Exponential Regime Research Articles

Charge transport across organic heterostructure: Role of interfacial density of states

The mechanism of carrier transport across organic-organic hetero-interfaces is crucial for organic devices. For purposes of this study, we choose two hole transport materials 4, 4′, 4″-tris(N-3-methylphenyl-N-phenyl-amino) triphenyl-amine (m-MTDATA) and N, N′-diphenyl-N, N′-bis(1-naphthyl) (1, 1′-biphenyl)-4, 4′diamine. We demonstrate that transport across such interfaces can be controlled by introducing a thin undoped layer, which is chosen to be 10–30 nm of m-MTDATA layer in this particular case. By correlating the low frequency capacitance-voltage and temperature dependence of current density-voltage (J-V) characteristics, we show that the occupation of local density of states (LDOS) on both sides controls the transport at the hetero-interface and that it can be modified by the introduction of interlayer. The thickness of the undoped interlayer effectively acts as a control on carrier concentration at the interface leading to the modification of the effective energy offset, and overlap of the LDOS. The slope of the J-V characteristics in the exponential regime has a temperature dependent term and a purely voltage dependent term. The temperature dependence of J-V characteristics is explained by including field dependence of mobility and tunneling across LDOS. We trace the origin of the offset at the hetero-interface and estimate its values for the different cases consistent with the proposed model of thermally assisted tunneling at the interface.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high‐order numerical tools

SUMMARYWe explore the recently developed snapshot‐based dynamic mode decomposition (DMD) technique, a matrix‐free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L‐shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non‐linear incompressible discontinuous Galerkin Navier–Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non‐linear and linearised Navier–Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier–Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three‐dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier–Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L‐shaped geometry and control the most unstable 3D mode. Copyright © 2014 John Wiley & Sons, Ltd.

Morphology and local transport characteristics of metalloporphyrin thin films

Organic systems such as porphyrin-based molecules stand as a promising alternative for molecular devices. These systems have important photophysical and electrochemical properties and can be easily prepared by well-established synthesis and deposition techniques. Nevertheless, not very much is known about their electrical properties and charge transport mechanisms. In this work, the local electrical properties of [5,10,15,20-tetra(p-methoxyphenyl)porphyrin]copper(II) (Cu-TMPP) thin films deposited on nickel substrates are investigated. The implementation of current-sensing atomic force microscopy (cs-AFM) allows the detection of local variations of the topographic and transport properties of Cu-TMPP thin films with nanometric spatial resolution. In particular, the electric current mapping approach adopted here allows the quantification of the local charge transfer through the organic structures in a reliable and controlled manner. The formation of organic dendrites with heights between 2 and 5nm and lengths in the micrometric scale is observed. On thicker organic films, a layered filamentary-like growth is observed. These dendrites behave as a semiconducting matrix structure over a conducting metallic substrate and could be used for tuning transport properties on a device scale by reducing the contact area at the organic film-metal electrode interface. In addition, a detailed investigation of the electrical evolution of the conducting sites in the organic thin films is presented as a function of the thickness and applied electric field. For the majority of the conducting sites (>70–80%), a field dependent transition from a linear-like to an exponential transport regime is identified. We relate the non-homogeneous electrical response to the formation of molecular dendrites and interface defects. This electrical analysis and the understanding of the underlying transport mechanism become important for future implementation of porphyrin-based devices.

The dichotomous Markov process with nonparametric test application; a decision support method in long-term river behavioural analysis: the Zayandeh Rud River; a case study from central Iran

We use the Dichotomous Markov Noise model with constant transition rates to describe the dynamics of fluctuations in the water level as a stochastic process, which is imposed on river discharge changes. By applying this model, two different regimes are determined for the long-term behaviour of the river. Based on these regimes, we define two nonparametric classes of the overall increasing/decreasing nature of the water level in the long-term behaviour, which are separated by an exponential steady state regime. In this paper, we develop a nonparametric testing procedure to test exponentially (steady state regime) against an alternative overall decreasing level distribution. The proposed test predicts the long-term regime behaviour of the river. The mathematical tools introduced to handle the problem should be of general use and the testing procedure can be considered as a new mathematical tool in the study of water level dynamics. Under conditions of data austerity and as a case of study, we examine the stochastic characteristics of the Zayandeh Rud (Zāyande-Rūd or Zāyanderūd, also spelled as Zayandeh-Rood or Zayanderood) River (Isfahan, Iran) water level.

Quasi-steady stages in the process of premixed flame acceleration in narrow channels

The present paper addresses the phenomenon of spontaneous acceleration of a premixed flame front propagating in micro-channels, with subsequent deflagration-to-detonation transition. It has recently been shown experimentally [M. Wu, M. Burke, S. Son, and R. Yetter, Proc. Combust. Inst. 31, 2429 (2007)]10.1016/j.proci.2006.08.098, computationally [D. Valiev, V. Bychkov, V. Akkerman, and L.-E. Eriksson, Phys. Rev. E 80, 036317 (2009)]10.1103/PhysRevE.80.036317, and analytically [V. Bychkov, V. Akkerman, D. Valiev, and C. K. Law, Phys. Rev. E 81, 026309 (2010)]10.1103/PhysRevE.81.026309 that the flame acceleration undergoes different stages, from an initial exponential regime to quasi-steady fast deflagration with saturated velocity. The present work focuses on the final saturation stages in the process of flame acceleration, when the flame propagates with supersonic velocity with respect to the channel walls. It is shown that an intermediate stage may occur during acceleration with quasi-steady velocity, noticeably below the Chapman-Jouguet deflagration speed. The intermediate stage is followed by additional flame acceleration and subsequent saturation to the Chapman-Jouguet deflagration regime. We elucidate the intermediate stage by the joint effect of gas pre-compression ahead of the flame front and the hydraulic resistance. The additional acceleration is related to viscous heating at the channel walls, being of key importance at the final stages. The possibility of explosion triggering is also demonstrated.

Premature shoot growth termination allows nutrient loading of seedlings with an indeterminate growth strategy

Nutrient loading of nursery seedling stock of species with an indeterminate growth strategy is challenging and poorly understood. Here, we explore the use of two potential techniques for nutrient loading of trembling aspen (Populus tremuloides Michx.) seedlings: (1) exponential fertilization and (2) early shoot growth termination in order to divert assimilated nutrients and carbon to storage rather than to growth. In the first study, aspen seedlings were treated with either exponential or constant fertilization rates, both of which supplied the same amount of nutrients over the growing season. Exponential fertilization resulted in overall poor planting stock form (stunted seedling growth and weak root development) and produced only marginal improvements of nutrient status. As a result, the exponential fertilization regime studied cannot be recommended as a treatment for aspen seedlings. In the second study we treated seedlings with a 2 × 2 factorial combination of fertilization and shoot growth inhibitor (SGI) applications with the fertilizer treatments varying in terms of mid-season fertilizer concentrations. Seedlings with SGI application had much higher tissue nutrient and carbon reserve concentrations than seedlings without a SGI application. In addition, nutrient uptake appeared to be more efficient in SGI treated seedlings, which could potentially result in significant reductions of nutrient application rates during aspen seedling production in nurseries. Overall, early shoot growth termination using a SGI appears to be an effective technique to produce nutrient loaded aspen seedlings.

Phosphonated oligoallylamine: Synthesis, characterization in water, and development of layer by layer assembly

ABSTRACTThe work focuses on the synthesis and layer by layer (LbL) assembly of oligoallylamine and phosphonated oligoallylamine. To this aim, the synthesis of oligoallylamine and the phosphonated form have been done by free radical polymerization in aqueous media. First, radical polymerization of acid salt of allylamine was performed. This charged polymer could not be characterized using classical analytical techniques such as size‐exclusion chromatography and matrix‐assisted laser desorption/ionisation‐time of flight mass spectroscopy due to presence of cations. This work demonstrated the interest of capillary electrophoresis (CE) to analyze charged oligomers, using very small amounts of samples. Entangled polymer solution CE was used as a size‐based separation technique for the characterization of the molar mass distribution using indirect ultraviolet detection and calibration based on vinyl pyridine standards. Phosphorus‐containing oligoallylamines having a number‐average molar mass of 1600 g mol−1 and a 2.3 polydispersity index were obtained. When combined using the LbL approach, prepared polymers showed an exponential growth regime as demonstrated by Fourier transform infrared spectroscopy measurements. Furthermore, thermogravimetric analyses of the LbL‐assembled polymers showed an extraordinary thermal and thermo‐oxidative stability. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym. Phys. 2013, 51, 1244–1251

End-Coupling Reactions in Incompatible Polymer Blends: From Droplets to Complex Micelles through Interfacial Instability

Simulations by dissipative particle dynamics revealed a possibility to produce micelles of diverse morphologies via irreversible end-coupling reaction in polymer melts containing a particulate phase. It is demonstrated that the reaction at the surface of a polymer A droplet immersed in a melt of polymer B leads to the droplet instability and subsequent micelle formation. Depending on the length ratio of reacting chains and its own size, the droplet is either emulsified into a set of small micelles or converted into a single micelle, which can have rather complex internal structure. A morphology diagram containing structures that are typical for polymer solutions, in particular vesicles, bowls, worms, star-like and crew-cut micelles with multiple internal domains, is first presented for polymer melts. Investigation of the reaction kinetics reveals subsequent linear, saturation, and exponential autoacceleration regimes. By simulations and using simple scaling arguments, it is explained how the barrier properties of a diblock copolymer layer formed at the A/B interface depend on the copolymer composition and droplet curvature. It is found that the scenario of the instability development is much different for flat and spherical A/B interfaces.

Exponential and nonexponential buildup in resonant tunneling

The exponential and nonexponential regimes of the buildup process in resonant tunneling structures are analyzed by considering an analytic solution of the time-dependent Schr\"odinger equation. It is found that the buildup exhibits a purely exponential behavior in a finite time interval followed by a clear transition to a nonexponential regime. The buildup of the probability amplitude in the nonexponential regime follows a ${t}^{\ensuremath{-}3/2}$ time dependence, in the same fashion as the survival amplitude in quantum decay. For incidence energies at higher isolated resonances, $E={\ensuremath{\varepsilon}}_{n}$ with $n>1$, it is found that the exponential regime is split into two exponential subregimes: the first one is governed by the width ${\ensuremath{\Gamma}}_{n}$ of the resonance chosen for the incidence energy, and the second one is dominated by the width ${\ensuremath{\Gamma}}_{1}$ of the lowest resonance. The transition occurs directly from $n$ to 1 without jumps to other intermediate resonant states. This dynamics is discussed in comparison with the (opposite) and well-studied process of quantum decay, with which we find that there are striking similarities in both the exponential and nonexponential regimes. We also analyze the buildup in systems with resonance doublets, where the interference effects produced by the interacting resonances play an important role. In the latter case we find that the buildup of the probability amplitude exhibits a complex oscillatory behavior that can be characterized by a mix of oscillating contributions with well-defined Rabi type frequencies of the form $|E\ensuremath{-}{\ensuremath{\varepsilon}}_{n}|/\ensuremath{\hbar}$, where ${\ensuremath{\varepsilon}}_{n}$ are the nearest resonances around the incidence energy $E$.

Multilayered Hierarchical Capsules Providing Cell Adhesion Sites

Liquified capsules featuring (i) an external shell by layer-by-layer assembly of poly(l-lysine), alginate, and chitosan, and encapsulating (ii) surface functionalized poly(l-lactic acid) (PLLA) microparticles were developed. We hypothesize that, while the liquified environment enhances the diffusion of essential molecules for cell survival, microparticles dispersed in the liquified core of capsules provide the physical support required for cellular functions of anchorage-dependent cells. The influence of the incorporation of PLL on the regime growth, thickness, and stability was analyzed. Results show a more resistant and thicker film with an exponential build-up growth regime. Moreover, capsules ability to support cell survival was assessed. Capsules containing microparticles revealed an enhanced biological outcome in cell metabolic activity and proliferation, suggesting their potential to boost the development of innovative biomaterial designs for bioencapsulation systems and tissue engineering products.

Purified self-amplified spontaneous emission free-electron lasers with slippage-boosted filtering

We propose a simple method to significantly enhance the temporal coherence and spectral brightness of a self-amplified spontaneous emission (SASE) free-electron laser (FEL). In this purified SASE (pSASE) FEL, a few undulator sections (called slippage-boosted sections) resonant at a subharmonic of the FEL radiation are used in the middle stage of the exponential growth regime to amplify the radiation while simultaneously reducing the FEL bandwidth. In this slippage-boosted section, the average longitudinal velocity of electrons is reduced, which effectively increases the FEL slippage length that allows the radiation fields initially far apart to create a phase relation, leading to $n$ times increase in FEL cooperation length, where $n$ is the ratio of the resonant wavelength of the slippage-boosted section to that of the original FEL radiation. The purified radiation, as a seed with improved temporal coherence, is further amplified to saturation in the undulator sections tuned to the FEL wavelength. Using the linac coherent light source II (LCLS-II) parameters as an example, we show that with the proposed configuration the temporal coherence and spectral brightness of a SASE FEL can be significantly enhanced. This scheme may be applied to many SASE FEL light sources to enhance the FEL performance.

Failure in a soft gel: Delayed failure and the dynamic yield stress

A soft thermo-reversible protein gel was studied with respect to failure. Flow curves recorded at constant shear-rates revealed a dynamic yield stress σy, seen as a stress plateau below about 10s−1. When a shear stress below σy was applied to fractured gels, they reformed after a time that increased with increasing stress and diverged at σy. Application of shear stress to fresh gels led to an initial elastic response followed by creep. Following this creep regime, the strain stagnated below the dynamic yield stress σy, while for σ>σy failure was observed after a time that increased with decreasing stress and diverged at σ=σy. The time-to-failure dependence on the stress for σ>σy, with two distinct exponential scaling regimes, agrees with existing proposed theories for the fracture of colloidal strands.

Polyallylamine–montmorillonite as super flame retardant coating assemblies by layer-by layer deposition on polyamide

In this paper, a polyamide-6 (PA6) substrate has been coated with a flame retardant film, made from polyallylamine (PAH) (polycation) and montmorillonite (MMT) (polyanion), elaborated by Layer-by-Layer (LbL) technique. The (PAH–MMT)n assembly (with n the number of bilayers deposited) exhibits an exponential growth regime. At n = 20 bilayers deposition of PAH and MMT, the film reaches a considerable thickness of ∼5 μm with the alignment of MMT in the direction parallel to the substrate. Scanning Electron Microscopy (SEM) analysis of the cross-section and Atomic Force Microscopy (AFM) analysis display a regular and continuous morphology of the obtained films. Thermogravimetric analysis shows that the presence of (PAH–MMT)n films at 10 and 20 bilayers enhances the thermal stability of the polyamide substrate. Cone calorimetry evidences excellent reaction to fire of the material since peak of heat release rate (HRR) is decreased by more than 60% in the presence of 20 bilayers of PAH–MMT film in comparison with uncoated PA6. Continuous charred layer was observed during the combustion and the thickness of the coating at the end of the combustion test is twice higher than that of the initial thickness. The presence of this expanded charred layer at the surface acts as protective limiting heat and mass transfer.

Chromium stress in Brassica juncea L. cv. 'Pusa Jai Kissan' under hydroponic culture

In this study, the effect of different irrigation levels on oleuropein content of olive ( Olea europaea L. cv. Memecik) was researched in the Aegean Region during the crop season of 2007. Six different irrigation water levels of drip irrigation were tested using class A pan evaporation technique [I 0 (kpc:0), I 0.25 (kpc:0.25), I 0.50 (kpc:0.50), I 0.75 (kpc:0.75), I 1.00 (kpc:1.00) and I 1.25 (kpc:1.25)]. Oleuropein contents of olive leaves were detected by high performance liquid chromatography (HPLC). Olive leaves showed considerable contents of oleuropein (16.25 ± 0.25%) collected from waterless regime applied trees during summer period. In the same regime, contents of oleuropein were decreased depending upon the increasing irrigation regimes: 0.25 (10.28 ± 0.13%); 0.50 (2.19 ± 0.12%); 0.75 (1.43 ± 0.03%); 1.00 (0.09 ± 0.05%), although in winter period, contents of oleuropein were approximately stable as 0.55 ± 0.01% in waterless regime (rain-fed olives), equal in 0.25 (0.25 ± 0.04%) and 0.50 (0.25 ± 0.01%), in 0.75 (0.21 ± 0.01%), 1.00 (0.16 ± 0.02%) and (0.14 ± 0.03%) in 1.25 irrigation regimes. Contents of oleuropein was observed to be increased inversely proportional with increased irrigation regimes in autumn period. The oleuropein values were 1.21 ± 0.01% in waterless, 0.76 ± 0.01% in 0.25 irrigation, 0.45 ± 0.03% in 0.50 irrigation, 0.44 ± 0.03% in 0.75 irrigation, 0.33 ± 0.01% in 1.00 irrigation and 0.25 ± 0.02% in 1.25 irrigation regimes. No important increase or decrease between contents of oleuropein depending upon the gradually increased irrigation regimes was observe in spring period [in waterless regime (0.51 ± 0.05%), 0.25 irrigation (0.39 ± 0.04%); 0.50 irrigation (0.38 ± 0.14%); 0.75 irrigation (0.11 ± 0.01%); 1.00 irrigation (0.55 ± 0.04%); and 1.25 irrigation (0.79 ± 0.06%)]. Statistically important increases in oleuropein contents were in inverse proportion with the exponential irrigation regimes. Key words : Olea europaea L., olive leaves, oleuropein, irrigation, seasonal variation.

Collagen-Based Fibrillar Multilayer Films Cross-Linked by a Natural Agent

Surface functionalization plays an important role in the design of biomedical implants, especially when layer forming cells, such as endothelial or epithelial cells, are needed. In this study, we define a novel nanoscale surface coating composed of collagen/alginate polyelectrolyte multilayers and cross-linked for stability with genipin. This buildup follows an exponential growth regime versus the number of deposition cycles with a distinct nanofibrillar structure that is not damaged by the cross-linking step. Stability and cell compatibility of the cross-linked coatings were studied with human umbilical vein endothelial cells. The surface coating can be covered by a monolayer of vascular endothelial cells within 5 days. Genipin cross-linking renders the surface more suitable for cell attachment and proliferation compared to glutaraldehyde (more conventional cross-linker) cross-linked surfaces, where cell clumps in dispersed areas were observed. In summary, it is possible with the defined system to build fibrillar structures with a nanoscale control of film thickness, which would be useful for in vivo applications such as inner lining of lumens for vascular and tracheal implants.

Theoretical Study of High Repetition Rate Short Pulse Generation With Fiber Optical Parametric Amplification

In this paper, we study theoretically the generation of high repetition rate short pulses using fiber optical parametric amplification. We show that the pulse shape and duration depend on the signal location relatively to the pump frequency. We demonstrate that in order to get the shortest pulse width, the signal must be located at one of the extremities of the gain spectrum associated with the pump peak power. We derive the analytical expression of the pulse shape in this case and compare it to the exponential gain regime case. Using numerical simulations, we also analyze the impact of walk-off and pump phase modulation that is required to suppress Stimulated Brillouin Scattering and derive guidelines to design stable train of short and high repetition rate pulses.

Exponential wealth distribution : a new approach from functional iteration theory

Different approaches are possible in order to derive the exponential regime in statistical systems. Here, a new functional equation is proposed in an economic context to explain the wealth exponential distribution. Concretely, the new iteration [1] given by

Wave propagation in random granular chains

The influence of randomness on wave propagation in one-dimensional chains of spherical granular media is investigated. The interaction between the elastic spheres is modeled using the classical Hertzian contact law. Randomness is introduced in the discrete model using random distributions of particle mass, Young's modulus, or radius. Of particular interest in this study is the quantification of the attenuation in the amplitude of the impulse associated with various levels of randomness: two distinct regimes of decay are observed, characterized by an exponential or a power law, respectively. The responses are normalized to represent a vast array of material parameters and impact conditions. The virial theorem is applied to investigate the transfer from potential to kinetic energy components in the system for different levels of randomness. The level of attenuation in the two decay regimes is compared for the three different sources of randomness and it is found that randomness in radius leads to the maximum rate of decay in the exponential regime of wave propagation.

Fidelity of fermionic-atom number states subjected to tunneling decay

Atom-number states are a valuable resource for ultracold chemistry, atom interferometry and quantum information processing. Recent experiments have achieved their deterministic preparation in trapped few-fermion systems. We analyze the tunneling decay of these states, both in terms of the survival probability, and the non-escape probability, which can be extracted from measurements of the full counting statistics. At short times, the survival probability exhibits deviations from the exponential law. The decay is governed by the multi-particle Zeno time which exhibits a signature of quantum statistics and contact interactions. The subsequent exponential regime governs most of the dynamics, and we provide accurate analytical expressions for the associated decay rates. Both dynamical regimes are illustrated in a realistic model. Finally, a global picture of multi-particle quantum decay is presented.

Phase transitions in the first-passage time of scale-invariant correlated processes.

A key quantity describing the dynamics of complex systems is the first-passage time (FPT). The statistical properties of FPT depend on the specifics of the underlying system dynamics. We present a unified approach to account for the diversity of statistical behaviors of FPT observed in real-world systems. We find three distinct regimes, separated by two transition points, with fundamentally different behavior for FPT as a function of increasing strength of the correlations in the system dynamics: stretched exponential, power-law, and saturation regimes. In the saturation regime, the average length of FPT diverges proportionally to the system size, with important implications for understanding electronic delocalization in one-dimensional correlated-disordered systems.