The response of an electrochemical reacting system to potential perturbations during electrochemi... more The response of an electrochemical reacting system to potential perturbations during electrochemical impedance spectrum measurement is investigated using numerical simulation. Electrochemical metal dissolution via an adsorbed intermediate species is analyzed and it is shown that applying the potential perturbation causes the average surface coverage to drift. For high frequency perturbations, the final value of the average surface coverage depends mainly on the kinetic parameters and the amplitude of the applied perturbation. Acquiring the data during the first few cycles of perturbations leads to an incorrect calculation of the impedance, particularly for large amplitude perturbations. Repeating the experiments will not identify this drift, while Kramers–Kronig Transform (KKT) can successfully detect this problem. The correct experimental methodology to overcome this effect and obtain the impedance spectra is also described. Another reaction with two adsorbed intermediates is also investigated and it is shown that in certain cases, the violations of linearity criteria can also be detected by KKT. The results illustrate the importance of validating the impedance data with KKT before further analysis.► EIS response of reaction via adsorbed intermediates analyzed. Numerical simulation. ► Surface coverage drifts during measurement. Analytical solution confirms results. ► Correct experimental strategy to overcome the drift effect identified. ► Kramers–Kronig Transforms identify the drift and in certain cases, nonlinearities.
The effect of solution resistance on the nonlinear electrochemical impedance spectra under quasi-... more The effect of solution resistance on the nonlinear electrochemical impedance spectra under quasi-potentiostatic conditions was investigated by numerical simulations. An electron transfer reaction, a reaction with an adsorbed intermediate and a reaction exhibiting negative resistance were chosen as the candidates and large amplitude perturbations were employed. The potential across the interface drifts initially and stabilizes after a certain time, which depends on the solution resistance and the kinetic parameter values. The fraction of the applied potential drop occurring across the metal–solution interface depends on the frequency and the amplitude of the perturbation as well as the value of solution resistance. This in turn leads to the possibility that, for a given conditions, a part of the spectrum may be acquired in the linear regime while the remaining part may be acquired in the nonlinear regime. The sensitivity of the Kramers Kronig transform (KKT) to identify these cases is evaluated. The results show that although the spectra are distorted by poorly conducting solution, the sensitivity of KKT to identify the nonlinear effects is not enhanced by the introduction of significant solution resistance.
Proceedings of The Indian Academy of Sciences-mathematical Sciences, 1997
Let Gn,k denote the oriented grassmann manifold of orientedk-planes in ℝn. It is shown that for a... more Let Gn,k denote the oriented grassmann manifold of orientedk-planes in ℝn. It is shown that for any continuous mapf: Gn,k → Gn,k, dim Gn,k = dim Gm,l = l(m −l), the Brouwer’s degree is zero, providedl > 1,n ≠ m. Similar results for continuous mapsg: ℂGm,l → ℂGn,k,h: ℍGm,l → ℍGn,k, 1 ≤ l < k ≤ n/2, k(n — k) = l(m — l) are also obtained.
Proceedings of The Indian Academy of Sciences-mathematical Sciences, 1999
We show that ifM is the total space of a holomorphic bundle with base space a simply connected ho... more We show that ifM is the total space of a holomorphic bundle with base space a simply connected homogeneous projective variety and fibre and structure group a compact complex torus, then the identity component of the automorphism group ofM acts trivially on the Dolbeault cohomology ofM. We consider a class of compact complex homogeneous spacesW, which we call generalized Hopf manifolds, which are diffeomorphic to S1 ×K/L whereK is a compact connected simple Lie group andL is the semisimple part of the centralizer of a one dimensional torus inK. We compute the Dolbeault cohomology ofW. We compute the Picard group of any generalized Hopf manifold and show that every line bundle over a generalized Hopf manifold arises from a representation of its fundamental group.
The response of an electrochemical reacting system to potential perturbations during electrochemi... more The response of an electrochemical reacting system to potential perturbations during electrochemical impedance spectrum measurement is investigated using numerical simulation. Electrochemical metal dissolution via an adsorbed intermediate species is analyzed and it is shown that applying the potential perturbation causes the average surface coverage to drift. For high frequency perturbations, the final value of the average surface coverage depends mainly on the kinetic parameters and the amplitude of the applied perturbation. Acquiring the data during the first few cycles of perturbations leads to an incorrect calculation of the impedance, particularly for large amplitude perturbations. Repeating the experiments will not identify this drift, while Kramers–Kronig Transform (KKT) can successfully detect this problem. The correct experimental methodology to overcome this effect and obtain the impedance spectra is also described. Another reaction with two adsorbed intermediates is also investigated and it is shown that in certain cases, the violations of linearity criteria can also be detected by KKT. The results illustrate the importance of validating the impedance data with KKT before further analysis.► EIS response of reaction via adsorbed intermediates analyzed. Numerical simulation. ► Surface coverage drifts during measurement. Analytical solution confirms results. ► Correct experimental strategy to overcome the drift effect identified. ► Kramers–Kronig Transforms identify the drift and in certain cases, nonlinearities.
The effect of solution resistance on the nonlinear electrochemical impedance spectra under quasi-... more The effect of solution resistance on the nonlinear electrochemical impedance spectra under quasi-potentiostatic conditions was investigated by numerical simulations. An electron transfer reaction, a reaction with an adsorbed intermediate and a reaction exhibiting negative resistance were chosen as the candidates and large amplitude perturbations were employed. The potential across the interface drifts initially and stabilizes after a certain time, which depends on the solution resistance and the kinetic parameter values. The fraction of the applied potential drop occurring across the metal–solution interface depends on the frequency and the amplitude of the perturbation as well as the value of solution resistance. This in turn leads to the possibility that, for a given conditions, a part of the spectrum may be acquired in the linear regime while the remaining part may be acquired in the nonlinear regime. The sensitivity of the Kramers Kronig transform (KKT) to identify these cases is evaluated. The results show that although the spectra are distorted by poorly conducting solution, the sensitivity of KKT to identify the nonlinear effects is not enhanced by the introduction of significant solution resistance.
Proceedings of The Indian Academy of Sciences-mathematical Sciences, 1997
Let Gn,k denote the oriented grassmann manifold of orientedk-planes in ℝn. It is shown that for a... more Let Gn,k denote the oriented grassmann manifold of orientedk-planes in ℝn. It is shown that for any continuous mapf: Gn,k → Gn,k, dim Gn,k = dim Gm,l = l(m −l), the Brouwer’s degree is zero, providedl > 1,n ≠ m. Similar results for continuous mapsg: ℂGm,l → ℂGn,k,h: ℍGm,l → ℍGn,k, 1 ≤ l < k ≤ n/2, k(n — k) = l(m — l) are also obtained.
Proceedings of The Indian Academy of Sciences-mathematical Sciences, 1999
We show that ifM is the total space of a holomorphic bundle with base space a simply connected ho... more We show that ifM is the total space of a holomorphic bundle with base space a simply connected homogeneous projective variety and fibre and structure group a compact complex torus, then the identity component of the automorphism group ofM acts trivially on the Dolbeault cohomology ofM. We consider a class of compact complex homogeneous spacesW, which we call generalized Hopf manifolds, which are diffeomorphic to S1 ×K/L whereK is a compact connected simple Lie group andL is the semisimple part of the centralizer of a one dimensional torus inK. We compute the Dolbeault cohomology ofW. We compute the Picard group of any generalized Hopf manifold and show that every line bundle over a generalized Hopf manifold arises from a representation of its fundamental group.
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Papers by Vimala Ramani