Uncoupled System Research Articles

Involvement of AOX and UCP pathways in the post-harvest ripening of papaya fruits

Enhanced respiration during ripening in climacteric fruits is sometimes associated with an uncoupling between the ATP synthesis and the mitochondrial electron transport chain. While the participation of two energy-dissipating systems, one of which is mediated by the alternative oxidase (AOX) and the other mediated by the uncoupling protein (UCP), has been linked to fruit ripening, the relation between the activation of both mitochondrial uncoupling systems with the transient increase of ethylene synthesis (ethylene peak) remains unclear. To elucidate this question, ethylene emission and the two uncoupling (AOX and UCP) pathways were monitored in harvested papaya fruit during the ripening, from green to fully yellow skin. The results confirmed the typical climacteric behavior for papaya fruit: an initial increase in endogenous ethylene emission which reaches a maximum (peak) in the intermediate ripening stage, before finally declining to a basal level in ripe fruit. Respiration of intact fruit also increased and achieved higher levels at the end of ripening. On the other hand, in purified mitochondria extracted from fruit pulp the total respiration and respiratory control decrease while an increase in the participation of AOX and UCP pathways was markedly evident during papaya ripening. There was an increase in the AOX capacity during the transition from green fruit to the intermediate stage that accompanied the transient ethylene peak, while the O2 consumption triggered by UCP activation increased by 80% from the beginning to end stage of fruit ripening. Expression analyses of AOX (AOX1 and 2) and UCP (UCP1–5) genes revealed that the increases in the AOX and UCP capacities were linked to a higher expression of AOX1 and UCP (mainly UCP1) genes, respectively. In silico promoter analyses of both genes showed the presence of ethylene-responsive cis-elements in UCP1 and UCP2 genes. Overall, the data suggest a differential activation of AOX and UCP pathways in regulation related to the ethylene peak and induction of specific genes such as AOX1 and UCP1.

Wave-Like Solutions of General 1-D Spatially Coupled Systems

We establish the existence of wave-like solutions to spatially coupled graphical models which, in the large size limit, can be characterized by a 1-D real-valued state. This is extended to a proof of the threshold saturation phenomenon for all such models, which includes spatially coupled irregular low-density parity-check codes over the binary erasure channel (BEC), but also addresses hard-decision decoding for transmission over general channels, the code division multiple access problem, compressed sensing, and some statistical physics models. For traditional uncoupled iterative coding systems with two components and transmission over the BEC, the asymptotic convergence behavior is completely characterized by the EXIT curves of the components. In particular, the system converges to the desired fixed point, which is the one corresponding to perfect decoding, if and only if the two EXIT functions describing the components do not cross. For spatially coupled systems whose state is 1-D a closely related graphical criterion applies. Now the curves are allowed to cross, but not by too much. More precisely, we show that the threshold saturation phenomenon is related to the positivity of the (signed) area enclosed by two EXIT-like functions associated to the component systems, a very intuitive, and easy-to-use graphical characterization. In the spirit of EXIT functions and Gaussian approximations, we also show how to apply the technique to higher dimensional and even infinite-dimensional cases. In these scenarios, the method is no longer rigorous, but it typically gives accurate predictions. To demonstrate this application, we discuss transmission over general channels using both the belief-propagation as well as the min-sum decoder.

Systems of fractional Langevin equations of Riemann-Liouville and Hadamard types

Fractional differential equations have been shown to be very useful in the study of models of many phenomena in various fields of science and engineering, such as physics, chemistry, biology, signal and image processing, biophysics, blood flow phenomena, control theory, economics, aerodynamics, and fitting of experimental data. Much of the work on the topic deals with the governing equations involving Riemann-Liouville- and Caputo-type fractional derivatives. Another kind of fractional derivative is the Hadamard type, which was introduced in 1892. This derivative differs from the aforementioned derivatives in the sense that the kernel of the integral in the definition of the Hadamard derivative contains a logarithmic function of arbitrary exponent. In the present paper we introduce a new class of boundary value problems for Langevin fractional differential systems. The Langevin equation is widely used to describe the evolution of physical phenomena in fluctuating environments. We combine Riemann-Liouville- and Hadamard-type Langevin fractional differential equations subject to Hadamard and Riemann-Liouville fractional integral boundary conditions, respectively. Some new existence and uniqueness results for coupled and uncoupled systems are obtained by using fixed point theorems. The existence and uniqueness of solutions is established by Banach’s contraction mapping principle, while the existence of solutions is derived by using the Leray-Schauder’s alternative. The obtained results are well illustrated with the aid of examples.

Coupled Mode Theory Applied to Resonators in the Presence of Conductors

Using the method of images, Energy Coupled Mode Theory (ECMT), a coupled mode equation in the frequency domain, is extended to deal with important cases where resonators are in close proximity to conducting surfaces. Depending on the type of conductors and the orientation of the resonators, the method of images determines the relative phases of the images. Using the formed images, the coupled frequencies and fields can be determined by applying ECMT. Two cases are studied. In the first case, it is shown that a dielectric resonator inserted in a cavity couples with both the mirror image and the cavity. The frequency behavior is described by the interaction with the image which counteracts that with the cavity. The second case is that of resonators sandwiched between conducting plates. It is shown that an infinite array of stacked images is formed. The coupling of the resonator with its images determines the coupled frequencies and fields. In this context, the main advantage of ECMT is its ability to separate the effects of the walls from the uncoupled system. This means that the system parameters are independent of the separation distances and/or the type of conductors, which renders the post processing analyses easier and predictable. Provided that the behaviors of the uncoupled resonators are known, ECMT is general and can be applied to more complex systems.

Two-dimensional spectroscopy: An approach to distinguish Förster and Dexter transfer processes in coupled nanostructures

The linear and two-dimensional coherent optical spectra of Coulomb-coupled quantum emitters are discussed with respect to the underlying coupling processes. We present a theoretical analysis of the two different resonance energy transfer mechanisms between coupled nanostructures: F\"orster and Dexter interaction. Our investigation shows that the features visible in optical spectra of coupled quantum dots can be traced back to the nature of the underlying coupling mechanism (F\"orster or Dexter). Therefore, we discuss how the excitation transfer pathways can be controlled by choosing particular laser polarizations and mutual orientations of the quantum emitters in coherent two-dimensional spectroscopy. In this context, we analyze to what extent the delocalized double-excitonic states are bound to the optical selection rules of the uncoupled system.

Global Diffusion on a Tight Three-Sphere

We consider an integrable Hamiltonian system weakly coupled with a pendulum-type system. For each energy level within some range, the uncoupled system is assumed to possess a normally hyperbolic invariant manifold diffeomorphic to a three-sphere, which bounds a strictly convex domain, and whose stable and unstable invariant manifolds coincide. The Hamiltonian flow on the three-sphere is equivalent to the Reeb flow for the induced contact form. The strict convexity condition implies that the contact structure on the three-sphere is tight. When a small, generic coupling is added to the system, the normally hyperbolic invariant manifold is preserved as a three-sphere, and the stable and unstable manifolds split, yielding transverse intersections. We show that there exist trajectories that follow any prescribed collection of invariant tori and Aubry–Mather sets within some global section of the flow restricted to the three-sphere. In this sense, we say that the perturbed system exhibits global diffusion on the tight three-sphere.

A coupled system of fractional q-integro-difference equations with nonlocal fractional q-integral boundary conditions

In this paper, we investigate the existence and the uniqueness of solutions for coupled and uncoupled systems of fractional q-integro-difference equations with nonlocal fractional q-integral boundary conditions. The existence and the uniqueness of the solutions are established by using the Banach contraction principle, while the existence of solutions is derived by applying Leray-Schauder’s alternative. Examples illustrating our results are also presented.

Kondo effect and the fate of bistability in molecular quantum dots with strong electron-phonon coupling

We investigate the properties of the molecular quantum dot (Holstein-Anderson) model using numerical and analytical techniques. Path integral Monte Carlo simulations for the cumulants of the distribution function of the phonon coordinate reveal that at intermediate temperatures the effective potential for the oscillator exhibits two minima rather than a single one, which can be understood as a signature of a bistability effect. A straightforward adiabatic approximation turns out to adequately describe the properties of the system in this regime. Upon lowering the temperature the two potential energy minima of the oscillator merge to a single one at the equilibrium position of the uncoupled system. Using the parallels to the x-ray edge problem in metals we derive the oscillator partition function. It turns out to be identical to that of the Kondo model, which is known to possess a universal low-energy fixed point characterized by a single parameter---the Kondo temperature ${T}_{K}$. We derive an analog of ${T}_{K}$ for the molecular quantum dot model, present numerical evidence pointing towards the appearance of the Kondo physics, and discuss experimental implications of the discovered phenomena.

A complex Noether approach for variational partial differential equations

Scalar complex partial differential equations which admit variational formulations are studied. Such a complex partial differential equation, via a complex dependent variable, splits into a system of two real partial differential equations. The decomposition of the Lagrangian of the complex partial differential equation in the real domain is shown to yield two real Lagrangians for the split system. The complex Maxwellian distribution, transonic gas flow, Maxwellian tails, dissipative wave and Klein–Gordon equations are considered. The Noether symmetries and gauge terms of the split system that correspond to both the Lagrangians are constructed by the Noether approach. In the case of coupled split systems, the same Noether symmetries are obtained. The Noether symmetries for the uncoupled split systems are different. The conserved vectors of the split system which correspond to both the Lagrangians are compared to the split conserved vectors of the complex partial differential equation for the examples. The split conserved vectors of the complex partial differential equation are the same as the conserved vectors of the split system of real partial differential equations in the case of coupled systems. Moreover a Noether-like theorem for the split system is proved which provides the Noether-like conserved quantities of the split system from knowledge of the Noether-like operators. An interesting result on the split characteristics and the conservation laws is shown as well. The Noether symmetries and gauge terms of the Lagrangian of the split system with the split Noether-like operators and gauge terms of the Lagrangian of the given complex partial differential equation are compared. Folklore suggests that the split Noether-like operators of a Lagrangian of a complex Euler–Lagrange partial differential equation are symmetries of the Lagrangian of the split system of real partial differential equations. This is not the case. They are proved to be the same if the Noether symmetries of the Lagrangian of the complex partial differential equation have either pure real or pure imaginary form.

A stochastic collocation method for stochastic Volterra equations of the second kind

This work describes and analyzes a stochastic collocation method for stochastic Volterra integral equations (SVIEs) of the second kind with random forcing terms. A collocation method is used in temporal direction, and a spectral collocation method is used in the stochastic dimension, which lead to an uncoupled linear system associated with the collocation points. The convergence analysis is carried out and the optimal error estimates are obtained. Numerical experiments are conducted to verify the error estimates and demonstrate the effectiveness of the proposed numerical method.

Bifurcation behaviors of synchronized regions in logistic map networks with coupling delay

Network synchronized regions play an extremely important role in network synchronization according to the master stability function framework. This paper focuses on network synchronous state stability via studying the effects of nodal dynamics, coupling delay, and coupling way on synchronized regions in Logistic map networks. Theoretical and numerical investigations show that (1) network synchronization is closely associated with its nodal dynamics. Particularly, the synchronized region bifurcation points through which the synchronized region switches from one type to another are in good agreement with those of the uncoupled node system, and chaotic nodal dynamics can greatly impede network synchronization. (2) The coupling delay generally impairs the synchronizability of Logistic map networks, which is also dominated by the parity of delay for some nodal parameters. (3) A simple nonlinear coupling facilitates network synchronization more than the linear one does. The results found in this paper will help to intensify our understanding for the synchronous state stability in discrete-time networks with coupling delay.

Qualitative analysis of a model for the classic dengue dynamics

A mathematical model for a non-linear continuous stochastic process is presented. Analysis of the stability by uncoupling system is realized.

Patterns for Competing Populations with Species Specific Nonlocal Coupling

We study a reaction-diffusion population model for two competing species, u and v , which also includes nonlocal integral terms that represent competition for resources. The integral terms have the form of a convolution of a given kernel function and the solution. They manifest the fact that consumption of resources by the species at a spatial location x depends not just on the populations at point x but rather on weighted averages of the populations in an interval about x . The kernel functions that we employ are characterized by two parameters, δ , which gives a spatial scale of the nonlocality, with δ = 0 corresponding to the local case, and α , a parameter associated with the extent of the asymmetry of the kernel, where α = 0 corresponds to a symmetric kernel, i.e., to a kernel that is an even function of its argument. We consider the parameter regime where for δ = 0 the system admits a stable coexistence equilibrium, which is destabilized for sufficiently large δ . Deeply in the instability region, the ensuing patterns involve arrays of islands, regions of nonzero population, separated by deadzones where the populations are essentially extinct. These structures are stationary if α = 0 and propagate if α ≠ 0. Unlike previous work, we study the patterns when the kernel parameters are different for the two species, focusing first on different δ with α = 0 and then on different α with the same δ . In the first case we numerically find stationary patterns consisting of (i) plateau regions for the more local species (v ), where the plateau value is essentially the v −component of the unstable equilibrium point, (ii) oscillatory patterns, where oscillations appear along the plateau and along the u −island and (iii) split patterns, where instead of an island, there is an island cluster of two or more neighbors separated by deadzones or near deadzones. In the second case we consider weakly coupled systems and show that there are two kinds of patterns, (i) bound waves, when each species propagates with the same speed and (ii) unbound patterns where each species propagates with its own speed, interacting with the other species when they intersect, i.e., when the two species occupy the same or closely spaced regions. We show that whether the patterns are bound or unbound depends on the stability of the decoupled system, i.e., the system when the coupling parameters are zero. When one of the species for the decoupled system is stable, then the ensuing patterns for weak coupling is bound, while if both species are unstable for the uncoupled systems, the resulting patterns are unbound for weak coupling.

Inelastic carrier lifetime in a coupled graphene/electron-phonon system: Role of plasmon-phonon coupling

We calculate the inelastic scattering rates and the hot electron inelastic mean free paths for both monolayer and bilayer graphene on a polar substrate. We study the quasiparticle self-energy by taking into account both electron-electron and electron-surface optical (SO) phonon interactions. In this calculation the leading order dynamic screening approximation (G$_0$W approximation) is used to obtain the quasiparticle self-energy by treating electrons and phonons on an equal footing. We find that the strong coupling between the SO phonon and plasmon leads to a new decay channel for the quasiparticle through the emission of the coupled mode, and gives rise to an abrupt increase in the scattering rate, which is absent in the uncoupled system. In monolayer graphene a single jump in the scattering rate occurs, arising from the emission of the low energy branch of the coupled plasmon-phonon modes. In bilayer graphene the emission of both low and high energy branches of the coupled modes contributes to the scattering rate and gives rise to two abrupt changes in the scattering rate. The jumps in the scattering rate can be potentially used in the hot electron device such as switching devices and oscillators.

Convergence of a level‐set algorithm in scalar conservation laws

This article is concerned with the convergence of the level‐set algorithm introduced by Aslam (J Comput Phys 167 (2001), 413–438) for tracking the discontinuities in scalar conservation laws in the case of linear or strictly convex flux function. The numerical method is deduced by the level‐set representation of the entropy solution: the zero of a level‐set function is used as an indicator of the discontinuity curves and two auxiliary states, which are assumed continuous through the discontinuities, are introduced. We rewrite the numerical level‐set algorithm as a procedure consisting of three big steps: (a) initialization, (b) evolution, and (c) reconstruction. In (a), we choose an entropy admissible level‐set representation of the initial condition. In (b), for each iteration step, we solve an uncoupled system of three equations and select the entropy admissible level‐set representation of the solution profile at the end of the time iteration. In (c), we reconstruct the entropy solution using the level‐set representation. We prove the convergence of the numerical solution to the entropy solution in for every , using ‐weak bounded variation (BV) estimates and a cell entropy inequality. In addition, some numerical examples focused on the elementary wave interaction are presented. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1310–1343, 2015

Radó-Kneser-Choquet theorem

We present a new approach to the celebrated theorem of Radó–Kneser–Choquet (RKC) on univalence of planar harmonic mappings. The novelty lies in establishing a continuous path (isotopy) from the given harmonic map to a conformal one. Along this path the mappings retain positive Jacobian determinant by virtue of so-called Minimum Principle. These ideas extend to nonlinear uncoupled systems of partial differential equations, as in Iwaniec, Koski and Onninen [‘Isotropic p-harmonic systems in 2D, Jacobian estimates and univalent solutions’, Rev. Mat. Iberoam, to appear]. Unfortunately, details of such digression would lead us too far afield. Nonetheless, one gains (in particular) the RKC-Theorem for the isotropic p-harmonic deformations.

A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions

Low-density parity-check (LDPC) convolutional codes (or spatially coupled codes) were recently shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this spectacular performance is now called threshold saturation via spatial coupling. This new phenomenon is characterized by the belief-propagation threshold of the spatially coupled ensemble increasing to an intrinsic noise threshold defined by the uncoupled system. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled scalar recursions. Our approach is based on constructing potential functions for both the coupled and uncoupled recursions. Our results actually show that the fixed point of the coupled recursion is essentially determined by the minimum of the uncoupled potential function and we refer to this phenomenon as Maxwell saturation. A variety of examples are considered including the density-evolution equations for: irregular LDPC codes on the BEC, irregular low-density generator-matrix codes on the BEC, a class of generalized LDPC codes with BCH component codes, the joint iterative decoding of LDPC codes on intersymbol-interference channels with erasure noise, and the compressed sensing of random vectors with independent identically distributed components.

Green-Kubo Formula for Weakly Coupled Systems with Noise

We study the Green-Kubo formula $${\kappa (\varepsilon, \varsigma)}$$ for the heat conductivity of an infinite chain of d-dimensional finite systems (cells) coupled by a smooth nearest neighbor potential $${\varepsilon V}$$ . The uncoupled systems evolve according to Hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength $${\varsigma}$$ . Noting that $${\kappa (\varepsilon, \varsigma)}$$ exists and is finite whenever $${\varsigma > 0}$$ , we are interested in what happens when the strength of the noise $${\varsigma \to 0}$$ . For this, we start in this work by formally expanding $${\kappa (\varepsilon, \varsigma)}$$ in a power series in $${\varepsilon}$$ , $${\kappa (\varepsilon, \varsigma) = \varepsilon^2 \sum_{n\geq 2} \varepsilon^{n-2} \kappa_n (\varsigma)}$$ and investigating the (formal) equations satisfied by $${\kappa_n (\varsigma)}$$ . We show in particular that $${\kappa_2 (\varsigma)}$$ is well defined when no pinning potential is present, and coincides formally with the heat conductivity obtained in the weak coupling (van Hove) limit, where time is rescaled as $${\varepsilon^{-2}t}$$ , for the cases where the latter has been established (Liverani and Olla, in JAMS 25:555–583, 2012; Dolgopyat and Liverani, in Commun Math Phys 308:201–225, 2011). For one-dimensional systems, we investigate $${\kappa_2 (\varsigma)}$$ as $${\varsigma \to 0}$$ in three cases: the disordered harmonic chain, the rotor chain and a chain of strongly an harmonic oscillators. Moreover, we formally identify $${\kappa_2 (\varsigma)}$$ with the conductivity obtained by having the chain between two reservoirs at temperature T and $${T+\delta T}$$ , in the limit $${\delta T \to 0}$$ , $${N \to \infty}$$ , $${\varepsilon \to 0}$$ .

Pull-In Instability and Vibrations of a Beam Micro-Gyroscope

Gyroscopes are used as rotation rate sensors. Conventional gyroscopes are heavy and bulky, which creates important problems regarding their usage in different applications. Micro-gyroscopes have solved these problems due to their small size. The beam micro-gyroscope is one of the popular types of inertial sensors. Their small dimensions and low energy consumption are key reasons for their popularity. In this investigation, the model of an electrostatically actuated beam-based micro-gyroscope is used to study the effect of design parameters on pull-in voltage and fundamental frequency. The micro-gyroscope includes a rotating cantilever beam and a tip mass attached to the free end. DC voltages are applied to both sense and drive electrodes to actuate the system. The tip mass is actuated by an AC voltage in the drive direction to produce oscillations in the sense direction. Equations of motion are solved numerically to study different pull-in and vibrational parameters. Eigenvalues of the uncoupled system are computed to obtain the fundamental frequency of the micro beam for different values of DC voltages and design parameters. The frequencies are computed and validated with those in the literature. The results are beneficial for the design process of micro-gyroscopes.

Toward Electrosynthesis with Uncoupled Extracellular Electron Uptake and Metabolic Growth: Enhancing Current Uptake with Rhodopseudomonas palustris

The production of metabolites from CO2 with microbes at cathodes (i.e., microbial electrosynthesis) is an attractive application of microbial electrochemistry. However, processes for the uptake of electrons from electrodes remain elusive, and microbial conservation of energy does not often occur at the cathode. One mechanism known for the uptake of electrons from electrodes is iron-mediated electron transfer to iron-oxidizing bacteria such as obligate aerobic chemolithotrophs and anaerobic photoautotrophs. However, for photoautotrophs, this requires an illuminated cathode to provide metabolic energy for growth. Here, we increased published iron-mediated electron uptake rates of Rhodopseudomonas palustris TIE-1 by uncoupling the electrochemical from the biological environment in a photobioelectrochemical system consisting of an electrochemical system and a photobioreactor. This uncoupled system resulted in a volumetric iron-mediated electron uptake rate (electric current) 56-fold higher than that in a single photobioelectrochemical system.