arXiv subjects

Debabrata Biswas

Publications and source records attributed to Debabrata Biswas.

At least 37 records · Page 2Linked to original sources

arXiv2019

Verification of shielding effect predictions for large area field emitters

A recent analytical model for large area field emitters, based on the line charge model (LCM), provides a simple approximate formula for the field enhancement on hemi-ellipsoidal emitter tips in terms of the ratio of emitter height and pairwise distance between neighboring emitters. The formula, verified against the exact solution of the linear LCM, was found to be adequate provided the mean separation between emitters is larger than half the emitter height. In this paper, we subject the analytical predictions to a more stringent test by simulating (i) an infinite regular array and (ii) an isolated cluster of 10 random emitters, using the finite element software COMSOL. In case of the array, the error in apex field enhancement factor (AFEF) is found to be less than $0.25\%$ for an infinite array when the lattice constant $c \geq 1.5h$, increasing to $2.9\%$ for $c = h$ and $8.1\%$ for $c = 0.75h$. For an isolated random cluster of 10 emitters, the error in large AFEF values is found to be small. Thus, the error in net emitted current is small for a random cluster compared to a regular infinite array with the same (mean) spacing. The line charge model thus provides a reasonable analytical tool for optimizing a large area field emitter.

physics.app-ph↗

arXiv2019

The anode proximity effect for generic smooth field emitters

The proximity of the anode to a curved field electron emitter alters the electric field at the apex and its neighbourhood. A formula for the apex field enhancement factor, $γ_a(D)$, for generic smooth emitters is derived using the line charge model when the anode is at a distance $D$ from the cathode plane. The resulting approximately modular form is such that the anode proximity contribution can be calculated separately (using geometric quantities such as the anode-cathode distance $D$, the emitter height $h$ and the emitter apex radius of curvature $R_a$) and plugged into the expression for $γ_a(\infty)$. It is also shown that the variation of the enhancement factor on the surface of the emitter close to the apex is unaffected by the presence of the anode and continues to obey the generalized cosine law. These results are verified numerically for various generic emitter shapes using COMSOL Multiphysics. Finally, the theory is applied to explain experimental observations on the scaling behavior of the $I-V$ field emission curve.

physics.app-ph↗

arXiv2018

Networks of coupled oscillators: from phase to amplitude chimeras

We show that amplitude-mediated phase chimeras and amplitude chimeras can occur in the same network of nonlocally coupled identical oscillators. These are two different partial synchronization patterns, where spatially coherent domains coexist with incoherent domains and coherence/incoherence refer to both amplitude and phase or only the amplitude of the oscillators, respectively. By changing the coupling strength the two types of chimera patterns can be induced. We find numerically that the amplitude chimeras are not short-living transients but can have a long lifetime. Also, we observe variants of the amplitude chimeras with quasiperiodic temporal oscillations. We provide a qualitative explanation of the observed phenomena in the light of symmetry breaking bifurcation scenarios. We believe that this study will shed light on the connection between two disparate chimera states having different symmetry-breaking properties.

nlin.AO↗

arXiv2018

The cosine law of field enhancement factor variation: generic emitter shapes

The cosine law of field enhancement factor variation was recently derived for a hemi-ellipsoidal emitter and numerically established for other smooth emitter shapes (Biswas et al, Ultramicroscopy, 185, 1 (2018)). An analytical derivation is provided here for general smooth vertical emitter shapes aligned in the direction of the asymptotic electrostatic field. The law is found to hold in the neighbourhood of the emitter apex from where field emisson pre-dominantly occurs.

physics.app-ph↗

arXiv2018

Curvature correction to the field emission current

The curvature of field emitter tips leads to an altered tunneling potential that assumes significance when the radius of curvature is small. We provide here an analytical curvature-corrected formula for the field emission current from smooth vertically aligned emitter tips and test its applicability across a range of apex radius, $R_a$, and local electric field, $E_a$. It is found to give excellent results for $R_a > 10$nm with errors generally less than $10\%$. Surprisingly, for the uncorrected potential, we find the errors to be high even at $R_a = 100$nm ($ > 35\%$ at $E_a = 3$V/nm) and conclude that curvature correction is essential for apex radius less than a micron.

physics.app-ph↗

arXiv2018

Shielding effects in random large area field emitters, the field enhancement factor distribution and current calculation

A finite-size uniform random distribution of vertically aligned field emitters on a planar surface is studied under the assumption that the asymptotic field is uniform and parallel to the emitter axis. A formula for field enhancement factor is first derived for a 2-emitter system and this is then generalized for $N$-emitters placed arbitrarily (line, array or random). It is found that geometric effects dominate the shielding of field lines. The distribution of field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area field emitter.

physics.app-ph↗

arXiv2018

Transition from homogeneous to inhomogeneous limit cycles: Effect of local filtering in coupled oscillators

We report an interesting symmetry-breaking transition in coupled identical oscillators, namely the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the Turing-type symmetry-breaking transition from amplitude death (i.e., stable homogeneous steady state) to oscillation death (i.e., stable inhomogeneous steady state). This novel transition occurs in the parametric zone of occurrence of rhythmogenesis and oscillation death as a consequence of the presence of local filtering in the coupling path. We consider paradigmatic oscillators, such as Stuart-Landau and van der Pol oscillators under mean-field coupling with low-pass or all-pass filtered self-feedback and through a rigorous bifurcation analysis we explore the genesis of this transition. Further, we experimentally demonstrate the observed transition, which establishes its robustness in the presence of parameter fluctuations and noise.

nlin.CD↗

arXiv2018

Field-emission from parabolic tips: current distributions, the net current and effective emission area

Field emission from nano-structured emitters primarily takes place from the tips. Using recent results on the variation of enhancement factor around the apex (Biswas et al, Ultramicroscopy 185, 1-4 (2018)), analytical expressions for surface distribution of net emitted electrons as well as the total and normal energy distributions are derived in terms of the apex radius $R_a$ and the local electric field at the apex $E_a$. Formulae for the net emitted current and effective emission area in terms of these quantities are also obtained.

physics.app-ph↗

arXiv2018

A universal formula for the field enhancement factor

The field enhancement factor (FEF) is an important quantity in field emission calculations since the tunneling electron current depends very sensitively on its magnitude. The exact dependence of FEF on the emitter height $h$, the radius of curvature at the apex $R_a$, as well as the shape of the emitter base is still largely unknown. In this work, a universal formula for the field enhancement factor is derived. It depends on the ratio $h/R_a$ and has the form $γ_a = (2h/R_a)/[α_1 \log(4h/R_a) - α_2 ]$ where $α_1$, $α_2$ depend on the charge distribution on the emitter. Numerical results show that a simpler form $γ_a = (2h/R_a)/[\log(4h/R_a) - α]$ is equally valid with $α$ depending on the class of emitter and indicative of the shielding by the emitter-base. For the hyperboloid, conical and ellipsoid emitters, the value of $α$ is $0, 0.88$ and $2$ while for the cylindrical base where shielding is minimum, $α\simeq 2.6$.

physics.app-ph↗

arXiv2017

The tunneling potential for field emission from nanotips

In the quasi-planar approximation of field emission, the potential energy due to an external electrostatic field $E_0$ is expressed as $-e γE_0 Δs$ where $Δs$ is the perpendicular distance from the emission site and $γ$ is the local field enhancement factor on the surface of the emitter. We show that for curved emitter tips, the current density can be accurately computed if terms involving $(Δs/R_2)^2$ and $(Δs/R_2)^3$ are incorporated in the potential where $R_2$ is the second (smaller) principle radius of curvature. The result is established analytically for the hemiellipsoid and hyperboloid emitters and it is found that for sharply curved emitters, the expansion coefficients are equal and coincide with that of a sphere. The expansion seems to be applicable to generic emitters as demonstrated numerically for an emitter with a conical base and quadratic tip. The correction terms in the potential are adequate for $R_a \gtrapprox 2$ nm for local field strengths of $5$ V/nm or higher. The result can also be used for nano-tipped emitter arrays or even a randomly placed bunch of sharp emitters.

cond-mat.mes-hall↗

arXiv2017

Control of birhythmicity: A self-feedback approach

Birhythmicity occurs in many natural and artificial systems. In this paper we propose a self-feedback scheme to control birhythmicity. To establish the efficacy and generality of the proposed control scheme, we apply it on three birhythmic oscillators from diverse fields of natural science, namely, an energy harvesting system, the p53-Mdm2 network for protein genesis (the OAK model) and a glycolysis model (modified Decroly-Goldbeter model). Using the harmonic decomposition technique and energy balance method we derive the analytical conditions for the control of birhythmicity. A detailed numerical bifurcation analysis in the parameter space establishes that the control scheme is capable of eliminating birhythmicity and it can also induce transitions between different forms of bistability. As the proposed control scheme is quite general, it can be applied for control of several real systems, particularly in biochemical and engineering systems.

nlin.AO↗

arXiv2017

Variation of field enhancement factor near the emitter tip

The field enhancement factor at the emitter tip and its variation in a close neighbourhood determines the emitter current in a Fowler-Nordheim like formulation. For an axially symmetric emitter with a smooth tip, it is shown that the variation can be accounted by a $\cos{\tildeθ}$ factor in appropriately defined normalized co-ordinates. This is shown analytically for a hemi-ellipsoidal emitter and confirmed numerically for other emitter shapes with locally quadratic tips.

physics.app-ph↗

arXiv2016

Control of birhythmicity through conjugate self-feedback: Theory and experiment

Birhythmicity arises in several physical, biological and chemical systems. Although, many control schemes are proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis and experimental demonstrations we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes.

nlin.CD↗

arXiv2015

Boundary conditions for the solution of the 3-dimensional Poisson equation in open metallic enclosures

Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations such as High Power Microwave (HPM) or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary condition (ABC) is best suited for large aspect ratios while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.

physics.comp-ph↗

arXiv2014

Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion

We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled {\it intrinsic time-delayed} hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of {\it intrinsic time-delays} associated with the individual systems, and has no analogue in non-delayed systems or coupled oscillators with {\it coupling time-delay}. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii--Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.

nlin.CD↗

arXiv2014

Improved transfer matrix methods for calculating quantum transmission-coefficient

Methods for calculating the transmission coefficient are proposed, all of which arise from improved non-reflecting WKB boundary conditions at the edge of the computational domain in 1-dimensional geometries. In the first, the Schrödinger equation is solved numerically while the second is a transfer matrix (TM) algorithm where the potential is approximated by steps, but with the first and last matrix modified to reflect the new boundary condition. Both methods give excellent results with first order WKB boundary conditions. The third uses the transfer matrix method with third order WKB boundary conditions. For the the parabolic potential, the average error for the modified third order TM method reduces by factor of 4100 over the unmodified TM method.

quant-ph↗

arXiv2014

Calculating field emission currents in nanodiodes - a multi-group formalism with space charge and exchange-correlation effects

Inclusion of electron-electron interaction is essential in nano-diodes to understand the underlying physical phenomenon and tailor devices accordingly. However, both space charge and exchange-correlation interactions involve electrons at different energies and hence a self-consistent multi-energy-group solution of the Schr\{o}dinger-Poisson system is required. It is shown here that the existence of a limiting density-dependent potential at low applied voltages allows calculation of the field emission current. Despite additional interactions, a Fowler-Nordheim behaviour is observed. It is also found that the exchange-correlation potential dominates at these voltages in nanogaps and possibly leads to a higher turn-on voltage.

cond-mat.mes-hall↗

arXiv2013

The Child-Langmuir law in the quantum domain

It is shown using dimensional analysis that the maximum current density J_{QCL} transported on application of a voltage V_g across a gap of size D follows the relation J_{QCL} ~ \hbar^{3 - 2α} V_g^α/D^{5 - 2α}. The classical Child-Langmuir result is recovered at α= 3/2 on demanding that the scaling law be independent of \hbar. For a nanogap in the deep quantum regime, additional inputs in the form of appropriate boundary conditions and the behaviour of the exchange-correlation potential show that α= 5/14. This is verified numerically for several nanogaps. It is also argued that in this regime, the limiting mechanism is quantum reflection from a downhill potential due to a sharp change in slope seen by the electron on emerging through the barrier.

cond-mat.mes-hall↗