

Pattern formation in the thiourea-iodate-sulfite system: Spatial bistability, waves, and stationary patterns

We present a detailed study of the reaction-diffusion patterns observed in the thiourea-iodate-sulfite (TuIS) reaction, operated in open one-side-fed reactors. Besides spatial bistability and spatio-temporal oscillatory dynamics, this proton autoactivated reaction shows stationary patterns, as a result of two back-to-back Turing bifurcations, in the presence of a low-mobility proton binding agent (sodium polyacrylate). This is the third aqueous solution system to produce stationary patterns and the second to do this through a Turing bifurcation. The stationary pattern forming capacities of the reaction are explored through a systematic design method, which is applicable to other bistable and oscillatory reactions. The spatio-temporal dynamics of this reaction is compared with that of the previous ferrocyanide-iodate-sulfite mixed Landolt system.     

Breathers in two-dimensional neural media

In this Letter we show how nontrivial forms of spatially localized oscillations or breathers can occur in two-dimensional excitable neural media with short-range excitation and long-range inhibition. The basic dynamical mechanism involves a Hopf bifurcation of a stationary pulse solution in the presence of a spatially localized input. Such an input could arise from external stimuli or reflect changes in the excitability of local populations of neurons as a precursor for epileptiform activity. The resulting dynamical instability breaks the underlying radial symmetry of the stationary pulse, leading to the formation of a nonradially symmetric breather. The number of breathing lobes is consistent with the order of the dominant unstable Fourier mode associated with perturbations of the stationary pulse boundary.     

Nonlinear polarization bistability in optical nanowires

Using the full vectorial nonlinear Schr?dinger equations that describe nonlinear processes in isotropic optical nanowires, we show that there exist structural anisotropic nonlinearities that lead to unstable polarization states that exhibit periodic bistable behavior. We analyze and solve the nonlinear equations for continuous waves by means of a Lagrangian formulation and show that the system has bistable states and also kink solitons that are limiting forms of the bistable states.     

Kink propagation induced by multiplicative noise

The influence of spatio-temporal external multiplicative fluctuations on a single kink in a bistable distributed system is studied. For this purpose we derive a stochastic dynamic equation for the position of the shifted kink. An analytical estimate for spatio-temporally uncorrelated fluctuations is represented and discussed. We draw the conclusion that multiplicative noise induces a propagation of the most probable kink into the region of larger noise. This effect is demonstrated in numerical simulations.     

Nonlinear transmission of ultrashort laser pulses by a thin semiconductor film under conditions of a two-photon two-pulse excitation of biexcitons

Specific features of the nonstationary transmission of two pulses exciting biexcitons from the ground state in a thin semiconductor film are studied. It is shown that one of the incident rectangular pulses is totally reflected from the film, whereas the second pulse passes through it as through an absolutely transparent medium. Criteria for appearance of a stationary bistable transmission are determined.     

Chirped optical pulse propagation in saturating nonlinear media

Using a variational method, we have investigated the propagation characteristics of a chirped optical pulse in anomalously dispersive media possessing saturating nonlinearity. For the special case of uniform loss less media, the dynamics of the temporal width of the pulse is shown to be equivalent to an oscillator of unit mass which is executing its motion under some effective potential well. The potential is examined and four different types of behavior of the pulse width are noticed. The role of saturation parameter and the initial chirp in determining the propagation characteristics have been examined. It is found that, both high value of chirp and saturation are detrimental to stable pulse propagation. Particularly, the effect of chirp becomes severe with the increase in the value of saturation. We have shown that incorporation of saturation in the nonlinearity leads to the existence of bistable soliton. For the case of a lossy medium, net broadening of width takes place over many cycles of oscillation. The net broadening decreases with the increase in the value of saturation.     

Anomalous pulse interaction in dissipative media

We review a number of phenomena occurring in one-dimensional excitable media due to modified decay behind propagating pulses. Those phenomena can be grouped in two categories depending on whether the wake of a solitary pulse is oscillatory or not. Oscillatory decay leads to nonannihilative head-on collision of pulses and oscillatory dispersion relation of periodic pulse trains. Stronger wake oscillations can even result in a bistable dispersion relation. Those effects are illustrated with the help of the Oregonator and FitzHugh-Nagumo models for excitable media. For a monotonic wake, we show that it is possible to induce bound states of solitary pulses and anomalous dispersion of periodic pulse trains by introducing nonlocal spatial coupling to the excitable medium.     

Theory of absorptive bistability

A model for a resonatorless absorptive optical bistability in laser-excited semiconductors is presented. The intensity-dependent absorption coefficient is calculated microscopically taking into account band-gap renormalization and band filling due to formation of an electron-hole plasma. The spatial and temporal variations of the carrier density and the light intensity in the crystal are calculated from solutions of their coupled transport equations. An intrinsically bistable propagation mechanism for a density kink is found, which gives rise to additional structures in the bistable hysteresis loop. The influence of different carrier diffusion coefficients on the results is calculated.     

非相干多分量空间双稳态孤子

非相干多分量光束在高阶非线性介质中可以形成双稳态孤子.利用相干密度法首次得到了非相干多分量双稳态孤子的解析表达式.介质的高阶非线性决定了双稳态孤子的存在范围和峰值强度.得到了光束的截止波长，最小宽度和介质的非线性条件，并研究了非相干多分量光束中相干分量的传输演化.利用稳定性条件，严格证明了非相干多分量双稳态孤子在介质中可以保持稳定传播. 关键词： 非相干多分量光束 空间孤子 双稳态     

Untersuchungen zu den Existenzbereichen und Typen von ac-Entladungen. II. Das Verhalten der Entladungstypen in Ne/Ar-Gemischen und der Vergleich mit Ne/N2-Gemischen

The investigations on the transition between the discharge modes in Ne? N₂ mixtures are described in [1]. In the present paper we investigate Ne? Ar mixtures with a view to comparing the behaviour of these different mixtures. The measurements confirm the transition mechanism between the bistable pulse mode and the non-bistable continous mode in Ne-Penning mixtures. The life time of metastable atoms is important for the existence of the continuous mode. If the life time is changed by varying the cross sections for the Penning ionization Q_p (e.g. in other mixtures), the transition frequency of both these discharge modes shows a corresponding shift, which, for both mixtures, is in good agreement with literature values of Q_p. The second part presents a study of the quasiglow mode. The transition between the pulse mode and the quasiglow mode correlates to the ion transit time. The three discharge modes are represented in the existence diagram.     

Oscillatory dispersion and coexisting stable pulse trains in an excitable medium

For planar wave trains in excitable media, we found a novel type of anomalous dispersion distinguished by bistable domains in the dependence of the propagation velocity on the wavelength. Within one medium alternative stable pulse trains can coexist having the same wavelength but different velocities. The phenomenon is related to oscillatory recovery of excitations, which causes small amplitude oscillations in the refractory tail of pulses. Crucial for the bistability is that the pulses in the trains are locked into one oscillation maximum in the tail of the preceding pulse in the train.     

Fermi-Dirac Kink Propagation in High-Order Nonlinear Media

We show analytically that addition of a quintic term to the positive Kerr-type nonlinearity offers a unique type of kink soliton-like solution with Fermi-Dirac profile. This type of optical kink allows, in contrast to other optical kinks discovered so far, stationary kink formation not only in the time domain but in the spatial domain. The latter could admit of a route for the first time to our knowledge to spatial kink solitons of intensified laser beams. The underlying principle of the optical kink propagation is described.     

带注入信号的双光子激光器的双稳性质

以原子均匀展宽的单模环形双光子激光器为模型,用半经典方法讨论有注入信号的双光子激光器的双稳性质。论证在谐调情况下该系统会出现双稳态,并且对于“好腔”和“坏腔”极限,通过绝热消除描述了双稳性导致的输出光的瞬态行为和滞后循环。发现在低分支是单调地趋向稳态,而在高分支是振荡地趋向稳态;在输出场不连续变化之处出现临界慢化现象。     

Optical regenerative oscillation and monostable pulse generation in hybrid bistable optical devices

Instability in the transient response of hybrid bistable optical devices is discussed. It is applied to determine the precise conditions for optical regenerative oscillation and monostable pulse generation in three types of electrooptic bistable devices. Theoretical results explain well the sequential behaviors of these phenomena.     

Boundary Effects on the Structural Stability of Stationary Patterns in a Bistable Reaction-Diffusion System

We study a piecewise linear version of a one-component, two-dimensional bistable reaction-diffusion system subjected to partially reflecting boundary conditions, with the aim of analyzing the structural stability of its stationary patterns. Dirichlet and Neumann boundary conditions are included as limiting cases. We find a critical line in the space of the parameters which divides different dynamical behaviors. That critical line merges as the locus of the coalescence of metastable and unstable nonuniform structures.     

Kink solutions of the classical transverse field Ising chain

We investigate stationary and travelling wave solutions of the classical one-dimensional transverse field Ising model. Results are given on the existence, shape and stability of kink solutions and periodic solutions. We review recent analytical results (e.g., the proof of existence of a one-parameter family of stationary kink solutions and the proof of existence of travelling wave kink solutions with nonzero velocity c≠ 0) and extend them by the use of numerical methods. Small oscillations arising in the tails of travelling kink solutions are investigated numerically. In the end, stability analysis puts some light on pinning effects. Received 23 February 2001 and Received in final form 4 October 2001     

All-Optical Bistability in Grating Coupling to Nonlinear Waveguide

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Untersuchungen zu den Existenzbereichen und Typen von ac-Entladungen III. Der Übergang zu reinem Neon und das Bistabilitätsverhalten der einzelnen Typen

The present paper investigates the discharge modes in neon. The Ne-discharge is shown to be sensitively influenced by impurities or small admixtures. If the Ne-filling is not pure enough, pulse mode and continuous mode occur in the same way as in a Ne? N₂ mixture. But below a nitrogen content of 0.01% the shift of the transition frequency between the pulse mode and continuous mode disappears. If the measurements were carried out in pure neon, the non-bistable continuous mode could not be observed, which indicated that the main ionization mechanism, the Penning ionization, had vanished. Instead, in the corresponding parameter range a bistable discharge occurred. This discharge, representing the quasiglow mode, is more intense and the discharge current persists for the whole half cycle. Furthermore, the present paper investigates the wall voltage build up. The charge-transfermethod was extended to the quasiglow mode and the continuous mode. The observed changes in the charge-transfer-curves can be explained by the different discharge mechanisms.