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We report measurements on the phase dynamics of a detuned single mode laser which has in the past shown correspondence to the complex Lorenz equation. The corresponding ranges of periodic pulsing, of detuned chaos and of windows within the chaotic domain are investigated.

We investigate the Poincare transformation dynamics describing the stochastic motion of a relativistic electron in the regular electrostatic field of a wave packet. The conditions of local instability of the phase trajectories are determined: it is shown that the system is a structurally stable Y system with an attracting set of the hyperbolic type. The relationship between the dynamics at the strange attractor characterized by Lyapunov indices and its statistical structure described by the Kolmogorov entropy is discussed. The fractal dimension of the phase space of the system is determined. The results of a numerical simulation of the effect are presented and discussed.

Analytical and numerical methods were used to study the dynamics of the mapping that describes a determinate dynamic system consisting of a relativistic electron and a wave packet of potential waves. The mapping dynamics is shown to depend essentially on a parameter that characterizes the wave-packet intensity. The system behaves in different ways, depending on that parameter: it executes ergodic motion with displacement or motion with simultaneous regular and irregular trajectories. This mapping is shown to be typical and structurally stable.

Recently there has been a surge of new interest in three-dimensional wake patterns. In the present work, we have devised a method to control the spanwise end conditions and wake patterns using “end suction”, which is both continuously-variable and admits transient control. Classical steady-state patterns, such as parallel or oblique shedding or the “chevron” patterns are simply induced. The wake, at a given Reynolds number, is receptive to a continuous range of oblique shedding angles (θ), rather than to discrete angles, and there is excellent agreement with the “cos θ” formula for oblique-shedding frequencies. We show that the laminar shedding regime exists up to Reynolds numbers (Re) of 205, and that the immense disparity among reported critical Re for wake transition (Re = 140–190) can be explained in terms of spanwise end contamination. Our transient experiments have resulted in the discovery of new phenomena such as “phase shocks” and “phase expansions”, which can be explained in terms of a simple model assuming constant normal wavelength of the wake pattern. Peter Monkewitz (Lausanne) also predicts such transient phenomena from a Guinzburg-Landau model for the wake.

The temperature-dependent helicity modulus Γ(T) of site-diluted triangular arrays of proximity-effect coupled Pb/Cu/Pb Josephson junctions has been extracted from measurements of the complex ac sheet conductance performed in the frequency range 0.1 Hz to 20 kHz in zero magnetic field. At low frequencies Γ(T) exhibits the characteristic superfluid drop predicted by the Kosterlitz-Thouless theory, demonstrating that a disordered array behaves like a homogeneous two-dimensional system at length scales-larger than the percolation correlation length.

Giant fractional Shapiro steps have been observed in Josephson junction arrays as resulting from magnetic flux quantization in the two-dimensional array. We demonstrate experimentally the appearance of giant fractional Shapiro steps in anisotropic Josephson junction arrays as unambiguous evidence of a skewed current phase relationship. Introducing anisotropy in the array results in a giant collective high frequency response that reflects the properties of a single junction, as evidenced by the observation of a Fraunhofer like magnetic field dependence of the total critical current of the system. The observed phase dynamics can be perfectly captured within an extended resistively shunted Josephson junction model. These results directly indicate the potential of Josephson junction arrays to explore the current phase relation in a very broad frequency range (down to 50 MHz) and in a wide variety of novel link materials exhibiting non-conventional current phase relationships. Giant fractional Shapiro steps have been observed in Josephson junction arrays as resulting from magnetic flux quantization in the two-dimensional array. Here, the authors demonstrate the observation of giant fractional Shapiro steps in an anisotropic Josephson junction array, as unambiguous evidence of a skewed current phase relationship.

We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on chimera states involving amplitude as well as phase dynamics, complex topologies like small-world or hierarchical (fractal), noise, and delay. We show that a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model. For the FitzHugh-Nagumo system, the Van der Pol oscillator, and the Stuart-Landau oscillator with symmetry-breaking coupling various multi-chimera patterns including amplitude chimeras and chimera death occur. To test the robustness of chimera patterns with respect to changes in the structure of the network, regular rings with coupling range R, small-world, and fractal topologies are studied. We also address the robustness of amplitude chimera states in the presence of noise. If delay is added, the lifetime of transient chimeras can be drastically increased.

The effects of the amplitude nonuniformity of the magnetic field in a betatron on the forced and betatron radial oscillations of electrons during extraction (or discharge toward the target) at the end of the acceleration cycle are examined. The amplitude and phase dynamics of radial betatron oscillations are studied by means of an analog computer.

Upon excitation with an intense laser pulse, a symmetry-broken ground state can undergo a non-equilibrium phase transition through pathways different from those in thermal equilibrium. The mechanism underlying these photoinduced phase transitions has long been researched in the study of condensed matter systems1, but many details in this ultrafast, non-adiabatic regime still remain to be clarified. To this end, we investigate the light-induced melting of a unidirectional charge density wave (CDW) in LaTe3. Using a suite of time-resolved probes, we independently track the amplitude and phase dynamics of the CDW. We find that a fast (approximately 1 picosecond) recovery of the CDW amplitude is followed by a slower re-establishment of phase coherence. This longer timescale is dictated by the presence of topological defects: long-range order is inhibited and is only restored when the defects annihilate. Our results provide a framework for understanding other photoinduced phase transitions by identifying the generation of defects as a governing mechanism. Three different ultrafast probes investigate a non-adiabatic phase transition and find substantial evidence of topological defects inhibiting the reformation of the equilibrium phase.

Intrinsically disordered regions (IDRs) are often fast-evolving protein domains of low sequence complexity that can drive phase transitions and are commonly found in many proteins associated with neurodegenerative diseases, including the RNA processing factor TDP43. Yet, how phase separation contributes to the physiological functions of TDP43 in cells remains enigmatic. Here, we combine systematic mutagenesis guided by evolutionary sequence analysis with a live-cell reporter assay of TDP43 phase dynamics to identify regularly-spaced hydrophobic motifs separated by flexible, hydrophilic segments in the IDR as a key determinant of TDP43 phase properties. This heuristic framework allows customization of the material properties of TDP43 condensates to determine effects on splicing function. Remarkably, even a mutant that fails to phase-separate at physiological concentrations can still efficiently mediate the splicing of a quantitative, single-cell splicing reporter and endogenous targets. This suggests that the ability of TDP43 to phase-separate is not essential for its splicing function., TDP43 regulates RNA processing and undergoes liquid-liquid phase separation. Here, the authors combine bioinformatic analysis and quantitative measurements of phase properties in living cells to uncover the rules that link the amino acid sequence of TDP43 with its phase properties and find that unexpectedly, mutants of TDP43 that are deficient in phase separation can still function to mediate splicing.

Theoretical and experimental studies of temporal dynamics of grazing incidence grating (GIG) cavity, single-mode dye laser pumped by high repetition rate copper vapour laser (CVL) are presented. Spectral chirp of the dye laser as they evolve in the cavity due to transient phase dynamics of the amplifier gain medium is studied. Effect of grating efficiency, focal spot size, pump power and other cavity parameters on the temporal behaviour of narrow band dye laser such as build-up time, pulse shape and pulse width is studied using the four level dye laser rate equation and photon evolution equation. These results are compared with experimental observations of GIG single-mode dye laser cavity. The effect of pulse stretching of CVL pump pulse on the temporal dynamics of the dye laser is studied.

Since the pioneering proposal of the replicon model of DNA replication 50 years ago, the predicted replicons have not been identified and quantified at the cellular level. Here, we combine conventional and super-resolution microscopy of replication sites in live and fixed cells with computational image analysis. We complement these data with genome size measurements, comprehensive analysis of S-phase dynamics and quantification of replication fork speed and replicon size in human and mouse cells. These multidimensional analyses demonstrate that replication foci (RFi) in three-dimensional (3D) preserved somatic mammalian cells can be optically resolved down to single replicons throughout S-phase. This challenges the conventional interpretation of nuclear RFi as replication factories, that is, the complex entities that process multiple clustered replicons. Accordingly, 3D genome organization and duplication can be now followed within the chromatin context at the level of individual replicons., Whether replication happens at individual replicons or in replication factories is a controversial debate. Here the authors use super-resolution microscopy and analysis of replication fork speed to present evidence in favour of replicons.

The characterization of medium- to low-energy shaped pulses at 1.55 μm through frequency-resolved optical gating (FROG) is illustrated. This capability enables the study of ultrafast pulse propagation through optical fibers. The phase dynamics detected furnishes insight on pulse evolution, specifically on soliton formation – a subject of great importance for telecommunication applications. The combination of shaping and propagation of ultrafast pulses in fibers is examined theoretically using an adaptive pulse-shaping model, based on genetic algorithms, that furnishes optimized pulse shapes for fiber propagation.

The active mode-locking process of the multimode laser with an external pump modulation is theoretically investigated in the frequency domain within the framework of the continuous-mode approximation. Intermode interaction and mode-coupling effects, including both AM and FM modulations, are naturally considered in a hierarchical equation of the mode components derived from the multimode Maxwell-Bloch equations. It is reduced to a continuous-mode equation that can be solved analytically in a stationary case, and used to discuss the spectral line shape and the phase dynamics of mode-components as a function of modulation amplitude and detuning of the modulation frequency. We predict a novel oscillation existing below the threshold of the ordinary complete mode-locking: The intensity of the total electric field yields a stable pulse train but its phase varies irregularly in time. This semi-locked state is characterized by a nonlinear chirping, an asymmetric spectrum, and drifting phases of the field mode-components.