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2018


Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective
Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

Tronarp, F., Kersting, H., Särkkä, S., Hennig, P.

ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consists of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a Bayesian state estimation problem and all widely-used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers, which were formulated in terms of generating synthetic measurements of the vector field, come out as specific approximations. We derive novel solvers, both Gaussian and non-Gaussian, from the Bayesian state estimation problem posed in this paper and compare them with other probabilistic solvers in illustrative experiments.

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link (url) Project Page [BibTex]

2018



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Convergence Rates of Gaussian ODE Filters

Kersting, H., Sullivan, T. J., Hennig, P.

arXiv preprint 2018, arXiv:1807.09737 [math.NA], July 2018 (article)

Abstract
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives a priori as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. We prove worst-case local convergence rates of order $h^{q+1}$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $h^q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyse how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Rational metareasoning and the plasticity of cognitive control

Lieder, F., Shenhav, A., Musslick, S., Griffiths, T. L.

PLOS Computational Biology, 14(4):e1006043, Public Library of Science, April 2018 (article)

Abstract
The human brain has the impressive capacity to adapt how it processes information to high-level goals. While it is known that these cognitive control skills are malleable and can be improved through training, the underlying plasticity mechanisms are not well understood. Here, we develop and evaluate a model of how people learn when to exert cognitive control, which controlled process to use, and how much effort to exert. We derive this model from a general theory according to which the function of cognitive control is to select and configure neural pathways so as to make optimal use of finite time and limited computational resources. The central idea of our Learned Value of Control model is that people use reinforcement learning to predict the value of candidate control signals of different types and intensities based on stimulus features. This model correctly predicts the learning and transfer effects underlying the adaptive control-demanding behavior observed in an experiment on visual attention and four experiments on interference control in Stroop and Flanker paradigms. Moreover, our model explained these findings significantly better than an associative learning model and a Win-Stay Lose-Shift model. Our findings elucidate how learning and experience might shape people’s ability and propensity to adaptively control their minds and behavior. We conclude by predicting under which circumstances these learning mechanisms might lead to self-control failure.

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Rational metareasoning and the plasticity of cognitive control DOI Project Page Project Page [BibTex]

Rational metareasoning and the plasticity of cognitive control DOI Project Page Project Page [BibTex]


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Over-Representation of Extreme Events in Decision Making Reflects Rational Use of Cognitive Resources

Lieder, F., Griffiths, T. L., Hsu, M.

Psychological Review, 125(1):1-32, January 2018 (article)

Abstract
People’s decisions and judgments are disproportionately swayed by improbable but extreme eventualities, such as terrorism, that come to mind easily. This article explores whether such availability biases can be reconciled with rational information processing by taking into account the fact that decision-makers value their time and have limited cognitive resources. Our analysis suggests that to make optimal use of their finite time decision-makers should over-represent the most important potential consequences relative to less important, put potentially more probable, outcomes. To evaluate this account we derive and test a model we call utility-weighted sampling. Utility-weighted sampling estimates the expected utility of potential actions by simulating their outcomes. Critically, outcomes with more extreme utilities have a higher probability of being simulated. We demonstrate that this model can explain not only people’s availability bias in judging the frequency of extreme events but also a wide range of cognitive biases in decisions from experience, decisions from description, and memory recall.

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DOI [BibTex]

DOI [BibTex]


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Active microrheology in corrugated channels

Puertas, A. M., Malgaretti, P., Pagonabarraga, I.

The Journal of Chemical Physics, 149(17), American Institute of Physics, Woodbury, N.Y., 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

Gross, M.

Journal of Statistical Mechanics: Theory and Experiment, 2018, Institute of Physics Publishing, Bristol, England, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Cu@TiO2 Janus microswimmers with a versatile motion mechanism

Wang, L. L., Popescu, M. N., Stavale, F., Ali, A., Gemming, T., Simmchen, J.

Soft Matter, 14(34):6969-6973, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Probing interface localization-delocalization transitions by colloids

Kondrat, S., Vasilyev, O., Dietrich, S.

Journal of Physics: Condensed Matter, 30(41), IOP Publishing, Bristol, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Medical imaging for the tracking of micromotors

Vilela, D., Coss\’\io, U., Parmar, J., Mart\’\inez-Villacorta, A. M., Gómez-Vallejo, V., Llop, J., Sánchez, S.

ACS Nano, 12(2):1220-1227, American Chemical Society, Washington, DC, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Noncontinuous Super-Diffusive Dynamics of a Light-Activated Nanobottle Motor

Xuan, M., Mestre, R., Gao, C., Zhou, C., He, Q., Sánchez, S.

Angewandte Chemie International Edition, 57(23):6838-6842, Wiley-VCH, Weinheim, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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On the origin of forward-backward multiplicity correlations in pp collisions at ultrarelativistic energies

Bravina, L., Bleibel, J., Zabrodin, E.

Physics Letters B, 787, pages: 146-152, North-Holland, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Autophoretic motion in three dimensions

Lisicki, M., Reigh, S., Lauga, E.

Soft Matter, 14(17):3304-3314, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Order-disorder transitions in lattice gases with annealed reactive constraints

Dudka, M., Bénichou, O., Oshanin, G.

Journal of Statistical Mechanics: Theory and Experiment, 2018, Institute of Physics Publishing, Bristol, England, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Bacterial Biohybrid Microswimmers

Bastos-Arrieta, J., Revilla-Guarinos, A., Uspal, W., Simmchen, J.

Frontiers in Robotics and AI, 5, Frontiers Media, Lausanne, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium

Soo, H., Krüger, M.

Physical Review B, 97(4), American Physical Society, Woodbury, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Local pressure for confined systems

Malgaretti, P., Bier, M.

Physical Review E, 97(2), American Physical Society, Melville, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

Kanagawa, M., Hennig, P., Sejdinovic, D., Sriperumbudur, B. K.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

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arXiv [BibTex]

arXiv [BibTex]


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Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper introduces a novel Hilbert space representation of a counterfactual distribution---called counterfactual mean embedding (CME)---with applications in nonparametric causal inference. Counterfactual prediction has become an ubiquitous tool in machine learning applications, such as online advertisement, recommendation systems, and medical diagnosis, whose performance relies on certain interventions. To infer the outcomes of such interventions, we propose to embed the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel. Under appropriate assumptions, the CME allows us to perform causal inference over the entire landscape of the counterfactual distribution. The CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also derive a rate of convergence which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Our framework can deal with not only real-valued outcome, but potentially also more complex and structured outcomes such as images, sequences, and graphs. Lastly, our experimental results on off-policy evaluation tasks demonstrate the advantages of the proposed estimator.

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arXiv [BibTex]

arXiv [BibTex]


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Model-based Kernel Sum Rule: Kernel Bayesian Inference with Probabilistic Models

Nishiyama, Y., Kanagawa, M., Gretton, A., Fukumizu, K.

Arxiv e-prints, arXiv:1409.5178v2 [stat.ML], 2018 (article)

Abstract
Kernel Bayesian inference is a powerful nonparametric approach to performing Bayesian inference in reproducing kernel Hilbert spaces or feature spaces. In this approach, kernel means are estimated instead of probability distributions, and these estimates can be used for subsequent probabilistic operations (as for inference in graphical models) or in computing the expectations of smooth functions, for instance. Various algorithms for kernel Bayesian inference have been obtained by combining basic rules such as the kernel sum rule (KSR), kernel chain rule, kernel product rule and kernel Bayes' rule. However, the current framework only deals with fully nonparametric inference (i.e., all conditional relations are learned nonparametrically), and it does not allow for flexible combinations of nonparametric and parametric inference, which are practically important. Our contribution is in providing a novel technique to realize such combinations. We introduce a new KSR referred to as the model-based KSR (Mb-KSR), which employs the sum rule in feature spaces under a parametric setting. Incorporating the Mb-KSR into existing kernel Bayesian framework provides a richer framework for hybrid (nonparametric and parametric) kernel Bayesian inference. As a practical application, we propose a novel filtering algorithm for state space models based on the Mb-KSR, which combines the nonparametric learning of an observation process using kernel mean embedding and the additive Gaussian noise model for a state transition process. While we focus on additive Gaussian noise models in this study, the idea can be extended to other noise models, such as the Cauchy and alpha-stable noise models.

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arXiv [BibTex]

arXiv [BibTex]


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Charge polarization, local electroneutrality breakdown and eddy formation due to electroosmosis in varying-section channels

Chinappi, M., Malgaretti, P.

Soft Matter, 14(45):9083-9087, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Critical Casimir interactions and percolation: The quantitative description of critical fluctuations

Vasilyev, O.

Physical Review E, 98(6), American Physical Society, Melville, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Shear-density coupling for a compressible single-component yield-stress fluid

Gross, M., Varnik, F.

Soft Matter, 14(22):4577-4590, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Shape-dependent guidance of active Janus particles by chemically patterned surfaces

Uspal, W. E., Popescu, M. N., Tasinkevych, M., Dietrich, S.

New Journal of Physics, 20, IOP Publishing, Bristol, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Extrapolation to nonequilibrium from coarse-grained response theory

Basu, U., Helden, L., Krüger, M.

Physical Review Letters, 120(18), American Physical Society, Woodbury, N.Y., 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Directed Flow of Micromotors through Alignment Interactions with Micropatterned Ratchets

Katuri, J., Caballero, D., Voituriez, R., Samitier, J., Sánchez, S.

ACS Nano, 12(7):7282-7291, American Chemical Society, Washington, DC, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Spontaneous symmetry breaking of charge-regulated surfaces

Majee, A., Bier, M., Podgornik, R.

Soft Matter, 14(6):985-991, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Electrostatic interaction between dissimilar colloids at fluid interfaces

Majee, A., Schmetzer, T., Bier, M.

Physical Review E, 97(4), American Physical Society, Melville, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Wetting transition of a cylindrical cavity engraved on a hydrophobic surface

Kim, H., Ha, M. Y., Jang, J.

The Journal of Physical Chemistry C, 122(4):2122-2126, American Chemical Society, Washington, D.C., 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Curvature corrections to the nonlocal interfacial model for short-ranged forces

Romero-Enrique, J.M., Squarcini, Alessio, Parry, A. O., Goldbart, P. M.

Physical Review E, 97(6), American Physical Society, Melville, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


A probabilistic model for the numerical solution of initial value problems
A probabilistic model for the numerical solution of initial value problems

Schober, M., Särkkä, S., Philipp Hennig,

Statistics and Computing, Springer US, 2018 (article)

Abstract
We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recast as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

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PDF Code DOI Project Page [BibTex]


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Effective squirmer models for self-phoretic chemically active spherical colloids

Popescu, M. N., Uspal, W. E., Eskandari, Z., Tasinkevych, M., Dietrich, S.

The European Physical Journal E, 41(12), EDP Sciences; Società Italiana di Fisica; Springer, Les Ulis; Bologna; Heidelberg, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Two time scales for self and collective diffusion near the critical point in a simple patchy model for proteins with floating bonds

Bleibel, J., Habiger, M., Lütje, M., Hirschmann, F., Roosen-Runge, F., Seydel, T., Zhang, F., Schreiber, F., Oettel, M.

Soft Matter, 14(39):8006-8016, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Globulelike Conformation and Enhanced Diffusion of Active Polymers

Bianco, V., Locatelli, E., Malgaretti, P.

Physical Review Letters, 121(21), American Physical Society, Woodbury, N.Y., 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Rheological behavior of colloidal suspension with long-range interactions

Arietaleaniz, S., Malgaretti, P., Pagonabarraga, I., Hidalgo, R. C.

Physical Review E, 98(4), American Physical Society, Melville, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Solvent coarsening around colloids driven by temperature gradients

Roy, S., Dietrich, S., Maciolek, A.

Physical Review E, 97(4), American Physical Society, Melville, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Cross-stream migration of active particles

Katuri, J., Uspal, W., Simmchen, J., López, A. M., Sanchez, S.

Science Advances, 4(1), AAAS, Washington, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation

Janssen, M., Bier, M.

Physical Review E, 97(5), American Physical Society, Melville, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Coalescence preference and droplet size inequality during fluid phase segregation

Roy, S.

EPL, 121(3), EDP Science, Les-Ulis, 2018 (article)

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DOI [BibTex]


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Structure of interfaces at phase coexistence. Theory and numerics

Delfino, G., Selke, W., Squarcini, A.

Journal of Statistical Mechanics: Theory and Experiment, 2018, Institute of Physics Publishing, Bristol, England, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Power spectral density of a single Brownian trajectory: what one can and cannot learn from it

Krapf, D., Marinari, E., Metzler, Ralf, Oshanin, Gleb, Xu, Xinran, Squarcini, A.

New Journal of Physics, 20, IOP Publishing, Bristol, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Diffusiophoretically induced interactions between chemically active and inert particles

Reigh, Shang-Yik, Chuphal, P., Thakur, S., Kapral, R.

Soft Matter, 14(29):6043-6057, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Collective behavior of colloids due to critical Casimir interactions

Maciolek, A., Dietrich, S.

Reviews of Modern Physics, 90(4), American Physical Society, Minneapolis, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Heat radiation and transfer in confinement

Asheichyk, K., Krüger, M.

Physical Review B, 98(19), American Physical Society, Woodbury, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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A ferronematic slab in external magnetic fields

Zarubin, G., Bier, M., Dietrich, S.

Soft Matter, 14(48):9806-9818, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Surface-induced nonequilibrium dynamics and critical Casimir forces for model B in film geometry

Gross, M., Gambassi, A., Dietrich, S.

Physical Review E, 98(3), American Physical Society, Melville, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Phase separation around a heated colloid in bulk and under confinement

Roy, S., Maciolek, A.

Soft Matter, 14(46):9326-9335, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Electrolyte solutions at heterogeneously charged substrates

Mu\ssotter, M., Bier, M., Dietrich, S.

Soft Matter, 14(20):4126-4140, Royal Society of Chemistry, Cambridge, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Vapor nucleation paths in lyophobic nanopores

Tinti, A., Giacomello, A., Casciola, C. M.

European Physical Journal E, 41(4), Springer, Berlin, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Fuel-Free Nanocap-Like Motors Actuated Under Visible Light

Wang, Xu, Sridhar, Varun, Guo, Surong, Talebi, Nahid, Miguel-Lopez, Albert, Hahn, Kersten, van Aken, Peter A., Sánchez, Samuel

Advanced Functional Materials, 28(25), Wiley-VCH Verlag GmbH, Weinheim, 2018 (article)

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DOI [BibTex]

DOI [BibTex]