Types Of Fluctuations Research Articles

Statistical regularities of self-intersection counts for geodesics on negatively curved surfaces

Let $\Upsilon $ be a compact, negatively curved surface. From the (finite) set of all closed geodesics on $\Upsilon$ of length $\leq L$, choose one, say $\gamma_{L}$, at random and let $N (\gamma_{L})$ be the number of its self-intersections. It is known that there is a positive constant $\kappa$ depending on the metric such that $N (\gamma_{L})/L^{2} \rightarrow \kappa$ in probability as $L\rightarrow \infty$. The main results of this paper concern the size of typical fluctuations of $N (\gamma_{L})$ about $\kappa L^{2}$. It is proved that if the metric has constant curvature -1 then typical fluctuations are of order $L$, in particular, $(N (\gamma_{L})-\kappa L^{2})/L$ converges weakly to a nondegenerate probability distribution. In contrast, it is also proved that if the metric has variable negative curvature then fluctuations of $N (\gamma_{L})$ are of order $L^{3/2}$, in particular, $(N (\gamma_{L})-\kappa L^{2})/L^{3/2}$ converges weakly to a Gaussian distribution. Similar results are proved for generic geodesics, that is, geodesics whose initial tangent vectors are chosen randomly according to normalized Liouville measure.

Guided wave tomography of pipes with high-order helical modes

The transmission of guided ultrasonic waves across corrosion or erosion damage encodes information about the defect depth. Tomography maps the depth profile from multiple transmission experiments performed under different insonification angles by solving the so-called inverse problem; the accuracy of the depth estimation being dependent on the range of angles available for the inversion. Practical application of tomography to tubular structures, such as pipes and bends, requires the use of two ring arrays of ultrasonic transducers at the two ends of the pipe section to be inspected. However, such a configuration leads to an insufficient angular coverage when considering the signals that travel along the shortest temporal path between a pair of transducers. This paper introduces a general inversion method that extends the range of insonification angles by exploiting the information carried by the signals that wrap around the pipe multiple times before reaching the receive array, thus resulting in superior image resolution and increased depth estimation accuracy. In addition, to address typical thermal fluctuations encountered during continuous monitoring, a strategy that combines a temperature compensation scheme with the intrinsic thermal stability of electromagnetic acoustic transducers (EMATs) is developed and tested with full-scale experiments performed on a schedule of 40, 8″ diameter steel pipe instrumented with two ring arrays of EMAT transducers. It is shown that for an irregularly shaped defect the proposed inversion method yields maximum depth estimations that are as accurate as single point ultrasonic thickness gaging measurements and over a wide temperature range up to 175°C. The results indicate that advanced inversion schemes in combination with EMAT transduction offer great potential for continuously monitoring the progression of corrosion or erosion damage in the oil and gas industry.

Efficient frequency doubling of a telecom 1560 nm laser in a waveguide and frequency stabilization to Rb D2 line

We experimentally demonstrate efficient frequency doubling of a telecom 1560 nm distributed feedback diode laser with a 3 cm long MgO:PPLN waveguide with a conversion coefficient of 114%/W. We investigate optical inhomogeneities by measuring the quasi-phase-matching temperature curve. The ~2.7 mW of second-harmonic power at 780 nm is sufficient to detect the Rb D2 features using modulation transfer spectroscopy. The laser frequency is locked to a hyperfine transition of Rb D2 line and typical residual frequency fluctuation of ±86 kHz (rms) is achieved within 30 min. Our experimental scheme can be used for realizing robust, compact, and highly accurate Rb stabilized 1560 nm laser systems for fiber-optic communication applications.

Top eigenvalue of a random matrix: large deviations and third order phase transition

We study the fluctuations of the largest eigenvalue λmax of N × N random matrices in the limit of large N. The main focus is on Gaussian β ensembles, including in particular the Gaussian orthogonal (β = 1), unitary (β = 2) and symplectic (β = 4) ensembles. The probability density function (PDF) of λmax consists, for large N, of a central part described by Tracy–Widom distributions flanked, on both sides, by two large deviation tails. While the central part characterizes the typical fluctuations of λmax—of order —the large deviation tails are instead associated with extremely rare fluctuations—of order . Here we review some recent developments in the theory of these extremely rare events using a Coulomb gas approach. We discuss in particular the third order phase transition which separates the left tail from the right tail, a transition akin to the so-called Gross–Witten–Wadia phase transition found in 2-d lattice quantum chromodynamics. We also discuss the occurrence of similar third order transitions in various physical problems, including non-intersecting Brownian motions, conductance fluctuations in mesoscopic physics and entanglement in a bipartite system.

Testing and Analysis on Building Thermal Stability in Hot-Humid and Cold-Humid Area in Summer

Relative humidity in hot-humid and cold-humid area in summer is high, the sun radiation intensity is low, and the existing building thermal stability condition basic research data is absence . Select the region typical residential building, the sun radiation, relative humidity, air temperature and surface temperature were measured and recorded; Test analysis shows that typical residential house in summer in the climate characteristics the typical average indoor temperature fluctuation in the cycle is 4.3 °C,fluctuations of temperature to a larger extent, and was obviously affected by such factors as orientations and envelope constructional detail.

Financial Crises and Recapitalizations

We develop a dynamic stochastic general equilibrium model with financial frictions on both financial intermediaries and goods‐producing firms. Since financial intermediaries are highly leveraged, we show that the welfare gains from their recapitalization in response to large but rare net worth losses are as large as those from eliminating typical business cycle fluctuations. We also find that these gains are increasing in the size of the net worth loss, are larger when recapitalization funds are raised from the household rather than the real sector, and can be larger when lower idiosyncratic risk leads to higher leverage.

Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation

We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated with a path in mesoscopic phase space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in nondissipative systems. This is a consequence of the quasielasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always Gaussian, as expected from the central limit theorem. On the other hand, strong separation from the Gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem, as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily suppressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion, and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases nonconvex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of describing in detail the fluctuating behavior of nonlinear driven dissipative media.

Laminarization mechanisms and extreme-amplitude states in rapidly rotating plane channel flow

AbstractFully developed plane channel flow rotating in the spanwise direction has been studied analytically and numerically. Linear stability analysis reveals that all cross-flow modes are stable for supercritical rotation numbers, $Ro\gt R{o}_{c} $, where $R{o}_{c} $ will approach 3 from below for increasing Reynolds number. Plane Tollmien–Schlichting (TS) waves are independent of rotation and always linearly unstable for supercritical Reynolds numbers. Direct numerical simulation (DNS) of the laminarization process reveals that the turbulence is damped when $Ro$ approaches $R{o}_{c} $. Hence, the laminarization is dominated by linear mechanisms. The flow becomes periodic for supercritical Reynolds numbers and rotation rates, i.e. when $Ro\gt R{o}_{c} $ and $Re\gt R{e}_{c} $. At such rotation rates, all oblique (cross-flow) modes are damped and when the disturbance amplitude becomes small enough, the TS modes start to grow exponentially. Secondary instabilities are initially blocked by the rotation since all cross-flow modes are linearly stable and the breakdown to turbulence will be strongly delayed. Hence, the TS waves will reach extremely high amplitudes, much higher than for typical turbulent fluctuations. Eventually, the extreme-amplitude state with TS-like waves will break down to turbulence and the flow will laminarize due to the influence of the rapid rotation, thus completing the cycle that will then be repeated. This flow is strongly dominated by linear mechanisms, which is remarkable considering the extremely high amplitudes involved in the processes of laminarization of the turbulence at $Ro\geq R{o}_{c} $ and the growth of the unstable TS waves.

Higher systemic antibiotic consumption in a population of South Korea (2008 – 2009)

This study was conducted to investigate overall systemic antibiotic consumption levels and specific patterns using standardized Anatomical Therapeutic Chemical/Defined Daily Dose (ATC/DDD) methodology. National Health Insurance claims data during 2008 and 2009 was used. Antibiotic prescription data was classified using the ATC system and converted into DDD. Consumption figures were presented as the number of DDD per 1,000 inhabitants per day (DID). Detailed information on indications and seasonal variations, age and institutional determinants on antibiotic consumption were also explored. Total consumption was slightly increased from 24.3 to 25.2 DID in 2009 compared to 2008. The most frequently prescribed antibiotic was amoxicillin/clavulanic acid (5.1 and 5.2 DID, in 2008 and 2009, respectively), followed by cefaclor (3.0 and 3.3 DID) and amoxicillin (3.3 and 3.2 DID). Respiratory system diseases were the main causes of antimicrobial prescription (47.3%) and acute forms of bronchitis, tonsillitis and sinusitis were the most common diseases. There were typical seasonal fluctuations with heightened winter peaks. Consumption figures under 5 years of age (41.6 and 43.3 DID) were even higher than figures in aged 65 - 80 (36.2 and 39.1 DID). Antibiotic consumption in South Korea remained high compared with other OECD countries. Efforts to increase prudent antibiotic use, especially for upper respiratory system infections and for younger children, should be made to decrease antibiotic use.

Lagrangian theory of structure formation in relativistic cosmology. II. Average properties of a generic evolution model

Kinematical and dynamical properties of a generic inhomogeneous cosmological model, spatially averaged with respect to free-falling (generalized fundamental) observers, are investigated for the matter model irrotational dust. Paraphrasing a previous Newtonian investigation, we present a relativistic generalization of a backreaction model based on volume-averaging the Relativistic Zeldovich Approximation. In this model we investigate the effect of kinematical backreaction on the evolution of cosmological parameters as they are defined in an averaged inhomogeneous cosmology, and we show that the backreaction model interpolates between orthogonal symmetry properties by covering subcases of the plane-symmetric solution, the Lemaitre-Tolman-Bondi solution and the Szekeres solution. We so obtain a powerful model that lays the foundations for quantitatively addressing curvature inhomogeneities as they would be interpreted as Dark Energy or Dark Matter in a quasi-Newtonian cosmology. The present model, having a limited architecture due to an assumed FLRW background, is nevertheless capable of replacing 1/4 of the needed amount for Dark Energy on domains of 200 Mpc in diameter for typical (one-sigma) fluctuations in a CDM initial power spectrum. However, the model is far from explaining Dark Energy on larger scales (spatially), where a 6% effect on 400 Mpc domains is identified that can be traced back to an on average negative intrinsic curvature today. One drawback of the quantitative results presented is the fact that the epoch when backreaction is effective on large scales and leads to volume acceleration lies in the future. We discuss this issue in relation to the initial spectrum, the Dark Matter problem, the coincidence problem, and the fact that large-scale Dark Energy is an effect on the past light cone (not spatial), and we pinpoint key elements of future research.

Low irradiance alters carbon metabolism and delays flower stalk development in two orchids

In Phalaenopsis, lowering irradiance has been used to delay flower stalk development but the accompanying biochemical changes remain poorly understood. We cultured two commercial Phalaenopsis-type orchids, Phalaenopsis cv. Sogo Yukidian V3, and Doritaneopsis cv. Walnut Valley Halo ES09 under reduced irradiance by under-bench shading (approximately 15 % of mean control irradiance) for 15 weeks in a greenhouse under the natural photoperiod. Besides delaying flower stalk development as expected, the treatment greatly decreased the activities of ribulose-1,5-bisphosphate carboxylase/oxygenase, phosphoenolpyruvate carboxylase, and NAD+-malic enzyme, and reduced the nocturnal malate accumulation and daytime starch deposition, the typical diurnal metabolite fluctuations of crassulacean acid metabolism (CAM) plants. As well, the content of sucrose and starch was reduced at dawn and dusk whereas the content of glucose and fructose only at dawn. The persistent decrease in the sucrose content under shading may be an inhibitory signal of flower stalk induction.

Lasing at half the Josephson frequency with exponentially long coherence times

We describe a superconducting device capable of producing laser light in the visible range at half the Josephson generation frequency, with the optical phase of the light locked to the superconducting phase difference. An earlier proposed device, the so called "half-Josephson laser" [Phys. Rev. Lett. 107, 073901 (2011)], cannot provide long coherence times, because of spontaneous switchings between the emitter states. To circumvent this we consider N >> 1 emitters driving an optical resonator mode. We derive a general model that captures essential physics of such devices while not depending on specific microscopic details. We find the conditions under which the coherence times are exponentially long, thus surpassing the fundamental limitation on the coherence times of common lasers. For this we study the noise in the device. In particular, we are interested in the rate of large fluctuations of the light field in the limit where the typical fluctuations are small. The large fluctuations are responsible for switching of the laser between stable states of radiation and therefore determine the coherence time.

Dynamical phase transition for current statistics in a simple driven diffusive system

We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents, where it becomes time-dependent. This instability corresponds to a dynamical phase transition in the system fluctuation behavior: while typical current fluctuations result from the sum of weakly-correlated local events and are still associated with the flat, steady-state density profile, for currents below a critical threshold the system self-organizes into a macroscopic jammed state in the form of a coherent traveling wave, that hinders transport of particles and thus facilitates a time-averaged current fluctuation well below the average current. We analyze in detail this phenomenon using advanced Monte Carlo simulations, and work out macroscopic fluctuation theory predictions, finding very good agreement in all cases. In particular, we study not only the current large deviation function, but also the critical current threshold, the associated optimal density profiles and the traveling wave velocity, analyzing in depth finite-size effects and hence providing a detailed characterization of the dynamical transition.

Imaging of Mitochondrial and Non-Mitochondrial Responses in Cultured Rat Hippocampal Neurons Exposed to Micromolar Concentrations of TMRM

Tetramethylrhodamine methyl ester (TMRM) is a fluorescent dye used to study mitochondrial function in living cells. Previously, we reported that TMRM effectively labeled mitochondria of neurons deep within mouse brain slices. Use of micromolar concentration of dye, which was required to get sufficient staining for two-photon imaging, resulted in typical fluctuations of TMRM. With prolonged exposure, we recorded additional responses in some neurons that included slow oscillations and propagating waves of fluorescence. (Note: We use the terms “fluctuation” to refer to a change in the fluorescent state of an individual mitochondrion, “oscillation” to refer to a localized change in fluorescence in the cytosol, and “wave” to refer to a change in cytosolic fluorescence that propagated within a cell. Use of these terms does not imply any underlying periodicity.) In this report we describe similar results using cultured rat hippocampal neurons. Prolonged exposure of cultures to 2.5 µM TMRM produced a spontaneous increase in fluorescence in some neurons, but not glial cells, after 45–60 minutes that was followed by slow oscillations, waves, and eventually apoptosis. Spontaneous increases in fluorescence were insensitive to high concentrations of FCCP (100 µM) and thapsigargin (10 µM) indicating that they originated, at least in part, from regions outside of mitochondria. The oscillations did not correlate with changes in intracellular Ca2+, but did correlate with differences in fluorescence lifetime of the dye. Fluorescence lifetime and one-photon ratiometric imaging of TMRM suggested that the spontaneous increase and subsequent oscillations were due to movement of dye between quenched (hydrophobic) and unquenched (hydrophilic) compartments. We propose that these movements may be correlates of intracellular events involved in early stages of apoptosis.

KINKS AND DENTS IN PROTOPLANETARY DISKS: RAPID INFRARED VARIABILITY AS EVIDENCE FOR LARGE STRUCTURAL PERTURBATIONS

We report on synoptic observations at 3.6 and 4.5micron of young stellar objects in IC 348 with 38 epochs covering 40 days. We find that among the detected cluster members, 338 at [3.6] and 269 at both [3.6] and [4.5], many are variable on daily to weekly timescales with typical fluctuations of ~0.1 mag. The fraction of variables ranges from 20% for the diskless pre-main sequence stars to 60% for the stars still surrounded by infalling envelopes. We also find that stars in the exposed cluster core are less variable than the stars in the dense, slightly younger, south-western ridge. This trend persists even after accounting for the underlying correlation with infrared SED type, suggesting that the change in variable fraction is not simply a reflection of the change in relative fraction of class I vs. class II sources across the cloud, but instead reflects a change in variability with age. We also see a strong correlation between infrared variability and X-ray luminosity among the class II sources. The observed variability most likely reflects large changes in the structure of the inner wall located at the dust sublimation radius. We explore the possibility that these structural perturbations could be caused by a hot spot on the star heating dust above the sublimation temperature, causing it to evaporate rapidly, and increasing the inner radius for a portion of the disk. Under a number of simplifying assumptions we show that this model can reproduce the size and timescale of the 3.6 and 4.5micron fluctuations. Regardless of its source, the infrared variability indicates that the inner disk is not a slowly evolving entity, but instead is a bubbling, warped, dented mass of gas and dust whose global size and shape fluctuate in a matter of days.

Effect of gap width on turbulent mixing of parallel flow in a square channel with a cylindrical rod

The turbulent mixing coefficient is an essential parameter to describe the energy and momentum transports between adjacent subchannels in a nuclear fuel assembly and affect the thermal–hydraulic characteristics in nuclear reactor core. Hence, its estimation is in close connection with the design and performance–prediction of nuclear reactor. In the present experimental study, the effect of gap width on the flow pulsation and turbulent mixing was investigated using PIV (Particle Image Velocimetry). The W/D (the ratio of distance to wall to rod diameter) covered from 1.03 to 1.14, and the single cylindrical rods with five different diameters were installed in a square channel to adjust the gap width. Among the W/D cases tested, in the W/D=1.03, 1.06, 1.08, and 1.10, the flow pulsation, a quasi-periodic oscillating flow motion, appeared at the rod gap center, while it was not observed for W/D=1.14. As an increase in Reynolds number and/or a decrease in W/D, the peak frequency and power spectral density of flow pulsation became higher and larger, respectively. On the other hand, the W/D cases with a flow pulsation exhibited higher RMS (Root–Mean–Square) values of lateral velocity than the case without a flow pulsation. The change in the RMS values of lateral velocity was more sensitive to the W/D conditions, particularly for the small W/D cases (i.e., W/D⩽1.10) showing the flow pulsation. This implies that the RMS values of lateral velocity are strongly influenced by the flow pulsation, which in turn, can determine the turbulent mixing between subchannels. To propose the turbulent mixing coefficient for nuclear reactor core application, the W/D ranges were divided into two groups dominated by (i) the large eddy motion of the flow pulsation, and (ii) the typical fluctuation of the turbulent flow. Finally, the empirical correlations of the turbulent mixing coefficient considering the effects of W/D and the Reynolds number were proposed using the RMS value of lateral velocity, which were in agreement with previous studies within a reasonable degree of accuracy.

Money for Nothing…: A Case Study of Financial Class Action Litigation

The class action law suit Annie Adams et al - Southern New York, 12-cv-07461, claims that banks increased 6-months USD LIBOR rates on first business days of a month in order to take advantage of mortgage holders due to inflated reset rates on the mortgages. The claims do not seem to be supported by the data. While some point estimates are correct as claimed in the law suit, the claimants do not account for random fluctuation in the LIBOR rates. Standard statistical analysis suggests that the observed differences in means are well within typical fluctuations in the data. Moreover, as some people argue that banks were artificially lowering LIBOR rates in order to make them look financially stronger in the crisis of 2007/2008, that effect would actually help the claimants as it would lower their reset mortgage rates.

Reunion Probability of N Vicious Walkers: Typical and Large Fluctuations for Large N

We consider three different models of N non-intersecting Brownian motions on a line segment [0,L] with absorbing (model A), periodic (model B) and reflecting (model C) boundary conditions. In these three cases we study a properly normalized reunion probability, which, in model A, can also be interpreted as the maximal height of N non-intersecting Brownian excursions on the unit time interval. We provide a detailed derivation of the exact formula for these reunion probabilities for finite N using a Fermionic path integral technique. We then analyse the asymptotic behavior of this reunion probability for large N using two complementary techniques: (i) a saddle point analysis of the underlying Coulomb gas and (ii) orthogonal polynomial method. These two methods are complementary in the sense that they work in two different regimes, respectively for L\ll O(\sqrt{N}) and L\geq O(\sqrt{N}). A striking feature of the large N limit of the reunion probability in the three models is that it exhibits a third-order phase transition when the system size L crosses a critical value L=L_c(N)\sim \sqrt{N}. This transition is akin to the Douglas-Kazakov transition in two-dimensional continuum Yang-Mills theory. While the central part of the reunion probability, for L \sim L_c(N), is described in terms of the Tracy-Widom distributions (associated to GOE and GUE depending on the model), the emphasis of the present study is on the large deviations of these reunion probabilities, both in the right [L \gg L_c(N)] and the left [L \ll L_c(N)] tails. In particular, for model B, we find that the matching between the different regimes corresponding to typical L \sim L_c(N) and atypical fluctuations in the right tail L \gg L_c(N) is rather unconventional, compared to the usual behavior found for the distribution of the largest eigenvalue of GUE random matrices.

Extremes of N Vicious Walkers for Large N: Application to the Directed Polymer and KPZ Interfaces

We compute the joint probability density function (jpdf) P_N(M, \tau_M) of the maximum M and its position \tau_M for N non-intersecting Brownian excursions, on the unit time interval, in the large N limit. For N \to \infty, this jpdf is peaked around M = \sqrt{2N} and \tau_M = 1/2, while the typical fluctuations behave for large N like M - \sqrt{2N} \propto s N^{-1/6} and \tau_M - 1/2 \propto w N^{-1/3} where s and w are correlated random variables. One obtains an explicit expression of the limiting jpdf P(s,w) in terms of the Tracy-Widom distribution for the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory and a psi-function for the Hastings-McLeod solution to the Painlev\'e II equation. Our result yields, up to a rescaling of the random variables s and w, an expression for the jpdf of the maximum and its position for the Airy_2 process minus a parabola. This latter describes the fluctuations in many different physical systems belonging to the Kardar-Parisi-Zhang (KPZ) universality class in 1+1 dimensions. In particular, the marginal probability density function (pdf) P(w) yields, up to a model dependent length scale, the distribution of the endpoint of the directed polymer in a random medium with one free end, at zero temperature. In the large w limit one shows the asymptotic behavior \log P(w) \sim - w^3/12.

Impact of temperature on raw wastewater composition and activated sludge filterability in full-scale MBR systems for municipal sewage treatment

The main objective of this study was to investigate the influence of seasonal temperature fluctuations on raw domestic wastewater composition and MBR sludge filterability. The influent and sludge samples were collected from a full-scale MBR in Heenvliet. All samples were analyzed in terms of filterability, particle size distribution, respirometry, fractionation and were further characterized by an extensive set of physicochemical measurements. Typical seasonal fluctuations and deterioration of activated sludge filterability during low temperature periods were observed. Filterability deterioration at low temperatures was linked to the incoming organic load, reduced MBR biomass concentrations, increased VSS/TSS ratio and reduced biodegradation of wastewater in the mixed liquor. Biological activity of the biomass was concomitantly decreased with temperature to reach a minimum during the winter period. Results show that the colloidal and soluble fraction (<1μm) represents the majority of the constituents, contains most of the COD, and plays an important role in the membrane resistance increase.