---
_id: '53474'
abstract:
- lang: eng
text: We present a novel approach to characterize and quantify microheterogeneity
and microphase separation in computer simulations of complex liquid mixtures.
Our post-processing method is based on local density fluctuations of the different
constituents in sampling spheres of varying size. It can be easily applied to
both molecular dynamics (MD) and Monte Carlo (MC) simulations, including periodic
boundary conditions. Multidimensional correlation of the density distributions
yields a clear picture of the domain formation due to the subtle balance of different
interactions. We apply our approach to the example of force field molecular dynamics
simulations of imidazolium-based ionic liquids with different side chain lengths
at different temperatures, namely 1-ethyl-3-methylimidazolium chloride, 1-hexyl-3-methylimidazolium
chloride, and 1-decyl-3-methylimidazolium chloride, which are known to form distinct
liquid domains. We put the results into the context of existing microheterogeneity
analyses and demonstrate the advantages and sensitivity of our novel method. Furthermore,
we show how to estimate the configuration entropy from our analysis, and we investigate
voids in the system. The analysis has been implemented into our program package
TRAVIS and is thus available as free software.
article_number: '322'
author:
- first_name: Michael
full_name: Lass, Michael
id: '24135'
last_name: Lass
orcid: 0000-0002-5708-7632
- first_name: Tobias
full_name: Kenter, Tobias
id: '3145'
last_name: Kenter
- first_name: Christian
full_name: Plessl, Christian
id: '16153'
last_name: Plessl
orcid: 0000-0001-5728-9982
- first_name: Martin
full_name: Brehm, Martin
id: '100167'
last_name: Brehm
citation:
ama: Lass M, Kenter T, Plessl C, Brehm M. Characterizing Microheterogeneity in Liquid
Mixtures via Local Density Fluctuations. Entropy. 2024;26(4). doi:10.3390/e26040322
apa: Lass, M., Kenter, T., Plessl, C., & Brehm, M. (2024). Characterizing Microheterogeneity
in Liquid Mixtures via Local Density Fluctuations. Entropy, 26(4),
Article 322. https://doi.org/10.3390/e26040322
bibtex: '@article{Lass_Kenter_Plessl_Brehm_2024, title={Characterizing Microheterogeneity
in Liquid Mixtures via Local Density Fluctuations}, volume={26}, DOI={10.3390/e26040322},
number={4322}, journal={Entropy}, publisher={MDPI AG}, author={Lass, Michael and
Kenter, Tobias and Plessl, Christian and Brehm, Martin}, year={2024} }'
chicago: Lass, Michael, Tobias Kenter, Christian Plessl, and Martin Brehm. “Characterizing
Microheterogeneity in Liquid Mixtures via Local Density Fluctuations.” Entropy
26, no. 4 (2024). https://doi.org/10.3390/e26040322.
ieee: 'M. Lass, T. Kenter, C. Plessl, and M. Brehm, “Characterizing Microheterogeneity
in Liquid Mixtures via Local Density Fluctuations,” Entropy, vol. 26, no.
4, Art. no. 322, 2024, doi: 10.3390/e26040322.'
mla: Lass, Michael, et al. “Characterizing Microheterogeneity in Liquid Mixtures
via Local Density Fluctuations.” Entropy, vol. 26, no. 4, 322, MDPI AG,
2024, doi:10.3390/e26040322.
short: M. Lass, T. Kenter, C. Plessl, M. Brehm, Entropy 26 (2024).
date_created: 2024-04-12T18:31:39Z
date_updated: 2024-04-12T18:34:32Z
department:
- _id: '27'
- _id: '518'
- _id: '803'
doi: 10.3390/e26040322
intvolume: ' 26'
issue: '4'
language:
- iso: eng
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
publisher: MDPI AG
status: public
title: Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations
type: journal_article
user_id: '24135'
volume: 26
year: '2024'
...
---
_id: '21820'
abstract:
- lang: eng
text: The reduction of high-dimensional systems to effective models on a
smaller set of variables is an essential task in many areas of science. For stochastic
dynamics governed by diffusion processes, a general procedure to find effective
equations is the conditioning approach. In this paper, we are interested in the
spectrum of the generator of the resulting effective dynamics, and how it compares
to the spectrum of the full generator. We prove a new relative error bound in
terms of the eigenfunction approximation error for reversible systems. We also
present numerical examples indicating that, if Kramers–Moyal (KM) type approximations
are used to compute the spectrum of the reduced generator, it seems largely insensitive
to the time window used for the KM estimators. We analyze the implications of
these observations for systems driven by underdamped Langevin dynamics, and show
how meaningful effective dynamics can be defined in this setting.
article_number: '134'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Lorenzo
full_name: Boninsegna, Lorenzo
last_name: Boninsegna
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective
Dynamics from Conditional Expectations. Entropy. 2021. doi:10.3390/e23020134
apa: Nüske, F., Koltai, P., Boninsegna, L., & Clementi, C. (2021). Spectral
Properties of Effective Dynamics from Conditional Expectations. Entropy.
https://doi.org/10.3390/e23020134
bibtex: '@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties
of Effective Dynamics from Conditional Expectations}, DOI={10.3390/e23020134},
number={134}, journal={Entropy}, author={Nüske, Feliks and Koltai, Péter and Boninsegna,
Lorenzo and Clementi, Cecilia}, year={2021} }'
chicago: Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi.
“Spectral Properties of Effective Dynamics from Conditional Expectations.” Entropy,
2021. https://doi.org/10.3390/e23020134.
ieee: F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties
of Effective Dynamics from Conditional Expectations,” Entropy, 2021.
mla: Nüske, Feliks, et al. “Spectral Properties of Effective Dynamics from Conditional
Expectations.” Entropy, 134, 2021, doi:10.3390/e23020134.
short: F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).
date_created: 2021-04-28T18:07:56Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e23020134
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/23/2/134
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Spectral Properties of Effective Dynamics from Conditional Expectations
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '21819'
abstract:
- lang: eng
text: Many dimensionality and model reduction techniques rely on estimating
dominant eigenfunctions of associated dynamical operators from data. Important
examples include the Koopman operator and its generator, but also the Schrödinger
operator. We propose a kernel-based method for the approximation of differential
operators in reproducing kernel Hilbert spaces and show how eigenfunctions can
be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms
are applied to molecular dynamics and quantum chemistry examples. Furthermore,
we exploit that, under certain conditions, the Schrödinger operator can be transformed
into a Kolmogorov backward operator corresponding to a drift-diffusion process
and vice versa. This allows us to apply methods developed for the analysis of
high-dimensional stochastic differential equations to quantum mechanical systems.
article_number: '722'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Boumediene
full_name: Hamzi, Boumediene
last_name: Hamzi
citation:
ama: Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator
and Schrödinger Operator. Entropy. 2020. doi:10.3390/e22070722
apa: Klus, S., Nüske, F., & Hamzi, B. (2020). Kernel-Based Approximation of
the Koopman Generator and Schrödinger Operator. Entropy. https://doi.org/10.3390/e22070722
bibtex: '@article{Klus_Nüske_Hamzi_2020, title={Kernel-Based Approximation of the
Koopman Generator and Schrödinger Operator}, DOI={10.3390/e22070722},
number={722}, journal={Entropy}, author={Klus, Stefan and Nüske, Feliks and Hamzi,
Boumediene}, year={2020} }'
chicago: Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. “Kernel-Based Approximation
of the Koopman Generator and Schrödinger Operator.” Entropy, 2020. https://doi.org/10.3390/e22070722.
ieee: S. Klus, F. Nüske, and B. Hamzi, “Kernel-Based Approximation of the Koopman
Generator and Schrödinger Operator,” Entropy, 2020.
mla: Klus, Stefan, et al. “Kernel-Based Approximation of the Koopman Generator and
Schrödinger Operator.” Entropy, 722, 2020, doi:10.3390/e22070722.
short: S. Klus, F. Nüske, B. Hamzi, Entropy (2020).
date_created: 2021-04-28T18:06:35Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e22070722
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/22/7/722
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator
type: journal_article
user_id: '81513'
year: '2020'
...
---
_id: '53274'
abstract:
- lang: eng
text: This paper studies the performance of improper Gaussian signaling
(IGS) over a 2-user Rayleigh single-input single-output (SISO) interference channel,
treating interference as noise. We assume that the receivers have perfect channel
state information (CSI), while the transmitters have access to only statistical
CSI. Under these assumptions, we consider a signaling scheme, which we refer to
as proper/improper Gaussian signaling or PGS/IGS, where at most one user may employ
IGS. For the Rayleigh fading channel model, we characterize the statistical distribution
of the signal-to-interference-plus-noise ratio at each receiver and derive closed-form
expressions for the ergodic rates. By adapting the powers, we characterize the
Pareto boundary of the ergodic rate region for the 2-user fading IC. The ergodic
transmission rates can be attained using fixed-rate codebooks and no optimization
is involved. Our results show that, in the moderate and strong interference regimes,
the proposed PGS/IGS scheme improves the performance with respect to the PGS scheme.
Additionally, we numerically compute the ergodic rate region of the full IGS scheme
when both users can employ IGS and their transmission parameters are optimized
by an exhaustive search. Our results suggest that most of the Pareto optimal points
for the 2-user fading IC channel are attained when either both users transmit
PGS or when one transmits PGS and the other transmits maximally improper Gaussian
signals and time sharing is allowed.
article_number: '922'
author:
- first_name: Mohammad
full_name: Soleymani, Mohammad
last_name: Soleymani
- first_name: Ignacio
full_name: Santamaria, Ignacio
last_name: Santamaria
- first_name: Christian
full_name: Lameiro, Christian
last_name: Lameiro
- first_name: Peter J.
full_name: Schreier, Peter J.
last_name: Schreier
citation:
ama: Soleymani M, Santamaria I, Lameiro C, Schreier PJ. Ergodic Rate for Fading
Interference Channels with Proper and Improper Gaussian Signaling. Entropy.
2019;21(10). doi:10.3390/e21100922
apa: Soleymani, M., Santamaria, I., Lameiro, C., & Schreier, P. J. (2019). Ergodic
Rate for Fading Interference Channels with Proper and Improper Gaussian Signaling.
Entropy, 21(10), Article 922. https://doi.org/10.3390/e21100922
bibtex: '@article{Soleymani_Santamaria_Lameiro_Schreier_2019, title={Ergodic Rate
for Fading Interference Channels with Proper and Improper Gaussian Signaling},
volume={21}, DOI={10.3390/e21100922},
number={10922}, journal={Entropy}, publisher={MDPI AG}, author={Soleymani, Mohammad
and Santamaria, Ignacio and Lameiro, Christian and Schreier, Peter J.}, year={2019}
}'
chicago: Soleymani, Mohammad, Ignacio Santamaria, Christian Lameiro, and Peter J.
Schreier. “Ergodic Rate for Fading Interference Channels with Proper and Improper
Gaussian Signaling.” Entropy 21, no. 10 (2019). https://doi.org/10.3390/e21100922.
ieee: 'M. Soleymani, I. Santamaria, C. Lameiro, and P. J. Schreier, “Ergodic Rate
for Fading Interference Channels with Proper and Improper Gaussian Signaling,”
Entropy, vol. 21, no. 10, Art. no. 922, 2019, doi: 10.3390/e21100922.'
mla: Soleymani, Mohammad, et al. “Ergodic Rate for Fading Interference Channels
with Proper and Improper Gaussian Signaling.” Entropy, vol. 21, no. 10,
922, MDPI AG, 2019, doi:10.3390/e21100922.
short: M. Soleymani, I. Santamaria, C. Lameiro, P.J. Schreier, Entropy 21 (2019).
date_created: 2024-04-05T09:07:05Z
date_updated: 2024-04-05T13:19:44Z
department:
- _id: '263'
doi: 10.3390/e21100922
intvolume: ' 21'
issue: '10'
keyword:
- General Physics and Astronomy
language:
- iso: eng
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
publisher: MDPI AG
status: public
title: Ergodic Rate for Fading Interference Channels with Proper and Improper Gaussian
Signaling
type: journal_article
user_id: '67076'
volume: 21
year: '2019'
...