A novel fitted mesh scheme involving Caputo–Fabrizio approach for singularly perturbed fractional-order differential equations with large negative shift

This review paper contains computational methods or solution methodologies for singularly perturbed differential difference equations with negative and/or positive shifts in a spatial variable. This survey limits its coverage to singular perturbation equations arising in the modeling of neuronal activity and the methods developed by numerous researchers between 2012 and 2022. The review covered singularly perturbed ordinary delay differential equations with small or large negative shift(s), singularly perturbed ordinary differential–differential equations with mixed shift(s), singularly perturbed delay partial differential equations with small or large negative shift(s) and singularly perturbed partial differential–difference equations of the mixed type. The main aim of this review is to find out what numerical and asymptotic methods were developed in the last ten years to solve such problems. Further, it aims to stimulate researchers to develop new robust methods for solving families of the problems under consideration.

Large tunable negative lateral shift from graphene-based hyperbolic metamaterials backed by a dielectric

In this study, we focus on the formulation and analysis of an exponentially fitted numerical scheme by decomposing the domain into subdomains to solve singularly perturbed differential equations with large negative shift. The solution of problem exhibits twin boundary layers due to the presence of the perturbation parameter and strong interior layer due to the large negative shift. The original domain is divided into six subdomains, such as two boundary layer regions, two interior (interfacing) layer regions, and two regular regions. Constructing an exponentially fitted numerical scheme on each boundary and interior layer subdomains and combining with the solutions on the regular subdomains, we obtain a second order ε‐uniformly convergent numerical scheme. To demonstrate the theoretical results, numerical examples are provided and analyzed.

I examined negative shifts in past self perceptions after a romantic breakup (i.e., toward thinking one's pre-breakup self was not as happy and not as positive of a version of themself as they thought at the time) as a means of preserving post-breakup well-being. I recruited 184 people who were in romantic relationships to complete satisfaction and self-related measures twice, four months apart (retrospectively at Time 2). Those who experienced a breakup between ratings indicated larger negative shifts in past self perceptions than those whose relationships remained intact and larger shifts were associated with greater post-breakup well-being. Secondary analyses suggested that these shifts may improve well-being in part by helping one disentangle their ex-partner from their self-concept. The results were inconclusive (due to methodological limitations) regarding whether they also do so by ameliorating emotional distress. Implications, limitations, and suggestions for future research are discussed.

An optimal fitted numerical scheme for solving singularly perturbed parabolic problems with large negative shift and integral boundary condition

In this paper a stabilized central difference method is presented for the boundary value problem of singularly perturbed differential equations with a large negative shift. The central difference approximations for the derivatives are modified by re-approximating the error terms, leading to a stabilizing effect. The method is found to be second order convergent. Several numerical examples are solved to demonstrate the efficiency of the method.

Both large positive and negative lateral shifts were observed for the reflected light beam on a symmetrical metal-cladding waveguide. The positive and negative shifts approach about 480 and 180 microm, respectively, which to our knowledge are the largest experimental results ever reported. The experiment also proves that the positive or the negative shift depends on sign of the difference between the intrinsic and radiative damping.

Accelerated parameter-uniform numerical method for singularly perturbed parabolic convection-diffusion problems with a large negative shift and integral boundary condition

A large negative or positive lateral shift of the beam reflected from a left-handed prism coated with a weakly absorbing dielectric film is investigated theoretically. It is shown that the large lateral shift can be negative as well as positive due to the formation of the unusual guided modes in the weakly absorbing film near the resonant condition, which acts the same effect as the surface wave. This unusual guided wave can travel a longer distance than the surface wave. These giant negative and positive lateral shifts are almost fifty times larger than that from the lossless structure [Wang in Appl. Phys. Lett. 87:221102, 2005]. The sign of this large lateral shift could be controlled easily by adjusting the parameters of the present structure.

Large positive and negative lateral shift in prism-waveguide system with left-handed material of weak absorption

Fine grain growth of nickel electrodeposit: effect of applied magnetic field during deposition

A large negative and positive lateral beam shift is presented in the midinfrared region based on the penetration enhancement effect of the ultrahigh order modes in the metal-cladding waveguide. The characteristics of the lateral beam shift have been discussed in theory, and the performance of the ultrahigh order modes is confirmed in an experiment at 5.4µm. The negative and positive lateral shift depends on the derivative of the imaginary part of the propagation constant.

A large negative lateral shift of a light beam reflected from the so-called Kretschmann–Raether configuration containing left-handed material is predicted due to the formation of the unusual standing wave. An analytical resonant condition is given when there is a large negative lateral shift.

The analytical expression for the complex amplitude of light reflected from a wedge-shaped thin film is derived. For plane wave incidence, a simple ray tracing approach is used to calculate Goos-Hanchen (GH) shifts; and for non-plane wave incidence, for example, a Gaussian beam, the angular spectrum approach of plane wave is used in simulation. The two approaches predict that a wedge-shaped thin film can produce large negative longitudinal GH shifts. Although the reflectivity is small near the condition of resonance, the large negative GH shifts can be more easily detected in comparison with the shift from a plane-parallel film in vacuum.

Introduction Previous studies (1-3) in this laboratory have involved electrochemical studies of the interaction of Zn(II) ions with L-cysteine in an attempt to more fully characterize the formation of “zinc finger” proteins (4). This interaction can be investigated both by the effect of Zn(II) addition upon the oxidation of the thiol group of L-cysteine, and by the effect of L-cysteine addition upon the reduction potential of Zn(II). In particular, the addition of L-cysteine to ZnSO4 dissolved in pH 7.4 MOPS buffer results in a large negative shift in the reduction potential for Zn(II) ions (2). This behavior is clear evidence for the formation of a Zn2+ : Cysteine complex. In the present study, we have extended this work to the interaction of bismuth(III) with L-cysteine and with glutathione, prompted by the significance of such interactions in human biochemistry (5-7). Experimental L-Cysteine, L-glutathione, and MOPS (3-(N-morpholino)propanesulfonic acid) were obtained from Sigma-Aldrich Corporation, and bismuth(III) nitrate was obtained from Baker. Electrochemical experiments were carried out under nitrogen using a Gamry Instruments Interface 1000 potentiostat and Gamry Framework software. Working electrodes were obtained from BASi (Glassy carbon, 3.0 mm diameter; platinum 1.6 mm) and eDAQ (gold, 1.0 mm diameter). Potentials were measured with respect to a silver/silver chloride saturated KCl reference electrode (BASi). Results and Discussion It has been found that Bi(NO3)3 is only slightly soluble in pH 7.4 MOPS buffer due to probable formation of hydroxyl complexes (8). It is, however, possible to observe small currents for deposition and subsequent stripping of bismuth at gold and glassy carbon in this solution. Upon addition of 1:1 bismuth(III):L-cysteine, the solution appearance changed from cloudy to clear, and voltammetric currents increased substantially, indicating a strong interaction between bismuth(III) and L-cysteine. In addition, a negative voltammetric shift for the bismuth reduction potential was observed, as was the case for the zinc(II):L-cysteine interaction (2). Further additions of L-cysteine were found to produce additional negative shifts for bismuth(III) reduction. Similar behavior for L-glutathione was observed. MALDI-TOF spectra for the 1:2 Bi(III):L-glutathione and similar complexes in aqueous solutions have been reported (9) and provide supporting evidence for the electrochemical results in the present study. A similar spectrum for the 1:2 Bi(III):L-glutathione complex in pH 7.4 MOPS buffer has been obtained in the present work. References G. T. Cheek and M. A. Worosz, ECS Transactions, 2016, 72(27), 1-8.M. Y. Doan, M. A. Worosz, and G.T. Cheek, ECS Transactions, 2017, 77(11), 1537-1544.G. T. Cheek, M. A. Worosz, M. Y. Doan, and D. C. Clark, ECS Transactions 2017, 80 ( 10 ), 1159-1166. C.K. Mathews, K.E. Van Holde, D.R. Appling, and S. J. Anthony-Cahill, Biochemistry, 4th Edition, Pearson Canada, Toronto, 2013.G. G. Briand and N. Burford, Chem. Rev., 1999, 99, 2601-2657.R. Ge and H. Sun, Acc. Chem. Res., 2007, 40, 267-274.Y. Hong, Y.-T Lai, G. C-F Chan, and H. Sun, PNAS, 2015, 112(11), 3211–3216. J. Kragten, L. G. Decnop-Weever, and P. Gründler, Talanta, 1993, 40(4), 485-490.N. Burford, M. D. Eelman, D. E. Mahony, and M. Morash, Chem. Commun., 2003, 146–147.