arXiv subjects

R. Gopal

Publications and source records attributed to R. Gopal.

At least 19 recordsLinked to original sources

arXiv2026

Effect of biharmonic coupling in frequency-weighted Kuramoto oscillators

We investigate the collective dynamics of globally coupled phase oscillators with frequency-weighted biharmonic coupling. Although frequency-weighted and biharmonic extensions of the Kuramoto model have each been studied independently, their combined effect has remained unexplored. By combining numerical branch continuation with analytical stability analysis, we construct the complete phase diagram in the two-parameter coupling plane. The competition between the first- and second-harmonic interactions gives rise to three distinct collective states: the incoherent state (IC), the antipodal multibranch state (APMS), and the symmetry-broken multibranch state (SBMS). These states are separated by three bistable regions and a narrow tristable region in which all three states coexist as stable attractors. The transitions from the incoherent state to both ordered states are discontinuous and hysteretic, reflecting the explosive synchronization induced by frequency weighting, while the transition between the APMS and SBMS is also abrupt. Analytically, we derive the linear instability thresholds of the incoherent state together with the existence and local stability conditions for the SBMS, and show that the theoretical predictions are in good agreement with extensive numerical simulations.

nlin.AO↗

arXiv2026

Self-oscillations induced by self-induced torque in magnetic double tunnel junction

Self-oscillations of the magnetization due to self-induced torque (SIT) in a magnetic double tunnel junction that consists of perpendicularly polarized, pinned and free layers is investigated along with the field-like torque (FLT). The associated Landau-Lifshitz-Gilbert-Slonczewski equation is numerically analysed to exhibit the oscillations of magnetization driven by the current. From the numerical analysis, we show that the SIT is essential to generate oscillations in the order of GHz and without it the magnetization reaches steady state after exhibiting switching. Without FLT, the frequency of the oscillations decreases with the current while the power of oscillations increases. In the presence of the negative strength of the FLT the power spectral density confirms that the frequency, power and the Q-factor increase with the current. Also the tunability range and the rate at which the frequency enhances increase with the magnitude of the FLT.

cond-mat.mes-hall↗

arXiv2025

Swarmalators with frequency-weighted interactions

We investigate the role of frequency-weighted interactions in a solvable model of one-dimensional (1D) swarmalators confined to a ring, where both spatial and phase couplings are scaled by the heterogeneous natural frequencies of individual agents. Our analysis identifies three distinct collective states: the asynchronous state , the phase-wave state , and the bistrip mixed state characterized by antipodal clusters that are internally split into frequency-dependent sub-strips. We further establish that the onset of abrupt transitions are driven by heterogeneous coupling. Using a self-consistency analysis, we precisely determine the conditions for dynamical transitions among the identified states, thereby extending the theoretical understanding of swarmalator dynamics under heterogeneous interaction rules, which are in good agreement with the numerical simulation results.

nlin.AO↗

arXiv2025

Frustration Induced Chimeras and Motion in Two Dimensional Swarmalators

Swarmalators are phase oscillators capable of simultaneous swarming and synchronization, making them potential candidates for replicating complex dynamical states. In this work, we explore the effects of a frustration parameter in the phase interaction functions of a two-dimensional swarmalator model inspired by the solvable Sakaguchi-swarmalators that move in a one-dimensional ring. The impact of the frustration parameter in these models has been a topic of great interest. Real-world coupled systems with frustration exhibit remarkable collective dynamical states, underscoring the relevance of this study. The frustration parameter induces various states exhibiting non-stationarity, chimeric clustering, and global translational motion, where swarmalators move spontaneously in two-dimensional space. We investigate the characteristics of these states and their responses to changes in the frustration parameter. Notably, the emergence of chimeric states suggests the crucial role of non-stationarity in phase interactions for spontaneous population clustering. Additionally, we examine how phase non-stationarity influences the spatial positions of swarmalators and provide a classification of these states based on different order parameters.

nlin.AO↗

arXiv2024

Observation of sequential three-body dissociation of camphor molecule -- a native frame approach

The three-body dissociation dynamics of the dicationic camphor molecule (C$_{10}$H$_{16}$O$^{2+}$) resulting from Auger decay are investigated using soft X-ray synchrotron radiation. A photoelectron-photoion-photoion coincidence (PEPIPICO) method, a combination of a velocity map imaging (VMI) spectrometer and a time-of-flight (ToF) spectrometer is employed to measure the 3D momenta of ions detected in coincidence. The ion mass spectra and the ion-ion coincidence map at photon energies of 287.9 eV (below the C 1s ionization potential) and 292.4 eV (above the C 1s ionization potential for skeletal carbon) reveal that fragmentation depends on the final dicationic state rather than the initial excitation. Using the native frame method, three new fragmentation channels are discussed; (1) CH$_2$CO$^+$ + C$_7$H$_{11}^+$ + CH$_3$, (2) CH$_3^+$ + C$_7$H$_{11}^+$ + CH$_2$CO, and (3) C$_2$H$_5^+$ + C$_6$H$_9^+$ + CH$_2$CO. The dominating nature of sequential decay with deferred charge separation is clearly evidenced in all three channels. The results are discussed based on the experimental angular distributions and momenta distributions, corroborated by geometry optimization of the ground, monocationic, and dicationic camphor molecule.

physics.chem-ph↗

arXiv2023

Exploration of field-like torque and field-angle tunability in coupled spin-torque nano oscillators for synchronization

We investigate the influence of field-like torque and the direction of the external magnetic field on a one-dimensional array of serially connected spin-torque nano oscillators, having free layers with perpendicular anisotropy, to achieve complete synchronization between them by analyzing the associated Landau-Lifshitz-Gilbert-Slonczewski equation. The obtained results for synchronization are discussed for the cases of 2, 10 and 100 oscillators separately. The roles of the field-like torque and the direction of the external field on the synchronization of the STNOs are explored through the Kuramoto order parameter. While the field-like torque alone is sufficient to bring out global synchronization in the system made up of a small number of STNOs, the direction of the external field is also needed to be slightly tuned to synchronize the one-dimensional array of a large number of STNOs. The formation of complete synchronization through the construction of clusters within the system is identified for the 100 oscillators. The large amplitude synchronized oscillations are obtained for small to large numbers of oscillators. Moreover, the tunability in frequency for a wide range of currents is shown for the synchronized oscillations up to 100 spin-torque oscillators. In addition to achieving synchronization, the field-like torque increases the frequency of the synchronized oscillations. The transverse Lyapunov exponents are deduced to confirm the stable synchronization in coupled STNOs due to the field-like torque and to validate the results obtained in the numerical simulations. The output power of the array is estimated to be enhanced substantially due to complete synchronization by the combined effect of field-like torque and tunability of the field angle.

cond-mat.mes-hall↗

arXiv2023

High frequency oscillations in spin-torque nano oscillator due to bilinear coupling

Exchange coupling in an interfacial context is crucial for spin-torque nano oscillator (STNO) that consists of a non-magnetic spacer which is alloyed with a ferromagnetic material. Currently, investigations on the dynamics of the free layer magnetization and frequency enhancement in the STNO with bilinear coupling are still being actively pursued. In the present work, we investigate the dynamics of the STNO in the presence of bilinear coupling but in the absence of an external magnetic field by analyzing the associated Landau-Lifshitz-Gilbert-Sloncewski(LLGS) equation, and consequently the impact of the bilinear coupling on the dynamics of the magnetization of the free layer is studied. It is observed that the frequency of the oscillations in the magnetization component along the direction of the pinned layer polarization can be enhanced above 300 GHz by positive bilinear coupling and up to around 30 GHz by negative bilinear coupling. We further reveal a transition from in-plane to out-of-plane precession both for positive and negative bi-linear couplings. We also analyze the switching of the magnetization for different values of current and bilinear coupling. Our detailed investigations of STNO with bilinear coupling aim at the possibilities of high-frequency devices by considering the applied current and bilinear coupling in the absence of a magnetic field.

cond-mat.mes-hall↗

arXiv2022

Analysis of COVID-19 in India using vaccine epidemic model incorporating vaccine effectiveness and herd immunity

COVID-19 will be a continuous threat to human population despite having a few vaccines at hand until we reach the endemic state through natural herd immunity and total immunization through universal vaccination. However, the vaccine acts as a practical tool for reducing the massive public health problem and the emerging economic consequences that the continuing COVID -19 epidemic is causing worldwide, while the vaccine efficacy wanes. In this work, we propose and analyze an epidemic model of Susceptible-Exposed-Infected-Recovered-Vaccinated (SEIRV) population taking into account the rate of vaccination and vaccine waning. The dynamics of the model has been investigated, and the condition for a disease-free endemic equilibrium state is obtained. Further, the analysis is extended to study the COVID-19 spread in India by considering the availability of vaccines and the related critical parameters such as vaccination rate, vaccine efficacy and waning of vaccine's impact on deciding the emerging fate of this epidemic. We have also discussed the conditions for herd immunity due to vaccinated individuals among the people. Our results highlight the importance of vaccines, the effectiveness of booster vaccination in protecting people from infection, and their importance in epidemic and pandemic modelling.

q-bio.PE↗

arXiv2022

Effect of interlayer exchange coupling in spin-torque nano oscillator

The dynamics of the magnetization of the free layer in a spin-torque nano oscillator (STNO) influenced by a noncollinear alignment between the magnetizations of the free and pinned layers due to an interlayer exchange coupling has been investigated theoretically. The orientations of the magnetization of the free layer with that of the pinned layer have been computed through the macrospin model and they are found to match well with experimental results. The bilinear and biquadratic coupling strengths make the current to switch the magnetization between two states or oscillate steadily. The expressions for the critical currents between which oscillations are possible and the critical bilinear coupling strength below which oscillations are not possible are derived. The frequency of the oscillations is shown to be tuned and increased to or above 300 GHz by the current which is the largest to date among nanopillar-shaped STNOs.

physics.app-ph↗

arXiv2022

Influence of Asymmetric Parameters in Higher-Order Coupling With Bimodal Frequency Distribution

We investigate the phase diagram of the Sakaguchi-Kuramoto model with a higher order interaction along with the traditional pairwise interaction. We also introduce asymmetry parameters in both the interaction terms and investigate the collective dynamics and their transitions in the phase diagrams under both unimodal and bimodal frequency distributions. We deduce the evolution equations for the macroscopic order parameters and eventually derive pitchfork and Hopf bifurcation curves. Transition from the incoherent state to standing wave pattern is observed in the presence of the unimodal frequency distribution. In contrast, a rich variety of dynamical states such as the incoherent state, partially synchronized state-I, partially synchronized state-II, and standing wave patterns and transitions among them are observed in the phase diagram, via various bifurcation scenarios including saddle-node and homoclinic bifurcations, in the presence of bimodal frequency distribution. Higher order coupling enhances the spread of the bistable regions in the phase diagrams and also leads to the manifestation of bistability between incoherent and partially synchronized states even with unimodal frequency distribution, which is otherwise not observed with the pairwise coupling. Further, the asymmetry parameters facilitate the onset of several bistable and multistable regions in the phase diagrams. Very large values of the asymmetry parameters allow the phase diagrams to admit only the monostable dynamical states.

nlin.AO↗

arXiv2021

Spin Torque Oscillations Triggered by In-plane Field

We study the dynamics of a spin torque nano oscillator that consists of parallelly magnetized free and pinned layers by numerically solving the associated Landau-Lifshitz-Gilbert-Slonczewski equation in the presence of a field-like torque. We observe that an in-plane magnetic field which is applied for a short interval of time ($<$1ns) triggers the magnetization to exhibit self-oscillations from low energy initial magnetization state. Also, we confirm that the frequency of oscillations can be tuned over the range $\sim$25 GHz to $\sim$72 GHz by current, even in the absence of field-like torque. We find the frequency enhancement up to 10 GHz by the presence of field-like torque. We determine the Q-factor for different frequencies and show that it increases with frequency. Our analysis with thermal noise confirms that the system is stable against thermal noise and the dynamics is not altered appreciably by it.

cond-mat.mes-hall↗

arXiv2021

Analysis of the second wave of COVID-19 in India based on SEIR model

India was under a grave threat from the second wave of the COVID-19 pandemic particularly in the beginning of May 2021. The situation appeared rather gloomy as the number of infected individuals/active cases had increased alarmingly during the months of May and June 2021 compared to the first wave peak. Indian government/state governments have been implementing various control measures such as lock-downs, setting up new hospitals, and putting travel restrictions at various stages to lighten the virus spread from the initial outbreak of the pandemic. Recently, we have studied the susceptible-exposed-infectious-removed(SEIR) dynamic modelling of the epidemic evolution of COVID-19 in India with the help of appropriate parameters quantifying the various governmental actions and the intensity of individual reactions. Our analysis had predicted the scenario of the first wave quite well. In this present article, we extend our analysis to estimate and analyze the number of infected individuals during the second wave of COVID-19 in India with the help of the above SEIR model. Our findings show that the people's individual effort along with governmental actions such as implementations of curfews, accelerated vaccine strategy are the most important factors to control the pandemic in the present situation and in the future.

physics.soc-ph↗

arXiv2021

Dynamics of coupled modified Rossler oscillators: the role of nonisochronicity parameter

The amplitude-dependent frequency of the oscillations, termed \emph{nonisochronicity}, is one of the essential characteristics of nonlinear oscillators. In this paper, the dynamics of the Rossler oscillator in the presence of nonisochronicity is examined. In particular, we explore the appearance of a new fixed point and the emergence of a coexisting limit-cycle and quasiperiodic attractors. We also describe the sequence of bifurcations leading to synchronized, desynchronized attractors and oscillation death states in the coupled Rossler oscillators as a function of the strength of nonisochronicity and coupling parameters. Further, we characterize the multistability of the coexisting attractors by plotting the basins of attraction. Our results open up the possibilities of understanding the emergence of coexisting attractors, and into a qualitative change of the collective states in coupled nonlinear oscillators in the presence of nonisochronicity.

nlin.CD↗

arXiv2021

Large Amplitude Spin-Hall Oscillations due to Field-like Torque

Large amplitude spin-Hall oscillations are identified in a ferromagnetic layer with two perpendicular in-plane easy axis in the presence of field-like torque without any polarizer and external field. The analytical study confirms the possibility of oscillations in the presence of field-like torque. The investigation shows that the oscillation frequency can be tuned from 2 GHz to 80 GHz by current and enhanced by field-like torque. Further, the enhancement of frequency along with the Q-factor by current and field-like torque is also observed.

nlin.AO↗

arXiv2020

Dynamical modelling and analysis of COVID-19 in India

We consider the pandemic spreading of COVID-19 in India after the outbreak of the coronavirus in Wuhan city, China. We estimate the transmission rate of the initial infecting individuals of COVID-19 in India by using the officially reported data at the early stage of the epidemic with the help of Susceptible (S), Exposed (E), Infected (I), and Removed (R) population model, the so-called SEIR dynamical model. Numerical analysis and model verification are performed to calibrate the system parameters with official public information about the number of people infected, and then to evaluate several COVID -19 scenarios potentially applicable to India. Our findings provide an estimation of disease occurrence in the near future and also demonstrate the importance of governmental and individual efforts to control the effects and time of the pandemic-related critical situations. We also give special emphasis to individual reactions in the containment process.

q-bio.PE↗

arXiv2020

Penning Spectroscopy and Structure of Acetylene Oligomers in He Nanodroplets

Embedded atoms or molecules in a photoexcited He nanodroplet are well-known to be ionized through inter-atomic relaxation in a Penning process. In this work, we investigate the Penning ionization of acetylene oligomers occurring from the photoexcitation bands of He nanodroplets. In close analogy to conventional Penning electron spectroscopy by thermal atomic collisions, the n = 2 photoexcitation band plays the role of the metastable atomic $1s2s$ $^{3,1}S$ He$^\ast$. This facilitates electron spectroscopy of acetylene aggregates in the sub-kelvin He environment, providing the following insight into their structure: The molecules in the dopant cluster are loosely bound van der Waals complexes rather than forming covalent compounds. In addition, this work reveals a Penning process stemming from the n = 4 band where charge-transfer from autoionized He in the droplets is known to be the dominant relaxation channel. This allows for excited states of the remnant dopant oligomer Penning-ions to be studied. Hence, we demonstrate Penning ionization electron spectroscopy of doped droplets as an effective technique for investigating dopant oligomers which are easily formed by attachment to the host cluster.

physics.atm-clus↗

arXiv2019

Influence of field-like torque in synchronization of spin torque oscillators

The magnetization dynamics of two parallelly coupled spin torque oscillators, destabilization of steady states and removal of multistability, are investigated by taking into account the influence of field-like torque. It is shown that the existence of such torque can cancel the effect of damping and can, therefore, cause the oscillators to exhibit synchronized oscillations in response to direct current. Further, our results show that the presence of field-like torque enhances the power and Q-factor of the synchronized oscillations. The validity of the above results is confirmed by numerical and analytical studies based on the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation.

nlin.AO↗

arXiv2019

Phase locking of spin transfer nano-oscillators using common microwave sources

In this paper, we study typical nonlinear phenomenon of phase-locking or synchronization in spin-torque nano oscillators (STNOs). To start with the oscillators are considered as uncoupled but interlinked through either a common microwave current or a microwave field. We identify the phase locking of an array of STNOs (first for two and then for 100 oscillators) by means of injection locking which represents locking the oscillations to a common alternating spin current or a common microwave magnetic field. We characterize the locking of STNOs through both first and second harmonic lockings in an array. We find that second harmonic lockings takes lesser value of microwave current and field when compared with the first harmonic lockings. Our results also show that oscillating microwave current can induce integer harmonic locking while microwave field can induce both integer and several fractional harmonic lockings. We also extend our analysis to study locking behavior of two STNOs by introducing time delay feedback and coupling through a current injection and bring out the associated locking characteristics. Finally, we have also analyzed the stability of synchronization of identical array of STNOs with current coupling by using master stability function formalism.

cond-mat.mes-hall↗