Thermodynamical Phase Noise in Oscillators Based on L-C Resonators

Using a new Admittance-based model for electrical noise able to handle Fluctuations and Dissipations of electrical energy, we explain the phase noise of oscillators that use feedback around L-C resonators. We show that Fluctuations produce the Line Broadening of their output spectrum around its mean frequency f0 and that the Pedestal of phase noise far from f0 comes from Dissipations modified by the feedback electronics. The charge noise power 4FkT/R C2/s that disturbs the otherwise periodic fluctuation of charge these oscillators aim to sustain in their L-C-R resonator, is what creates their phase noise proportional to Leeson’s noise figure F and to the charge noise power 4kT/R C2/s of their capacitance C that today’s modelling would consider as the current noise density in A2/Hz of their resistance R. Linked with this (A2/Hz?C2/s) equivalence, R becomes a random series in time of discrete chances to Dissipate energy in Thermal Equilibrium (TE) giving a similar series of discrete Conversions of electrical energy into heat when the resonator is out of TE due to the Signal power it handles. Therefore, phase noise reflects the way oscillators sense thermal exchanges of energy with their environment.

Thermodynamical Phase Noise in Oscillators Based on L-C Resonators (Foundations)

Using a new Admittance-based model for electrical noise able to handle Fluctuations and Dissipations of electrical energy, we explain the phase noise of oscillators that use feedback around L-C resonators. We show that Fluctuations produce the Line Broadening of their output spectrum around its mean frequency f0 and that the Pedestal of phase noise far from f0 comes from Dissipations modified by the feedback electronics. The charge noise power 4FkT/R C2/s that disturbs the otherwise periodic fluctuation of charge these oscillators aim to sustain in their L-C-R resonator, is what creates their phase noise proportional to Leeson’s noise figure F and to the charge noise power 4kT/R C2/s of their capacitance C that today’s modelling would consider as the current noise density in A2/Hz of their resistance R. Linked with this (A2/Hz?C2/s) equivalence, R becomes a random series in time of discrete chances to Dissipate energy in Thermal Equilibrium (TE) giving a similar series of discrete Conversions of electrical energy into heat when the resonator is out of TE due to the Signal power it handles. Therefore, phase noise reflects the way oscillators sense thermal exchanges of energy with their environment

From patterns to processes: Phase and density dependencies in the Canadian lynx cycle

Across the boreal forest of North America, lynx populations undergo 10-year cycles. Analysis of 21 time series from 1821 to the present demonstrates that these fluctuations are generated by nonlinear processes with regulatory delays. Trophic interactions between lynx and hares cause delayed density-dependent regulation of lynx population growth. The nonlinearity, in contrast, appears to arise from phase dependencies in hunting success by lynx through the cycle. Using a combined approach of empirical, statistical, and mathematical modeling, we highlight how shifts in trophic interactions between the lynx and the hare generate the nonlinear process primarily by shifting functional response curves during the increase and the decrease phases.

Critical fluctuations and entanglement in the nondegenerate parametric oscillator

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

Contemporaneous fluctuations in T cell responses to persistent herpes virus infections

The classical paradigm for T cell dynamics suggests that the resolution of a primary acute virus infection is followed by the generation of a long-lived pool of memory T cells that is thought to be highly stable. Very limited alteration in this repertoire is expected until the immune system is re-challenged by reactivation of latent viruses or by cross-reactive pathogens. Contradicting this view, we show here that the T cell repertoire specific for two different latent herpes viruses in the peripheral blood displayed significant contemporaneous co-fluctuations of virus-specific CD8(+) T cells. The coordinated responses to two different viruses suggest that the fluctuations within the T cell repertoire may be driven by sub-clinical viral reactivation or a more generalized 'bystander' effect. The later contention was supported by the observation that, while absolute number of CD3(+) T cells and their subsets and also the cell surface phenotype of antigen-specific T cells remained relatively constant, a loss of CD62L expression in the total CD8(+) T cell population was coincident with the expansion of tetramer-positive virus-specific T cells. This study demonstrates that the dynamic process of T cell expansion and contractions in persistent viral infections is not limited to the acute phase of infection, but also continues during the latent phase of infection.

Matter-wave amplification and phase conjugation via stimulated dissociation of a molecular Bose-Einstein condensate

We propose a scheme for parametric amplification and phase conjugation of an atomic Bose-Einstein condensate (BEC) via stimulated dissociation of a BEC of molecular dimers consisting of bosonic atoms. This can potentially be realized via coherent Raman transitions or using a magnetic Feshbach resonance. We show that the interaction of a small incoming atomic BEC with a (stationary) molecular BEC can produce two counterpropagating atomic beams - an amplified atomic BEC and its phase-conjugate or "time-reversed" replica. The two beams can possess strong quantum correlation in the relative particle number, with squeezed number-difference fluctuations.

Phase transitions in wave turbulence

We consider turbulence within the Gross-Pitaevsky model and look into the creation of a coherent condensate via an inverse cascade originating at small scales. The growth of the condensate leads to a spontaneous breakdown of statistical symmetries of overcondensate fluctuations: First, isotropy is broken, then a series of phase transitions marks the changing symmetry from twofold to threefold to fourfold. We describe respective anisotropic flux flows in the k space. At the highest level reached, we observe a short-range positional and long-range orientational order (as in a hexatic phase). In other words, the more one pumps the system, the more ordered the system becomes. The phase transitions happen when the system is pumped by an instability term and does not occur when pumped by a random force. We thus demonstrate nonuniversality of an inverse-cascade turbulence with respect to the nature of small-scale forcing.

A hierarchy of phase transitions in optimal neuronal coding:from binary to M-ary discrete optimal codes

We have investigated how optimal coding for neural systems changes with the time available for decoding. Optimization was in terms of maximizing information transmission. We have estimated the parameters for Poisson neurons that optimize Shannon transinformation with the assumption of rate coding. We observed a hierarchy of phase transitions from binary coding, for small decoding times, toward discrete (M-ary) coding with two, three and more quantization levels for larger decoding times. We postulate that the presence of subpopulations with specific neural characteristics could be a signiture of an optimal population coding scheme and we use the mammalian auditory system as an example.

Directed phase separation of PFO:PS blends during spin-coating using feedback controlled in situ stroboscopic fluorescence microscopy

Uniform thin-films of polymer blends can be produced through spin-coating, which is used on an industrial scale for the production of light emitting diodes, and more recently organic photovoltaic devices. Here, we present the results of the direct observation, and control, over the phase separation of polystyrene and poly(9,9′-dioctylfluorene) during spin-coating using high speed stroboscopic fluorescence microscopy. This new approach, imaging the fluorescence, from a blend of fluorescent + non-fluorescent polymers allows for intensity to be directly mapped to composition, providing a direct determination of composition fluctuations during the spin-coating process. We have studied the compositional development and corresponding structural development for a range of compositions, which produce a range of different phase separated morphologies. We initially observe domains formed by spinodal decomposition, coarsening via Ostwald Ripening until an interfacial instability causes break-up of the bicontinuous morphology. Ostwald ripening continues, and depending upon composition a bicontinuous morphology is re-established. By observing compositional and morphological development in real-time, we are able to direct and control morphological structure development through control of the spin coating parameters via in situ feedback. © 2013 The Royal Society of Chemistry.

Unveiling temporal correlations characteristic of a phase transition in the output intensity of a fiber laser

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

Mode-locking intracavity dynamics:modeling nonlinear power and energy fluctuations

Modern high-power, pulsed lasers are driven by strong intracavity fluctuations. Critical in driving the intracavity dynamics is the nontrivial phase profiles generated and their periodic modification from either nonlinear mode-coupling, spectral filtering or dispersion management. Understanding the theoretical origins of the intracavity fluctuations helps guide the design, optimization and construction of efficient, high-power and high-energy pulsed laser cavities. Three specific mode-locking component are presented for enhancing laser energy: waveguide arrays, spectral filtering and dispersion management. Each component drives a strong intracavity dynamics that is captured through various modeling and analytic techniques.

Characterization of design and economic sensitivity of vapor phase carbon adsorption systems to environmental uncertainties

Vapor phase carbon adsorption systems are used to remove aromatics, aliphatics, and halogenated hydrocarbons. The adsorption capacity of granular activated carbon is reduced when environmental parameters (temperature, pressure, and humidity) interfere with homogeneous surface diffusion and pore distribution dynamics. The purpose of this study was to investigate the effects of parametric uncertainties in adsorption efficiency. ^ Modified versions of the Langmuir isotherm in conjunction with thermodynamic equations described gaseous adsorption of single component influent onto microporous media. Experimental test results derived from Wang et al. (1999) simulated adsorption kinetics while the Myer and monsoon Langmuir constant accounted for isothermal gas compression and energetic heterogeneity under thermodynamic equilibrium conditions. Responsiveness of adsorption capacity to environmental uncertainties was analyzed by statistical sensitivity and modeled by breakthrough curves. Results indicated that extensive fluctuations in adsorption capacity significantly reduced carbon consumption while isothermal variations had a pronounced effect on saturation capacity. ^

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

Phase Transitions in Engineered Ultracold Quantum Systems

The study of quantum degenerate gases has many applications in topics such as condensed matter dynamics, precision measurements and quantum phase transitions. We built an apparatus to create 87Rb Bose-Einstein condensates (BECs) and generated, via optical and magnetic interactions, novel quantum systems in which we studied the contained phase transitions. For our first experiment we quenched multi-spin component BECs from a miscible to dynamically unstable immiscible state. The transition rapidly drives any spin fluctuations with a coherent growth process driving the formation of numerous spin polarized domains. At much longer times these domains coarsen as the system approaches equilibrium. For our second experiment we explored the magnetic phases present in a spin-1 spin-orbit coupled BEC and the contained quantum phase transitions. We observed ferromagnetic and unpolarized phases which are stabilized by the spin-orbit coupling’s explicit locking between spin and motion. These two phases are separated by a critical curve containing both first-order and second-order transitions joined at a critical point. The narrow first-order transition gives rise to long-lived metastable states. For our third experiment we prepared independent BECs in a double-well potential, with an artificial magnetic field between the BECs. We transitioned to a single BEC by lowering the barrier while expanding the region of artificial field to cover the resulting single BEC. We compared the vortex distribution nucleated via conventional dynamics to those produced by our procedure, showing our dynamical process populates vortices much more rapidly and in larger number than conventional nucleation.