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Self-propelling microparticles are often proposed as synthetic models for biological microswimmers, yet they lack the internally regulated adaptation of their biological counterparts. Conversely, adaptation can be encoded in larger-scale soft-robotic devices but remains elusive to transfer to the colloidal scale. Here, we create responsive microswimmers, powered by electro-hydrodynamic flows, which can adapt their motility via internal reconfiguration. Using sequential capillary assembly, we fabricate deterministic colloidal clusters comprising soft thermo-responsive microgels and light-absorbing particles. Light absorption induces preferential local heating and triggers the volume phase transition of the microgels, leading to an adaptation of the clusters’ motility, which is orthogonal to their propulsion scheme. We rationalize this response via the coupling between self-propulsion and variations of particle shape and dielectric properties upon heating. Harnessing such coupling allows for strategies to achieve local dynamical control with simple illumination patterns, revealing exciting opportunities for developing tactic active materials.
L. Alvarez; M. A. Fernandez-Rodriguez; A. Alegria; S. Arrese-Igor; K. Zhao; M. Kröger; Lucio Isa. Reconfigurable artificial microswimmers with internal feedback. Nature Communications 2021, 12, 1 .
AMA StyleL. Alvarez, M. A. Fernandez-Rodriguez, A. Alegria, S. Arrese-Igor, K. Zhao, M. Kröger, Lucio Isa. Reconfigurable artificial microswimmers with internal feedback. Nature Communications. 2021; 12 ():1.
Chicago/Turabian StyleL. Alvarez; M. A. Fernandez-Rodriguez; A. Alegria; S. Arrese-Igor; K. Zhao; M. Kröger; Lucio Isa. 2021. "Reconfigurable artificial microswimmers with internal feedback." Nature Communications 12, no. : 1.
Based on hospital capacities, facts from past experience with the coronavirus disease 2019 (COVID-19) virus and the number of dark infections during the second wave (
Reinhard Schlickeiser; Martin Kröger. Reasonable Limiting of 7-Day Incidence per Hundred Thousand and Herd Immunization in Germany and Other Countries. COVID 2021, 1, 130 -136.
AMA StyleReinhard Schlickeiser, Martin Kröger. Reasonable Limiting of 7-Day Incidence per Hundred Thousand and Herd Immunization in Germany and Other Countries. COVID. 2021; 1 (1):130-136.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2021. "Reasonable Limiting of 7-Day Incidence per Hundred Thousand and Herd Immunization in Germany and Other Countries." COVID 1, no. 1: 130-136.
An analytic evaluation of the peak time of a disease allows for the installment of effective epidemic precautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of the fraction of infected persons during an outbreak within the susceptible–infectious–recovered/removed (SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existing approximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation that allow one to come up with different explicit expressions for the peak time of the infected compartment (Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressions for any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far (countries, ss, cities). For small populations with less than hundreds of individuals (families, small towns), however, the approximant MT outperforms the other approximants. To be able to compare the various approaches, we clarify the equivalence between the four-parametric dimensional SIR equations and their two-dimensional dimensionless analogue. Using Covid-19 data from various countries and sources we identify the relevant regime within the parameter space of the SIR model.
Martin Kröger; Mustafa Turkyilmazoglu; Reinhard Schlickeiser. Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use? Physica D. Nonlinear Phenomena 2021, 425, 132981 .
AMA StyleMartin Kröger, Mustafa Turkyilmazoglu, Reinhard Schlickeiser. Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use? Physica D. Nonlinear Phenomena. 2021; 425 ():132981.
Chicago/Turabian StyleMartin Kröger; Mustafa Turkyilmazoglu; Reinhard Schlickeiser. 2021. "Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?" Physica D. Nonlinear Phenomena 425, no. : 132981.
Conformations, entanglements and dynamics in attractive polymer nanocomposites are investigated in this work by means of coarse-grained molecular dynamics simulation, for both weak and strong confinements, in the presence of nanoparticles (NPs) at NP volume fractions ϕ up to 60%. We show that the behavior of the apparent tube diameter dapp in such nanocomposites can be greatly different from nanocomposites with nonattractive interactions. We find that this effect originates, based on a mean field argument, from the geometric confinement length dgeo at strong confinement (large ϕ) and not from the bound polymer layer on NPs (interparticle distance ID <2Rg) as proposed recently based on experimental measurements. Close to the NP surface, the entangled polymer mobility is reduced in attractive nanocomposites but still faster than the NP mobility for volume fractions beyond 20%. Furthermore, entangled polymer dynamics is hindered dramatically by the strong confinement created by NPs. For the first time using simulations, we show that the entangled polymer conformation, characterized by the polymer radius of gyration Rg and form factor, remains basically unperturbed by the presence of NPs up to the highest volume fractions studied, in agreement with various experiments on attractive nanocomposites. As a side-result we demonstrate that the loose concept of ID can be made a microscopically well defined quantity using the mean pore size of the NP arrangement.
Ahmad Moghimikheirabadi; Martin Kroger; Argyrios V. Karatrantos. Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites. Soft Matter 2021, 17, 6362 -6373.
AMA StyleAhmad Moghimikheirabadi, Martin Kroger, Argyrios V. Karatrantos. Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites. Soft Matter. 2021; 17 (26):6362-6373.
Chicago/Turabian StyleAhmad Moghimikheirabadi; Martin Kroger; Argyrios V. Karatrantos. 2021. "Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites." Soft Matter 17, no. 26: 6362-6373.
We investigate the flow of viscous interfaces carrying an insoluble surface active material, using numerical methods to shed light on the complex interplay between Marangoni stresses, compressibility, and surface shear and dilatational viscosities. We find quantitative relations between the drag on a particle and interfacial properties as they are required in microrheology, i.e., going beyond the asymptotic limits. To this end, we move a spherical particle probe at constant tangential velocity, symmetrically immersed at either the incompressible or compressible interface, in the presence and absence of surfactants, for a wide range of system parameters. A full three-dimensional finite element calculation is used to reveal the intimate coupling between the bulk and interfacial flows and the subtle effects of the different physical effects on the mixed-type velocity field that affects the drag coefficient, both in the bulk and at the interface. For an inviscid interface, the directed motion of the particle leads to a gradient in the concentration of the surface active species, which in turn drives a Marangoni flow in the opposite direction, giving rise to a force exerted on the particle. We show that the drag coefficient at incompressible interfaces is independent of the origin of the incompressibility (dilatational viscosity, Marangoni effects or a combination of both) and that its higher value can not only be related to the Marangoni effects, as suggested earlier. In confined flows, we show how the interface shear viscosity suppresses the vortex at the interface, generates a uniform flow, and consequently increases the interface compressibility and the Marangoni force on the particle. We mention available experimental data and provide analytical approximations for the drag coefficient that can be used to extract surface viscosities.
Meisam Pourali; Martin Kröger; Jan Vermant; Patrick D. Anderson; Nick O. Jaensson. Drag on a spherical particle at the air–liquid interface: Interplay between compressibility, Marangoni flow, and surface viscosities. Physics of Fluids 2021, 33, 062103 .
AMA StyleMeisam Pourali, Martin Kröger, Jan Vermant, Patrick D. Anderson, Nick O. Jaensson. Drag on a spherical particle at the air–liquid interface: Interplay between compressibility, Marangoni flow, and surface viscosities. Physics of Fluids. 2021; 33 (6):062103.
Chicago/Turabian StyleMeisam Pourali; Martin Kröger; Jan Vermant; Patrick D. Anderson; Nick O. Jaensson. 2021. "Drag on a spherical particle at the air–liquid interface: Interplay between compressibility, Marangoni flow, and surface viscosities." Physics of Fluids 33, no. 6: 062103.
With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to a fourth compartment, V, of vaccinated persons. This extension involves the time t-dependent effective vaccination rate,
Reinhard Schlickeiser; Martin Kröger. Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. Physics 2021, 3, 386 -426.
AMA StyleReinhard Schlickeiser, Martin Kröger. Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. Physics. 2021; 3 (2):386-426.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2021. "Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations." Physics 3, no. 2: 386-426.
Supramolecular polymers are fascinating materials due to their strikingly self-healing capabilities empowered by reversible bonds. However, due to the lack of knowledge about the molecular structure evolution at the fractured interfaces, there is no existing theory to explain and predict the diverse healing times of different supramolecular materials observed in experiments. Here, we systematically study the self-adhesion of both unentangled and entangled supramolecular polymer networks through molecular simulations. We find that the recovery of macroscopic interfacial strength almost linearly depends on the microscopic molecular formations at fractured interfaces of supramolecular polymers, including reversible bonds and entanglements (entangled systems only). More importantly, we place the healing time into the context of intrinsic relaxation timescales of supramolecular polymer networks. It is found that the intrinsic sticky Rouse time features the self-adhesion process of all fractured supramolecular polymers, representing the full recovery of interfacial strength. At this critical timescale, two things happened to guarantee the full recovery of fractured systems: (i) polymer chains have diffused across the fractured interface with a displacement comparable to their sizes; (ii) the crossed stickers and polymer chains have updated their reversible bonds and entanglements (entangled systems only), respectively. The clear molecular description and suggested characteristic self-adhesion time will help the molecular design of supramolecular polymers.
Zhiqiang Shen; Huilin Ye; Qiming Wang; Martin Kröger; Ying Li. Sticky Rouse Time Features the Self-Adhesion of Supramolecular Polymer Networks. Macromolecules 2021, 54, 5053 -5064.
AMA StyleZhiqiang Shen, Huilin Ye, Qiming Wang, Martin Kröger, Ying Li. Sticky Rouse Time Features the Self-Adhesion of Supramolecular Polymer Networks. Macromolecules. 2021; 54 (11):5053-5064.
Chicago/Turabian StyleZhiqiang Shen; Huilin Ye; Qiming Wang; Martin Kröger; Ying Li. 2021. "Sticky Rouse Time Features the Self-Adhesion of Supramolecular Polymer Networks." Macromolecules 54, no. 11: 5053-5064.
With the now available vaccination against Covid-19 it is quantitatively explored how vaccination campaigns influence the mathematical modeling of epidemics. The standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to the fourth compartment V of vaccinated persons and the vaccination rate v(t) that regulates the relation between susceptible and vaccinated persons. The vaccination rate v(t) competes with the infection (a(t)) and recovery (\mu(t)) rates in determining the time evolution of epidemics. In order for a pandemic outburst with rising rates of new infections it is required that k+b<1-2\eta, where k=\mu_0/a_0 and b=v_0/a_0 denote the initial ratios of the three rates, respectively, and \eta << 1 is the initial fraction of infected persons. Exact analytical inverse solutions t(Q) for all relevant quantities Q=[S,I,R,V] of the resulting SIRV-model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy yielding the explicit time-dependences Q(t) by inverting the Lambert functions. The values of the three parameters k, b and \eta completely determine the reduced time evolution the SIRV-quantities Q(\tau). The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from Israel this can happen in all countries considered.
Reinhard Schlickeiser; Martin Kröger. Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. 2021, 1 .
AMA StyleReinhard Schlickeiser, Martin Kröger. Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. . 2021; ():1.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2021. "Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations." , no. : 1.
The earlier analytical analysis (part A) of the Susceptible-Infectious-Recovered (SIR) epidemics model for a constant ratio $k$ of infection to recovery rates is extended here to the semi-time case which is particularly appropriate for modeling the temporal evolution of later (than the first) pandemic waves when a greater population fraction from the first wave has been infected. In the semi-time case the SIR model does not describe the quantities in the past; instead they only hold for times later than the initial time $t=0$ of the newly occurring wave. Simple exact and approximative expressions are derived for the final and maximum values of the infected, susceptible and revovered/removed population fractions as well the daily rate and cumulative number of new infections. It is demonstrated that two types of temporal evolution of the daily rate of new infections $j(\tau)$ occur depending on the values of $k$ and the initial value of the infected fraction $I(0)=\eta$: in the decay case for $k\ge 1-2\eta $ the daily rate monotonically decreases at all positive times from its initial maximum value $j(0)=\eta (1-\eta )$. Alternatively, in the peak case for $k<1-2\eta $ the daily rate attains a maximum at a finite positive time. By comparing the approximated analytical solutions for $j(\tau )$ and $J(\tau)$ with the exact ones obtained by numerical integration, it is shown that the analytical approximations are accurate within at most only 2.5 percent. It is found that the initial fraction of infected persons sensitively influences the late time dependence of the epidemics, the maximum daily rate and its peak time. Such dependencies do not exist in the earlier investigated all-time case.
Reinhard Schlickeiser; Martin Kröger. Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case. Journal of Physics A: Mathematical and Theoretical 2021, 54, 175601 .
AMA StyleReinhard Schlickeiser, Martin Kröger. Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case. Journal of Physics A: Mathematical and Theoretical. 2021; 54 (17):175601.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2021. "Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case." Journal of Physics A: Mathematical and Theoretical 54, no. 17: 175601.
We start out by deriving simple analytic expressions for all measurable amounts of cases and fatalities during a pandemic evolution exhibiting multiple waves, described by the semi-time SIR model. The approximant shares all relevant features with the exact solution, including time and position of the peak of daily new infections, as well as the asymptotic behaviors at small and large times. We derive exact analytic expressions for the early doubling time, late half decay time, and a half-early peak law, characterizing the dynamical evolution. We show, in particular, how the asymmetry of the first epidemic wave and its exponential tails are affected by the initial conditions; a feature that has no analogue in the all-time SIR model. We apply the approach to available data from different continents. Our analysis reveals that the immunity is very strongly increasing during the 2nd wave, while it was still at a very moderate level of a few percent in several countries at the end of the first wave. The wave-specific SIR parameters describing the infection and recovery rates we find to behave in a similar fashion, while their ratio k was decreasing only by a about 5% for most countries. Still, an apparently moderate change of k can have significant consequences for the relevant numbers like the final amount of infected or deceased population. As we show, the probability for an additional wave is however low in several countries due to the fraction of immune inhabitants at the end of the 2nd wave, irrespective the currently ongoing vaccination efforts. We compare with alternate approaches.
Martin Kröger; Reinhard Schlickeiser. Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate. 2021, 1 .
AMA StyleMartin Kröger, Reinhard Schlickeiser. Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate. . 2021; ():1.
Chicago/Turabian StyleMartin Kröger; Reinhard Schlickeiser. 2021. "Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate." , no. : 1.
Due to the current COVID-19 epidemic plague hitting the worldwide population it is of utmost medical, economical and societal interest to gain reliable predictions on the temporal evolution of the spreading of the infectious diseases in human populations. Of particular interest are the daily rates and cumulative number of new infections, as they are monitored in infected societies, and the influence of non-pharmaceutical interventions due to different lockdown measures as well as their subsequent lifting on these infections. Estimating quantitatively the influence of a later lifting of the interventions on the resulting increase in the case numbers is important to discriminate this increase from the onset of a second wave. The recently discovered new analytical solutions of Susceptible-Infectious-Recovered (SIR) model allow for such forecast. In particular, it is possible to test lockdown and lifting interventions because the new solutions hold for arbitrary time dependence of the infection rate. Here we present simple analytical approximations for the rate and cumulative number of new infections.
Reinhard Schlickeiser; M. Kröger. Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions. Frontiers in Physics 2021, 8, 1 .
AMA StyleReinhard Schlickeiser, M. Kröger. Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions. Frontiers in Physics. 2021; 8 ():1.
Chicago/Turabian StyleReinhard Schlickeiser; M. Kröger. 2021. "Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions." Frontiers in Physics 8, no. : 1.
Based on the hospital capacities, facts from the past experience with the Covid-19 virus and the dark number of infections D=10D_{10} a reasonable limiting value of 170/D_{10} for the monitored 7-day incidence per 100000 persons value (MSDIHT) in Germany is calculated. If the MSDIHT is held below this limiting value the German hospital system can cope with the number of new seriously infected persons without any triage decisions. A significant improvement to an almost complete testing of the population would lead to dramatic reduction of the current dark numer value to D_{10}=0.1 so that ten times higher MSDIHT values of 1700 are acceptable. Such a high limiting value would spare Germany from its currently imposed strict lockdown. The costs for such extensive and complete testing campaigns are highly justified as they are orders of magnitudes below the estimated economical costs of more than 3.6 billion Euros for each lockdown day.
Martin Kröger; Reinhard Schlickeiser. Reasonable Limiting 7-day Incidence per Hundred Thousand Value in Germany. 2021, 1 .
AMA StyleMartin Kröger, Reinhard Schlickeiser. Reasonable Limiting 7-day Incidence per Hundred Thousand Value in Germany. . 2021; ():1.
Chicago/Turabian StyleMartin Kröger; Reinhard Schlickeiser. 2021. "Reasonable Limiting 7-day Incidence per Hundred Thousand Value in Germany." , no. : 1.
This editorial deals with the most cited papers published in the years 2018–2019 in the section “Polymer Theory and Simulation” of the journal Polymers
Martin Kröger. Top Cited 2018–2019 Papers in the Section “Polymer Theory and Simulation”. Polymers 2020, 13, 43 .
AMA StyleMartin Kröger. Top Cited 2018–2019 Papers in the Section “Polymer Theory and Simulation”. Polymers. 2020; 13 (1):43.
Chicago/Turabian StyleMartin Kröger. 2020. "Top Cited 2018–2019 Papers in the Section “Polymer Theory and Simulation”." Polymers 13, no. 1: 43.
M Kröger; R Schlickeiser. Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor. Journal of Physics A: Mathematical and Theoretical 2020, 53, 505601 .
AMA StyleM Kröger, R Schlickeiser. Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor. Journal of Physics A: Mathematical and Theoretical. 2020; 53 (50):505601.
Chicago/Turabian StyleM Kröger; R Schlickeiser. 2020. "Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor." Journal of Physics A: Mathematical and Theoretical 53, no. 50: 505601.
We investigate nanoparticle (NP) dispersion, polymer conformations, entanglements and dynamics in ionic nanocomposites. To this end, we study nanocomposite systems with various spherical NP loadings, three different molecular weights, two different Bjerrum lengths, and two types of charge-sequenced polymers by means of molecular dynamics simulations. NP dispersion can be achieved in either oligomeric or entangled polymeric matrices due to the presence of electrostatic interactions. We show that the overall conformations of ionic oligomer chains, as characterized by their radii of gyration, are affected by the presence and the amount of charged NPs, while the dimensions of charged entangled polymers remain unperturbed. Both the dynamical behavior of polymers and NPs, and the lifetime and amount of temporary crosslinks, are found to depend on the ratio between the Bjerrum length and characteristic distance between charged monomers. Polymer–polymer entanglements start to decrease beyond a certain NP loading. The dynamics of ionic NPs and polymers is very different compared with their non-ionic counterparts. Specifically, ionic NP dynamics is getting enhanced in entangled matrices and also accelerates with the increase of NP loading.
Ahmad Moghimikheirabadi; Clément Mugemana; Martin Kröger; Argyrios Karatrantos. Polymer Conformations, Entanglements and Dynamics in Ionic Nanocomposites: A Molecular Dynamics Study. Polymers 2020, 12, 2591 .
AMA StyleAhmad Moghimikheirabadi, Clément Mugemana, Martin Kröger, Argyrios Karatrantos. Polymer Conformations, Entanglements and Dynamics in Ionic Nanocomposites: A Molecular Dynamics Study. Polymers. 2020; 12 (11):2591.
Chicago/Turabian StyleAhmad Moghimikheirabadi; Clément Mugemana; Martin Kröger; Argyrios Karatrantos. 2020. "Polymer Conformations, Entanglements and Dynamics in Ionic Nanocomposites: A Molecular Dynamics Study." Polymers 12, no. 11: 2591.
We identify the influence of dipolar and steric interactions on the Brownian and Néel contributions to the magnetization dynamics of magnetic nanoparticles from extensive computer simulations using a combined Brownian dynamics/Monte-Carlo method.
Patrick Ilg; Martin Kröger. Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation. Physical Chemistry Chemical Physics 2020, 22, 22244 -22259.
AMA StylePatrick Ilg, Martin Kröger. Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation. Physical Chemistry Chemical Physics. 2020; 22 (39):22244-22259.
Chicago/Turabian StylePatrick Ilg; Martin Kröger. 2020. "Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation." Physical Chemistry Chemical Physics 22, no. 39: 22244-22259.
We use an efficient molecular theory approach to study electrokinetic flow within a pH-responsive nanopore grafted with a polyelectrolyte (PE) brush. The flow rate, migration and convective conductance, electric potential and velocity fields, species distributions and the degree of ionization of the weak PE functional groups and nanopore selectivity are obtained and interpreted while considering pH-induced surface charges. The theory is generally based on writing the overall free energy of the system including the entropies arising from the conformations of flexible, excluded volume chains, the mixing of mobile species, electrostatic contribution, and the free energy due to the chemical acid–base equilibrium reactions. We demonstrate how, by controlling the bulk salt concentration, pH, surface grafting density, and PE drag coefficient, the flow inside the pore can be controlled. Generally, the flow rate gets enhanced upon decreasing pH, but the effect of salt concentration is more complex. As long as the pH is small (large), the flow rate decreases (increases) by increasing the salt concentration, while a nonmonotonic trend is evident at moderate pH values. We find that, when the PE drag coefficient is high (low), the flow rate decreases (increases) by increasing surface grafting density. For intermediate drag coefficients, the flow rate varies nonmonotonically with surface grafting density. It is observed that the convective ionic conductance obeys almost the same trend as the flow rate. It is also illustrated that the mean degree of ionization of the polymer chains and the migration ionic conductance enhance on increasing the background salt concentration, whereas the opposite is true for nanopore selectivity. However, when very low salt concentration is accompanied by a high pH value, there is a minimum in the nanopore selectivity. The present approach allows investigation of the application of PE-coated nanopores as smart nanovalves.
Morteza Sadeghi; Mohammad Hassan Saidi; Ali Moosavi; Martin Kröger. Tuning Electrokinetic Flow, Ionic Conductance, and Selectivity in a Solid-State Nanopore Modified with a pH-Responsive Polyelectrolyte Brush: A Molecular Theory Approach. The Journal of Physical Chemistry C 2020, 124, 1 .
AMA StyleMorteza Sadeghi, Mohammad Hassan Saidi, Ali Moosavi, Martin Kröger. Tuning Electrokinetic Flow, Ionic Conductance, and Selectivity in a Solid-State Nanopore Modified with a pH-Responsive Polyelectrolyte Brush: A Molecular Theory Approach. The Journal of Physical Chemistry C. 2020; 124 (34):1.
Chicago/Turabian StyleMorteza Sadeghi; Mohammad Hassan Saidi; Ali Moosavi; Martin Kröger. 2020. "Tuning Electrokinetic Flow, Ionic Conductance, and Selectivity in a Solid-State Nanopore Modified with a pH-Responsive Polyelectrolyte Brush: A Molecular Theory Approach." The Journal of Physical Chemistry C 124, no. 34: 1.
Due to the current COVID-19 epidemic plague hitting the worldwide population it is of utmost medical, economical and societal interest to gain reliable predictions on the temporal evolution of the spreading of the infectious diseases in human populations. Of particular interest are the daily rates and cumulative number of new infections, as they are monitored in infected societies, and the influence of non-pharmaceutical interventions due to different lockdown measures as well as their subsequent lifting on these infections. Estimating quantitatively the influence of a later lifting of the interventions on the resulting increase in the case numbers is important to discriminate this increase from the onset of a second wave. The recently discovered new analytical solutions of Susceptible-Infectious-Recovered (SIR) model allow for such forecast and the testing of lockdown and lifting interventions as they hold for arbitrary time dependence of the infection rate. Here we present simple analytical approximations for the rate and cumulative number of new infections.
Reinhard Schlickeiser; Martin Kroger. Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions. 2020, 1 .
AMA StyleReinhard Schlickeiser, Martin Kroger. Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions. . 2020; ():1.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kroger. 2020. "Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions." , no. : 1.
We revisit the Susceptible-Infectious-Recovered/Removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic solution to the SIR model is known in parametric form for the case of a time-independent infection rate, we derive an analytic solution for the more general case of a time-dependent infection rate, that is not limited to a certain range of parameter values. Our approach allows us to derive several exact analytic results characterizing all quantities, and moreover explicit, non-parametric, and accurate analytic approximants for the solution of the SIR model for time-independent infection rates. We relate all parameters of the SIR model to a measurable, usually reported quantity, namely the cumulated number of infected population and its first and second derivatives at an initial time t=0, where data is assumed to be available. We address the question on how well the differential rate of infections is captured by the Gauss model (GM). To this end we calculate the peak height, width, and position of the bell-shaped rate analytically. We find that the SIR is captured by the GM within a range of times, which we discuss in detail. We prove that the SIR model exhibits an asymptotic behavior at large times that is different from the logistic model, while the difference between the two models still decreases with increasing reproduction factor. This part A of our work treats the original SIR model to hold at all times, while this assumption will be released in part B. Releasing this assumption allows to formulate initial conditions incompatible with the original SIR model.
Martin Kröger; Reinhard Schlickeiser. Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor. 2020, 1 .
AMA StyleMartin Kröger, Reinhard Schlickeiser. Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor. . 2020; ():1.
Chicago/Turabian StyleMartin Kröger; Reinhard Schlickeiser. 2020. "Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor." , no. : 1.
The Gauss model for the time evolution of the first corona pandemic wave is rendered useful in the estimation of peak times, amount of required equipment, and the forecasting of fade out times. At the same time, it is probably the simplest analytically tractable model that allows us to quantitatively forecast the time evolution of infections and fatalities during a pandemic wave. In light of the various descriptors, such as doubling times and reproduction factors, currently in use to judge the lockdowns and other measures that aim to prevent spreading of the virus, we hereby provide both exact and simple approximate relationships between the two relevant parameters of the Gauss model (peak time and width), the transient behavior of two versions of doubling times, and three variants of reproduction factors, including basic reproduction numbers.
Martin Kröger; Reinhard Schlickeiser. Gaussian Doubling Times and Reproduction Factors of the COVID-19 Pandemic Disease. Frontiers in Physics 2020, 8, 1 .
AMA StyleMartin Kröger, Reinhard Schlickeiser. Gaussian Doubling Times and Reproduction Factors of the COVID-19 Pandemic Disease. Frontiers in Physics. 2020; 8 ():1.
Chicago/Turabian StyleMartin Kröger; Reinhard Schlickeiser. 2020. "Gaussian Doubling Times and Reproduction Factors of the COVID-19 Pandemic Disease." Frontiers in Physics 8, no. : 1.