arXiv subjects

Debabrata Biswas

Publications and source records attributed to Debabrata Biswas.

At least 19 recordsLinked to original sources

arXiv2026

Emergence of minimal chimera in uncoupled oscillators under common frequency-modulated driving: Theory and experiment

We report the experimental realization of minimal chimera states in a system of three uncoupled oscillators driven solely by frequency-modulated forcing. Unlike conventional scenarios where chimera states emerge due to interactions among oscillators, here the coexistence of coherent and incoherent dynamics arises entirely from a common external modulation of a system parameter. By tuning the modulation amplitude and frequency, the system exhibits transitions between global synchronization, global incoherence, and minimal chimera states. The stability of these regimes is quantified using the maximal Lyapunov exponent, while a synchronization order parameter is employed to characterize the degree of coherence. A systematic exploration of the parameter space reveals well-defined regions associated with distinct dynamical behaviors. To provide analytical understanding, we employ a phase-reduction approach and derive the corresponding phase dynamics, which elucidate the mechanisms underlying phase locking and desynchronization. The robustness of the proposed mechanism is further demonstrated in a time-delayed chaotic system. Finally, experimental results obtained from an electronic circuit realization confirm the emergence of minimal chimera states under frequency-modulated driving. These findings establish external modulation as a viable route to chimera formation without coupling, offering a new perspective on collective dynamics in driven nonlinear systems.

nlin.CD↗

arXiv2025

Competitive binding of Activator-Repressor in Stochastic Gene Expression

Regulation of gene expression is the consequence of interactions between the promoter of the gene and the transcription factors (TFs). In this paper, we explore the features of a genetic network where the TFs (activators and repressors) bind the promoter in a competitive way. We develop an analytical theory that offers detailed reaction kinetics of the competitive activator-repressor system which could be the powerful tools for extensive study and analysis of the genetic circuit in future research. Moreover, the theoretical approach helps us to find a most probable set of parameter values which was unavailable in experiments. We study the noisy behaviour of the circuit and compare the profile with the network where the activator and repressor bind the promoter non-competitively. We further notice that, due to the effect of transcriptional reinitiation in the presence of the activator and repressor molecules, there exits some anomalous characteristic features in the mean expressions and noise profiles. We find that, in presence of the reinitiation the noise in transcriptional level remains low while it is higher in translational level than the noise when the reinitiation is absent. In addition, it is possible to reduce the noise further below the Poissonian level in competitive circuit than the non-competitive one with the help of some noise reducing parameters.

q-bio.MN↗

arXiv2023

Fast and accurate determination of the curvature-corrected field emission current

The curvature-corrected field emission current density, obtained by linearizing at or below the Fermi energy, is investigated. Two special cases, corresponding to the peak of the normal energy distribution and the mean normal energy, are considered. It is found that the current density evaluated using the mean normal energy results in errors in the net emission current below 3% for apex radius of curvature, $R_a \geq 5$nm and for apex fields $E_a$ in the range $3-10$ V/nm for an emitter having work-function $ϕ= 4.5$eV. An analytical expression for the net field emission current is also obtained for locally parabolic tips using the generalized cosine law. The errors are found to be below 6% for $R_a \geq 5$nm over an identical range of apex field strengths. The benchmark current is obtained by numerically integrating the current density over the emitter surface and the current density itself computed by integrating over the energy states using the exact Gamow factor and the Kemble form for the WKB transmission coefficient. The analytical expression results in a remarkable speed-up in the computation of the net emission current and is especially useful for large area field emitters having tens of thousands of emission sites.

physics.app-ph↗

arXiv2022

Semi-analytical theory of emission and transport in a LAFE-based diode

A large area field emitter (LAFE) typically consists of several thousands of nanoscale emitting tips. These are difficult to simulate using purely numerical methods based on finite/boundary element or finite difference methods. We show here that a semi-analytically obtained electrostatic field allows tracking of field emitted electrons of a LAFE fairly accurately using the knowledge of only the LAFE geometry. Using a single and a 9-emitter configuration, the beam parameters calculated using this method are compared with the results of tracking using fields generated by COMSOL. The net emission current, energy conservation and the transverse trace-emittance are found to be reproduced with reasonable accuracy.

physics.app-ph↗

arXiv2022

Gamow factors and current densities in cold field emission theory: a comparative study

The factors that contribute to the accuracy of the cold field emission current within the contemporary frameworks are investigated. It is found that so long as the net current is evaluated using an expression for the local current density obtained by linearizing the Gamow factor, the primary source of error is the choice of the energy at which the Taylor expansion is done, but not as much on the choice of the method used to arrive at the approximate Gamow factor. A suitable choice of linearization energy and the implementation of the Kemble correction, allows the restriction of errors to below 3\% across a wide range of local fields.

physics.app-ph↗

arXiv2022

Effects of time-varying habitat connectivity on metacommunity persistence

Network structure or connectivity pattern is critical in determining collective dynamics among interacting species in ecosystems. Conventional research on species persistence in spatial populations has focused on static network structure, though most real network structures change in time, forming time-varying networks. This raises the question, in metacommunities, how does the pattern of synchrony vary with temporal evolution in the network structure. The synchronous dynamics among species are known to reduce metacommunity persistence. Here, we consider a time-varying metacommunity small-world network consisting of a chaotic three-species food chain oscillator in each patch/node. The rate of change in the network connectivity is determined by the natural frequency or its subharmonics of the constituent oscillator to allow sufficient time for the evolution of species in between successive rewirings. We find that over a range of coupling strengths and rewiring periods, even higher rewiring probabilities drive a network from asynchrony towards synchrony. Moreover, in networks with a small rewiring period, an increase in average degree (more connected networks) pushes the asynchronous dynamics to synchrony. On the contrary, in networks with a low average degree, a higher rewiring period drives the synchronous dynamics to asynchrony resulting in increased species persistence. Our results also follow the calculation of synchronization time and robust across other ecosystem models. Overall, our study opens the possibility of developing temporal connectivity strategies to increase species persistence in ecological networks.

q-bio.PE↗

arXiv2022

Interpreting the empirical field emission equation for large area field emitters

Both single emitters and large area field emitters (LAFE) are generally characterized using the slope and intercept of a Murphy-Good (or Fowler-Nordheim) plot which are used to extract the field enhancement factor and the emission area. Using a shielding model that has been developed recently for a LAFE, the validity of the underlying assumption is investigated. It is found that in case of a LAFE, the slope has contributions from the enhancement factor {\it as well as} the rate at which the effective number of super-emitters changes with the applied field. As a consequence, the emission area is related to both the slope and the intercept in a LAFE. When the mean spacing in a LAFE is much larger than the height of emitter, the usual interpretation of the slope and intercept are recovered.

physics.app-ph↗

arXiv2021

Predicting space-charge affected field emission current from curved tips

Field emission studies incorporating the effect of space charge reveal that for planar emitters, the steady-state field $E_P$, after initial transients, settles down to a value lower than the vacuum field $E_L$. The ratio $\vartheta = E_P/E_L$ is a measure of the severity of space charge effect with $\vartheta = 0$ being most severe and $\vartheta \simeq 1$ denoting the lack of significant effect. While, $E_L$ can be determined from a single numerical evaluation of the Laplace equation, $E_P$ is largely an unknown quantity whose value can be approximately found using physical models or can be determined `exactly' by particle-in-cell or molecular dynamics codes. We propose here a simple model that applies to planar as well as curved emitters based on an application of Gauss's law. The model is then refined using simple approximations for the magnitude of the anode field and the spread of the beam when it reaches the anode. The predictions are compared with existing molecular dynamics results for the planar case and particle-in-cell simulation results using PASUPAT for curved emitters. In both cases, the agreement is good. The method may also be applied to large area field emitters if the individual enhancement factors are known, for instance, using the hybrid model (D.Biswas, J. Vac. Sci. Technol. B 38, 063201 (2020)).

physics.acc-ph↗

arXiv2021

Approximate universality in the electric field variation on a field-emitter tip in the presence of space charge

The electric field at the surface of a curved emitter is necessary to calculate the field emission current. For smooth parabolic emitting tips where space charge is negligible, variation of the electric field at the surface is known to follow the generalized cosine law. Here we investigate the validity of the cosine law in the regime where space charge due to emitted electrons is important. Particle-in-Cell (PIC) simulations with an emission algorithm based on the cosine law is employed for this study. It is shown that if $E_P$ and $E_L$ be the field at the apex of tip with and without space charge respectively, then for $\vartheta=E_P/E_L \geq 0.9$, the average relative deviation of the electric field from the cosine law is less than $3\%$ over the endcap. Thus, an emission scheme based on cosine law may be used in PIC simulations of field emission of electrons from curved emitter tips in the weak space charge regime. The relation between $\vartheta$ and normalized current $ζ$ for curved emitters in this regime is also investigated. A linear relation, $\vartheta=1 - δζ$ (where $δ$ is a constant), similar to that obtained theoretically for flat emitting surfaces is observed but the value of $δ$ indicates that the extension of the theory for curved emitters may require incorporation of the field enhancement factor.

physics.app-ph↗

arXiv2021

Scaling in large area field emitters and the emission dimension

Electrostatic shielding is an important consideration for large area field emitters (LAFE) and results in a distribution of field enhancement factors even when the constituent emitters are identical. Ideally, the mean and variance together with the nature of the distribution should characterize a LAFE. In practice however, it is generally characterized by an effective field enhancement factor obtained from a linear fit to a Fowler-Nordheim plot of the $\text{I V}$ data. An alternate characterization is proposed here based on the observation that for a dense packing of emitters, shielding is large and LAFE emission occurs largely from the periphery, while well separated emitter tips show a more uniform or 2-dimensional emission. This observation naturally leads to the question of the existence of an emission-dimension, $D_e$ for characterizing LAFEs. We show here that the number of patches of size $L_P$ in the ON-state (above average emission) scales as $N(L_P) \sim L_P^{-D_e}$ in a given LAFE. The exponent $D_e$ is found to depend on the applied field (or voltage) and approaches $D_e = 2$ asymptotically.

physics.app-ph↗

arXiv2021

Approximate universality in the tunneling potential for curved field emitters -- a line charge model approach

Field emission tips with apex radius of curvature below 100nm are not adequately described by the standard theoretical models based on the Fowler-Nordheim and Murphy-Good formalisms. This is due to the breakdown of the `constant electric field' assumption within the tunneling region leading to substantial errors in current predictions. A uniformly applicable curvature-corrected field emission theory requires that the tunneling potential be approximately universal irrespective of the emitter shape. Using the line charge model, it is established analytically that smooth generic emitter tips approximately follow this universal trend when the anode is far away. This is verified using COMSOL for various emitter shapes including the locally non-parabolic `hemisphere on a cylindrical post'. It is also found numerically that the curvature-corrected tunneling potential provides an adequate approximation when the anode is in close proximity as well as in the presence of other emitters.

physics.app-ph↗

arXiv2021

Higher order curvature corrections to the field emission current density

A simple expression for the Gamow factor is obtained using a second order curvature corrected tunneling potential. Our results show that it approximates accurately the `exact-WKB' transmission coefficient obtained by numerically integrating over the tunneling region to obtain the Gamow factor. The average difference in current density using the respective transmission coefficients is about $1.5 \%$, across a range of work-functions $ϕ\in [3-5.5]$eV, Fermi energy ${\cal{E}}_F$ in [5-10]eV, local electric fields $E_l$ in[3-9]eV and radius of curvature $R \geq 5$nm). An easy-to-use correction factor $λ_P$ is also provided to approximately map the `exact-WKB' current density to the `exact' current density in terms of ${\cal{E}}_F/ϕ$. The average error on using $λ_P$ is found to be around $3.5\%$. This is a vast improvement over the average error of $15\%$ when $λ_P = 1$. Finally, an analytical expression for the curvature-corrected current density is obtained using the Gamow factor. It is found to compare well with the `exact-WKB' current density even at small values of local electric field and radius of curvature.

physics.app-ph↗

arXiv2020

Simulating multiscale gated field emitters -- a hybrid approach

Multi-stage cathodes are promising candidates for field emission due to the multiplicative effect in local field predicted by the Schottky conjecture and its recent corrected counterpart [J. Vac. Sci. Technol. B 38, 023208 (2020)]. Due to the large variation in length scales even in a 2-stage compound structure consisting of a macroscopic base and a microscopic protrusion, the simulation methodology of a gated field emitting compound diode needs to be revisited. As part of this strategy, the authors investigate the variation of local field on the surface of a compound emitter near its apex and find that the generalized cosine law continues to hold locally near the tip of a multi-scale gated cathode. This is used to emit charges with appropriate distributions in position and velocity components with a knowledge of only the electric field at the apex. The distributions are consistent with contemporary free-electron field emission model and follow from the joint distribution of launch angle, total energy, and normal energy. For a compound geometry with local field enhancement by a factor of around 1000, a hybrid model is used where the vacuum field calculated using COMSOL is imported into the Particle-In-Cell code PASUPAT where the emission module is implemented. Space charge effects are incorporated in a multi-scale adaptation of PASUPAT using a truncated geometry with `open electrostatic boundary' condition. The space charge field, combined with the vacuum field, is used for particle-emission and tracking.

physics.app-ph↗

arXiv2020

Quantum manifestations of homogeneous and inhomogeneous oscillation suppression states

We study the quantum manifestations of homogeneous and inhomogeneous oscillation suppression states in coupled identical quantum oscillators. We consider quantum van der Pol oscillators coupled via weighted mean-field diffusive coupling and using the formalism of open quantum system we show that depending upon the coupling and the density of mean-field, two types of quantum amplitude death occurs, namely squeezed and nonsqueezed quantum amplitude death. Surprisingly, we find that the inhomogeneous oscillation suppression state (or the oscillation death state) does not occur in the quantum oscillators in the classical limit. However, in the deep quantum regime we discover an oscillation death-like state which is manifested in the phase space through the symmetry-breaking bifurcation of Wigner function. Our results also hint towards the possibility of the transition from quantum amplitude death to oscillation death state through the "quantum" Turing-type bifurcation. We believe that the observation of quantum oscillation death state will deepen our knowledge of symmetry-breaking dynamics in the quantum domain.

nlin.CD↗

arXiv2020

A hybrid approach to modelling large area field emitters

Large area field electron emitters, typically consisting of several thousands of nanotips, pose a major challenge since numerical modeling requires enormous computational resources. We propose a hybrid approach where the local electrostatic field enhancement parameters of an individual emitter is determined numerically while electrostatic shielding and anode-proximity effects are incorporated using recent analytical advances. The hybrid model is tested numerically on an ordered arrangement of emitters and then applied to recent experimental results on randomly distributed gold nanocones. Using the current-voltage data of two samples with vastly different emitter densities but having similar nanocone sizes, we show that an appropriate modeling of the emitter-apex together with the analytical results on shielding and anode-proximity effects, leads to consistent results for the apex radius of curvature. In both cases, the $\text{I-V}$ data is approximately reproduced for $R_a \simeq 9$nm. Importantly, it is found that anode-proximity plays a significant role in counter-balancing electrostatic shielding and ignoring this effect results in the requirement of a much smaller value of $R_a$.

physics.app-ph↗

arXiv2020

Enhanced space charge limited current for curved electron emitters

The maximum current that can be transported across a vacuum diode is limited by forces arising due to space charge. In a planar diode configuration, the space charge limited (SCL) current density from a planar emitting patch is given by the Child-Langmuir (CL) law $J_{CL} \sim V_g^{3/2}/D^2$ where $V_g$ is the potential difference across the diode and $D$ is the separation between the anode and cathode. We show here analytically using the nonlinear line charge model that for a curved emitter in a planar diode configuration, the limiting current obeys the scaling relationship $J_{SCL} \sim γ_a V_g^{3/2}/D^2$ where $γ_a$ is the apex field enhancement factor of the curved emitter. For an emitter with large height ($h$) to apex radius of curvature ($R_a$) ratio, the limiting current far exceeds the planar value. The result is verified using the particle-in-cell code PASUPAT for two curved emitters shapes.

physics.plasm-ph↗

arXiv2020

The Schottky Conjecture and beyond

The `Schottky Conjecture' deals with the electrostatic field enhancement at the tip of compound structures such as a hemiellipsoid on top of a hemisphere. For such a 2-primitive compound structure, the apex field enhancement factor $γ_a^{(C)}$ is conjectured to be multiplicative ($γ_a^{(C)} = γ_a^{(1)} γ_a^{(2)}$) provided the structure at the base (labelled 1, e.g. the hemisphere) is much larger than the structure on top (referred to as crown and labelled 2, e.g. the hemi-ellipsoid). We first demonstrate numerically that for generic smooth structures, the conjecture holds in the limiting sense when the apex radius of curvature of the primitive-base $R_a^{(1)}$, is much larger than the height of the crown $h_2$ (i.e. $h_2/R_a^{(1)} \rightarrow 0$). If the condition is somewhat relaxed, we show that it is the electric field above the primitive-base (i.e. in the absence of the crown), averaged over the height of the crown, that gets magnified instead of the field at the apex of the primitive-base. This observation leads to the Corrected Schottky Conjecture (CSC), which for 2-primitive structures reads as $γ_a^{(C)}\simeq \langle γ_a^{(1)}\rangleγ_a^{(2)}$ where $\langle . \rangle$ denotes the average value over the height of the crown. For small protrusions ($h_2/h_1$ typically less than 0.2), $\langle γ_a^{(1)}\rangle$ can be approximately determined using the Line Charge Model so that $γ_a^{(C)} \simeq γ_a^{(1)}γ_a^{(2)} (2R_a^{(1)}/h_2)\ln(1 + h_2/2R_a^{(1)})$. The error is found to be within $1\%$ for $h_2/R_a^{(1)} < 0.05$, increasing to about $3\%$ (or less) for $h_2/R_a^{(1)} = 0.1$ and bounded below $5\%$ for $h_2/R_a^{(1)}$ as large as 0.5. The CSC is also found to give good results for 3-primitive compound structures. The relevance of the Corrected Schottky Conjecture for field emission is discussed.

physics.app-ph↗

arXiv2020

Electrostatic shielding versus anode-proximity effect in large area field emitters

Field emisison of electrons crucially depends on the enhancement of the local electric field around nanotips. The enhancement is maximum when individual emitter-tips are well separated. As the distance between two or more nanotips decreases, the field enhancement at individual tips reduces due to the shielding effect. The anode-proximity effect acts in quite the opposite way, increasing the local field as the anode is brought closer to the emitter. For isolated emitters, this effect is pronounced when the anode is at a distance less than three times the height of the emitter. It is shown here that for a large area field emitter (LAFE), the anode proximity effect increases dramatically and can counterbalance shielding effects to a large extent. Also, it is significant even when the anode is far away. The apex field enhancement factor for a LAFE in the presence of an anode is derived using the line charge model. It is found to explain the observations well and can accurately predict the apex enhancement factors. The results are supported by numerical studies using COMSOL Multiphysics.

physics.app-ph↗