Lambert W-function Research Articles

NMR based real-time enzyme kinetics on estimating the inhibitory effect of sucralose in the enzymatic conversion of sucrose

Sucralose, one of the popular non-caloric artificial sweeteners, has been known to influence the enzymatic conversion of sucrose to glucose and fructose by invertase. In continuing the use of real-time NMR experiments and reaction progress curve analysis to measure enzyme kinetics, here we investigate the role of sucralose as an inhibitor. NMR based kinetic experiments were performed as a function of the substrate concentration for a range of sucralose concentrations, and the results were analyzed by fitting the progress curve to the Lambert-W function. The Michaelis-Menten parameters were then used to estimate the inhibitory constant of sucralose. To estimate the extent of sucralose inhibition on the enzymatic production of glucose, control experiments were performed with lactose as the inhibitor under similar experimental conditions. The results show that sucralose is a much more potent inhibitor than lactose, inhibiting the enzymatic conversion at least seven times more.

A Comprehensive Physics-Based Current–Voltage SPICE Compact Model for 2-D-Material-Based Top-Contact Bottom-Gated Schottky-Barrier FETs

In this article, we report the development of a novel physics-based analytical model for explaining the current-voltage relationship in Schottky barrier (SB) 2-D-material field effect transistors (FETs). The model has at its core the calculation of the surface-potential (SP) which is accomplished by invoking 2-D density of states in conjunction with Fermi-Dirac (FD) distribution for electron and hole statistics. The explicit computation for the SP, carried out using the Lambert-W function together with Halley's method, is used to construct the SP-based band-diagram for realizing the transparency of the SBs. Thereafter, the ambipolar current is derived in terms of the electron and hole injection phenomena-the thermionic emission and Fowler-Nordheim tunneling mechanisms-at the SB contacts. Furthermore, drift-diffusion current is derived in terms of the SP and incorporated in the model to account for the scattering in the intrinsic 2-D channel. Finally, the Verilog-A model is validated against experimental I-V data reported in the literature for two different 2-D-material systems. This is the first demonstration of an explicit SP-based SPICE model for ambipolar SB-2-D-FETs that is simultaneously built on tunneling-emission and drift-diffusion formalisms.

The ANSDM Converters Dynamic Range Design Process

The results of analytic and simulating works proved that for nonstationary sources, the delta converters with adaptive sampling expose higher coding efficiency than the former proposals, based on uniform sampling methods. The knowledge of the sampling interval range and the algorithm of the Nonuniform Sampling Delta Modulation and Adaptive Nonuniform Sampling Delta Modulation allows finding the necessary number of the sampling intervals and their values that maximizes SNR. The total dynamic range of the ANSDM modulator is the product of the dynamic range both from sampling interval and step size adaptation. Due to the high complexity of the calculations, the ANSDMsoft program was developed to support computing. All computational works were carried out using the Maple environment. Maple allows to solve complex mathematical functions and display their results in a simple way. Most importantly, it supports the LambertW function, used in the computing of NSDM or ANSDM modulators parameters. Graphic illustrations of the NSDM and ANSDM modulator dynamic range as a function of the minimum and maximum sampling frequency are presented.

A Fast and Accurate Single-Diode Model for Photovoltaic Design

The precise extraction of the I-V curve of photovoltaic (PV) cells is necessary for designing an efficient PV system. To achieve this, this article examines different models to investigate the best fit for the I- V curve of a PV solar module. Those models are based on using different sets of equations and assumptions. New PV single-diode models are then proposed which consist of the Lambert W-function, iterative loop, and approximate equations. Furthermore, a substitution method is proposed to reduce the complexity that emerges when using the Newtown-Raphson method to solve a set of nonlinear equations. Those processes allow solving the complex nonlinear PV model in a simple way, thus making the proposed model fast, straightforward, and easy solution.

Modeling and parameters extraction of photovoltaic cell and modules using the genetic algorithms with lambert W-function as objective function

Modeling and parameters extraction of photovoltaic cell and modules using the genetic algorithms with lambert W-function as objective function

Influence of Different Surface Morphologies on the Performance of High-Voltage, Low-Resistance Diamond Schottky Diodes

Vertical diamond Schottky diodes with blocking voltages $V_{\text{BD}} > 2.4 \text{ kV}$ and on-resistances $R_{\text{On}} < 400 \text{ m}\Omega \text{cm}^{2}$ were fabricated on homoepitaxially grown diamond layers with different surface morphologies. The morphology (smooth as-grown, hillock-rich, polished) influences the Schottky barrier, the carrier transport properties, and consequently the device performance. The smooth as-grown sample exhibited a low reverse current density $J_{\text{Rev}} < 10^{-4} \text{ A}/\text{cm}^{2}$ for reverse voltages up to $2.2 \text{ kV}$. The hillock-rich sample blocked similar voltages with a slight increase in the reverse current density ($J_{\text{Rev}} < 10^{-3} \text{ A}/\text{cm}^{2}$). The calculated 1D-breakdown field, however, was reduced by $30 \text{ } \%$, indicating a field enhancement induced by the inhomogeneous surface. The polished sample demonstrated a similar breakdown voltage and reverse current density as the smooth as-grown sample, suggesting that a polished surface can be suitable for device fabrication. However, a statistical analysis of several diodes of each sample showed the importance of the substrate quality: A high density of defects both reduces the feasible device area and increases the reverse current density. In forward direction, the hillock-rich sample exhibited a secondary Schottky barrier, which could be fitted with a modified thermionic emission model employing the Lambert W-function. Both polished and smooth sample showed nearly ideal thermionic emission with ideality factors $1.08$ and $1.03$, respectively. Compared with literature, all three diodes exhibit an improved Baliga Figure of Merit for diamond Schottky diodes with $V_{\text{BD}} > 2 \text{ kV}$.

Distribution of extreme first passage times of diffusion.

Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However, the more relevant timescale in many biological systems is the time it takes the fastest searcher(s) out of many searchers to find a target, which is called an extreme FPT. In this paper, we apply extreme value theory to find a tractable approximation for the full probability distribution of extreme FPTs of diffusion. This approximation can be easily applied in many diverse scenarios, as it depends on only a few properties of the short time behavior of the survival probability of a single FPT. We find this distribution by proving that a careful rescaling of extreme FPTs converges in distribution as the number of searchers grows. This limiting distribution is a type of Gumbel distribution and involves the LambertW function. This analysis yields new explicit formulas for approximations of statistics of extreme FPTs (mean, variance, moments, etc.) which are highly accurate and are accompanied by rigorous error estimates.

Chemical, optical and photovoltaic properties of TiO2/reduced graphene oxide photoanodes sensitized with Roselle and N719 dyes for dye-sensitized solar cell application

PurposeThe purpose of this paper is to investigate the chemical, optical and photovoltaic properties of titanium dioxide/reduced graphene oxide (TiO2/rGO) photoanodes immersed in natural Roselle and synthetic (N719) dyes for dye-sensitized solar cell (DSSC) application.Design/methodology/approachTiO2 mixed with rGO were doctor-bladed on fluorine doped tin oxide (FTO) glass substrate. The chemical and optical properties of TiO2/rGO photoanodes immersed in Roselle and N719 dyes were characterized using Fourier-transformed infrared (FTIR) and ultraviolet–visible (UV–vis) spectroscopies, respectively. The DSSC’s photovoltaic performances were tested using Visiontec Solar I-V tester at standard illumination of AM1.5 and irradiance level of 100 mW/cm2.FindingsThe presence of anthocyanin dye from Roselle flower was detected at 604 nm and 718 nm. TiO2/rGO+Roselle dye sample revealed the smallest energy gap of 0.17 eV for ease of electron movement from valence band to conduction band. The TiO2/rGO-based DSSC fabricated with Roselle dye had a power conversion efficiency, ƞ of 0.743 per cent higher than TiO2/rGO photoanode sensitized with N719 dye (0.334 per cent). The obtained J-V curves were analyzed by a single-diode model of Lambert W-function and manual optimization to determine the internal electrical parameters of the DSSC. The average and uncertainty values of Jsc and ƞ were evaluated at different Rsh range of 1362 Ω to 32 k Ω.Research limitations/implicationsRs values were kept constant during optimization work.Originality/valueNew ideality factor of TiO2/rGO-based DSSC was re-determined around 0.9995.

Parasitic resistance calculation of PV module at various irradiance based on three condition Lambert-W

Serial and parallel parasitic resistances of the photovoltaic (PV) module are needed to determine the characteristics and performance of the module. Its values are constant for a long period operation. Characterization of PV modules using direct irradiation of sunlight is rather difficult to obtain constant radiation under a clear sky condition and the measurement should be taken in a short time period less than 5 minutes. In this work, Rs and Rsh values were determined by characterizing PV module at various levels of sunlight intensity and modeled after Lambert-W function. A Solarland SLP100S-12 monocrystalline 100Wp photovoltaic module was illuminated at different intensity 100%, 75%, 50%, and 25 % using filters covered the PV module surface. Based on the measured I-U curves, three important parameters are generated for the Lambert-W calculation: short-circuit current (Isc), open-circuit voltage (Uoc), and also the current-voltage at the Maximum Power Point (Imp, Ump). The calculated values were 0.63Q + 0.027 for Rs and 93.2Q + 0.588 for Rsh and relative constant for filter variation which are not influenced by the intensity of the sun.

Incremental Diversity Order for Characterization of FSO Communication Systems Over Lognormal Fading Channels

Free space optical (FSO) communication systems experience atmospheric turbulence-induced fading, which is typically modelled by lognormal distribution. Since the decreasing rate of error probability over lognormal fading channels does not converge to a finite value, the conventional definition of diversity order yields infinity and does not provide any insight into system design. In this letter, we propose the so-called incremental diversity order (IDO), which is defined as the incremental change in the decreasing rate of bit error rate (BER) on a log-log scale. As an example, we consider multiple-input multiple-output (MIMO) FSO system over lognormal turbulence channels. We derive a novel closed-form BER expression in terms of Lambert-W function and obtain IDO as a function of the number of laser sources, the number of photodetectors and the variance of the log-amplitude coefficient. We further present numerical results to validate the derived BER expression and associated IDO.

A unified model for vertical doped and polarized superjunction GaN devices

A unified model is proposed to characterize the breakdown voltage (BV) and specific on-resistance (Ron,sp) for vertical doped superjunction (d-SJ) and polarized superjunction (p-SJ) GaN power devices. This study is based on the recently published compensated-pillar superjunction (cp-SJ) structure. A two-dimensional model for the electric field is analytically formulated using the Green's function method. Numerical calculations and TCAD simulations demonstrate that, for a given pillar depth, the p-SJ device has a lower BV than the d-SJ device with a wide pillar width. However, when the pillar width is less than 200 nm, both devices demonstrate a maximum BV that is close to the intrinsic structure. The Ron,sp unified model for the cp-SJ device, taking into account the junction field-effect transistor (JFET) effect in the drift region, also demonstrates that the p-SJ device has a superior Ron,sp over the d-SJ device. Considering the recently published impact ionization coefficients, the BV of the p-SJ device is analytically modeled as a function of the pillar depth. Finally, by applying the Lambert W-function, an exact closed-form relationship between Ron,sp and BV is presented.

A Solution of Implicit Model of Series-Parallel Photovoltaic Arrays by Using Deterministic and Metaheuristic Global Optimization Algorithms

The implicit model of photovoltaic (PV) arrays in series-parallel (SP) configuration does not require the LambertW function, since it uses the single-diode model, to represent each submodule, and the implicit current-voltage relationship to construct systems of nonlinear equations that describe the electrical behavior of a PV generator. However, the implicit model does not analyze different solution methods to reduce computation time. This paper formulates the solution of the implicit model of SP arrays as an optimization problem with restrictions for all the variables, i.e., submodules voltages, blocking diode voltage, and strings currents. Such an optimization problem is solved by using two deterministic (Trust-Region Dogleg and Levenberg Marquard) and two metaheuristics (Weighted Differential Evolution and Symbiotic Organism Search) optimization algorithms to reproduce the current–voltage (I–V) curves of small, medium, and large generators operating under homogeneous and non-homogeneous conditions. The performance of all optimization algorithms is evaluated with simulations and experiments. Simulation results indicate that both deterministic optimization algorithms correctly reproduce I–V curves in all the cases; nevertheless, the two metaheuristic optimization methods only reproduce the I–V curves for small generators, but not for medium and large generators. Finally, experimental results confirm the simulation results for small arrays and validate the reference model used in the simulations.

Accurate modelling of power amplifier energy consumption for resource allocation in wireless networks

A new model for the power consumption of RF power amplifiers (PAs) in terms of the input power based on Lambert W-function is presented. In the derivation of the model, the knee voltage effect of the field effect transistors is taken into account. Accordingly, the model can capture the behaviour of the PA power consumption in saturation. The proposed model can be used for energy efficient resource allocation of the wireless systems considering the consumed power by the PAs.

On finite-size spiky strings in AdS3\xd7 S3\xd7 T4 with mixed fluxes

We discuss finite-size corrections to the spiky strings in AdS space which is dual to the long \U0001d4a9 = 4 SYM operators of the form Tr( {varDelta}_{+}^{J_1}{phi}_1{varDelta}_{+}^{J_2}{phi}_2dots {varDelta}_{+}^{J_n}{phi}_n ). We express the finite-size dispersion relation in terms of Lambert W-function. We further establish the finite-size scaling relation between energy and angular momentum of the spiky string in presence of mixed fluxes in terms of W-function. We comment on the solution in pure NS-NS background as well.

Localization of Mobile Submerged Sensors using Lambert-W Function and Cayley-Menger Determinant

This paper demonstrates a new mechanism to localize mobile submerged sensors using only a single beacon node. In range-based localization, fast and accurate distance measurement is vital in underwater wireless sensor networks (UWSN). The knowledge of exact coordinates of the sensors is as important as the actuated data in underwater wireless sensor networks. Mostly bouncing technique is used to determine the distance between the beacon and the sensors. Moreover, to determine the coordinates, trilateration and multilateration technique is used; where using multiple beacons (usually three or more) is the most common approach. Nevertheless, because of many factors, this method gives less accurate results in distance measurements, which finally leads to determine erroneous coordinates. As TDOA is very ponderous to achieve in underwater environment because of time synchronization; again, using AOA is extremely difficult and challenging; TOA is the most common approach and is widely employed. However, it still needs precise synchronization. So, to determine the distances between beacon and sensor nodes, we have used a method based on Lambert-W function in this study, which is an approach based on RSS, and it avoids any synchronization. Besides, coordinates of the mobile sensors are calculated using Cayley-Menger determinant. In this paper, the method is derived and the accuracy is verified by simulation results.

Geometric branching reproduction Markov processes

We present a model of a continuous-time Markov branching process with the infinitesimal generating function defined by the geometric probability distribution. It is proved that the solution of the backward Kolmogorov equation is expressed by the composition of special functions – Wright function in the subcritical case and Lambert-W function in the critical case. We found the explicit form of conditional limit distribution in the subcritical branching reproduction. In the critical case, the extinction probability and probability mass function are expressed as a series containing Bell polynomial, Stirling numbers, and Lah numbers.

Analytic structure of thermodynamic systems with repulsive interactions

Thermodynamic properties of systems with repulsive interactions, are considered in the grand canonical ensemble. The analytic structure of the excluded-volume model in the complex plane of the system chemical potential (fugacity) is elaborated, based on the fact that the pressure function can be given in terms of the Lambert W-function. Even though the excluded volume model has no phase transitions at real values of the chemical potential, it does exhibit a branch cut singularity in the complex plane, thus limiting the convergence range of the Taylor expansion in the chemical potential. Close similarities to analytic properties of the other models with repulsive interactions, such as a cluster expansion model, the mean-field model, and the ideal Fermi gas model, are pointed out. As an example, repulsive baryonic interactions in a hadron gas, with a focus on the fugacity/virial and Taylor expansion methods used in lattice QCD, are presented. The asymptotic behavior of the Fourier expansion coefficients in these various models suggests that the singular part of net baryonic density can to leading order be universally expressed in terms of polylogarithms.

A solvable tensor field theory

We solve the closed Schwinger-Dyson equation for the 2-point function of a tensor field theory with a quartic melonic interaction, in terms of Lambert's W-function, using a perturbative expansion and Lagrange-B\"{u}rmann resummation. Higher-point functions are then obtained recursively.

Distributed Multi-robot Circumnavigation with Dynamic Spacing and Time Delay

Circumnavigation is the process whereby a single agent or multiple agents rotate around a target while preserving a circular formation, which has promising potential in real-world applications such as entrapping a malicious target or escorting an important member. For the multi-robot circumnavigation problem, spacing (i.e., the angle differences) among robots plays an important role in forming a desirable circular formation. The spacing is usually assumed to be a unified constant in most of the studies. However, when robots have different or even time-varying kinematic capabilities, a fixed and equal spacing is probably not effective for accomplishing such task as preventing an enclosed target from fleeing, and thus dynamic spacing is naturally proposed and preferred. The variations of spacing are caused by the “weights” (termed utilities) of robots. This paper relaxes the condition of piecewise constant utilities and provides the ultimate bound and the input-to-state (ISS) stability conditions for the spacing error and its dynamics respectively. In addition, since time delay is ubiquitous in practical engineering systems while seldom considered in the current studies on circumnavigation, the maximum allowable time delay within which the circumnavigation remains stable is derived using both the frequency domain method and the Lambert-W function. Finally, the theoretical results are validated by a practical simulation system.

Correction: Brkić, D., and Praks, P. Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function. Mathematics 2019, 7, 34

Having in mind that in the title of the article contains term “Wright ω-function” and not its cognate “Lambert W-function”, the authors would like to change Equation (2) of [1] in order to contain both expressions, as follows [...]