Equilibrium Population Research Articles

Synthesis and up-conversion luminescence of erbium-doped yttrium silicate single crystal nanoparticles tailored by the mesoporous silica template

Erbium-activated yttrium silicate nanoparticles were tailored using a mesoporous silica template. Transmission electron microscopy (TEM) revealed that the synthesized particles are single crystals of yttrium pyrosilicate (α−Y2Si2O7:Er), possessing a spherical shape (with an average size of about 210 nm) and a narrow size distribution. Up-conversion luminescence of the synthesized particles was investigated in the green spectral region under excitation by a laser diode operating at a wavelength of 808 nm. In the range of 510-580 nm, intense narrow lines with a Lorentzian shape were observed, attributed to radiative transitions from two thermally coupled energy levels of the Er3+ ion [2H11/2→4I15/2 (520–540 nm) and 4S3/2→4I15/2 (545–570 nm)]. It was experimentally demonstrated that within the temperature range of 250–520 K, the equilibrium populations of the 2H11/2 and 4S3/2 levels follow the Boltzmann distribution. This result provides a basis for the potential use of the synthesized particles as temperature sensors in various applications, including biomedical ones.

Carbon monoxide cooling in radiative transfer modelling of supernovae

ABSTRACT Carbon monoxide (CO) emission has been observed in a number of core-collapse supernovae (SNe) and is known to be an important coolant at late times. We have implemented a chemical reaction network in the radiative-transfer code cmfgen to investigate the formation of CO and its impact on SN ejecta. We calculate two 1D SN models with and without CO: a BSG explosion model at one nebular epoch and a full time-sequence (50–300 d) for a red supergiant explosion. In both models, CO forms at nebular times in the dense, inner regions at velocities <2000 km s$^{-1}$ where line emission from CO can dominate the cooling and reduce the local temperature by as much as a factor of 2, weakening emission lines and causing the optical light curve to fade faster. That energy is instead emitted in CO bands, primarily the fundamental band at $\sim 4.5 \mathrm{\mu m}$, which accounts for up to 20 per cent of the total luminosity at late times. However, the non-monotonic nature of the CO cooling function can cause numerical difficulties and introduce multiple temperature solutions. This issue is compounded by the sensitivity of the CO abundance to a few reaction rates, many of which have large uncertainties or disparate values across literature sources. Our results also suggest that, in many SNe, CO-level populations are far from their local thermodynamic equilibrium values. Unfortunately, accurate collisional data, necessary to compute non-local thermodynamic equilibrium populations, are limited to a few transitions.

M6A Methylation of Transcription Leader Sequence of SARS-CoV-2 Impacts Discontinuous Transcription of Subgenomic mRNAs.

The SARS-CoV-2 genome has been shown to be m6A methylated at several positions in vivo. Strikingly, a DRACH motif, the recognition motif for adenosine methylation, resides in the core of the transcriptional regulatory leader sequence (TRS-L) at position A74, which is highly conserved and essential for viral discontinuous transcription. Methylation at position A74 correlates with viral pathogenicity. Discontinuous transcription produces a set of subgenomic mRNAs that function as templates for translation of all structural and accessory proteins. A74 is base-paired in the short stem-loop structure 5'SL3 that opens during discontinuous transcription to form long-range RNA-RNA interactions with nascent (-)-strand transcripts at complementary TRS-body sequences. A74 can be methylated by the human METTL3/METTL14 complex in vitro. Here, we investigate its impact on the structural stability of 5'SL3 and the long-range TRS-leader:TRS-body duplex formation necessary for synthesis of subgenomic mRNAs of all four viral structural proteins. Methylation uniformly destabilizes 5'SL3 and long-range duplexes and alters their relative equilibrium populations, suggesting that the m6A74 modification acts as a regulator for the abundance of viral structural proteins due to this destabilization.

Boundary Effects Cause False Signals of Range Expansions in Population Genomic Data.

Studying range expansions is central for understanding genetic variation through space and time as well as for identifying refugia and biological invasions. Range expansions are characterized by serial founder events causing clines of decreasing genetic diversity away from the center of origin and asymmetries in the two-dimensional allele frequency spectra. These asymmetries, summarized by the directionality index (ψ), are sensitive to range expansions and persist for longer than clines in genetic diversity. In continuous and finite meta-populations, genetic drift tends to be stronger at the edges of the species distribution in equilibrium populations and populations undergoing range expansions alike. Such boundary effects are expected to affect geographic patterns in genetic diversity and ψ. Here we demonstrate that boundary effects cause high false positive rates in equilibrium meta-populations when testing for range expansions. In the simulations, the absolute value of ψ (|ψ|) in equilibrium data sets was proportional to the fixation index (FST). By fitting signatures of range expansions as a function of ɛ |ψ|/FST and geographic clines in ψ, strong evidence for range expansions could be detected in data from a recent rapid invasion of the cane toad, Rhinella marina, in Australia, but not in 28 previously published empirical data sets from Australian scincid lizards that were significant for the standard range expansion tests. Thus, while clinal variation in ψ is still the most sensitive statistic to range expansions, to detect true signatures of range expansions in natural populations, its magnitude needs to be considered in relation to the overall levels of genetic structuring in the data.

Understanding the Fast-Triggering Unfolding Dynamics of FK-11 upon Photoexcitation of Azobenzene.

Photoswitchable molecules can control the activity and functions of biomolecules by triggering conformational changes. However, it is still challenging to fully understand such fast-triggering conformational evolution from nonequilibrium to equilibrium distribution at the molecular level. Herein, we successfully simulated the unfolding of the FK-11 peptide upon the photoinduced trans-to-cis isomerization of azobenzene based on the Markov state model. We found that the ensemble of FK-11 contains five conformational states, constituting two unfolding pathways. More intriguingly, we observed the microsecond-scale conformational propagation of the FK-11 peptide from the fully folded state to the equilibrium populations of the five states. The computed CD spectra match well with the experimental data, validating our simulation method. Overall, our study not only offers a protocol to study the photoisomerization-induced conformational changes of enzymes but also could orientate the rational design of a photoswitchable molecule to manipulate biological functions.

Carrying Capacity of Low Earth Orbit Computed Using Source-Sink Models

The low-Earth-orbit (LEO) environment will likely experience an exponential growth of the anthropogenic space object population, also due to the many proposed large constellations, which could negatively affect the sustainability of the space environment if no proper regulatory actions are introduced. This paper introduces a methodology to analyze high-capacity sustainable solutions of the LEO region from 200 to 900 km altitude. Sustainability is assessed through the stable equilibrium points of a source-sink model called MIT Orbital Capacity Assessment Tool 3 (MOCAT-3). Capacity is estimated using an optimization procedure that aims to compute the optimal launch rate that maximizes the number of satellites in LEO, subject to a risk-rate constraint. Results show that the sustainable number of satellites increases with the risk rate constraint. Moreover, the resilience of the proposed solutions is tested against a more accurate time-varying atmospheric density model and perturbations of the initial equilibrium population. The compatibility of the proposed solutions with future traffic launches and a strategy to accommodate future traffic needs are presented. Limitations of the current work are discussed, chiefly the importance of validation of model coefficients and behavior before resulting capacity estimates are used to guide actual decision-making.

Population Balance Equations for Reactive Separation in Polymer Upcycling.

Many polymer upcycling efforts aim to convert plastic waste into high-value liquid hydrocarbons. However, the subsequent cleavage of middle distillates to light gases can be problematic. The reactor often contains a vapor phase (light gases and middle distillates) and a liquid phase (molten polymers and waxes with a suspended or dissolved catalyst). Because the catalyst resides in the liquid phase, middle distillates that partition into the vapor phase are protected against further cleavage into light gases. In this paper, we consider a simple reactive separation strategy, in which a gas outflow removes the volatile products as they form. We combine vapor-liquid equilibrium models and population balance equations (PBEs) to describe polymer upcycling in a two-phase semibatch reactor. The results suggest that the temperature, headspace volume, and flow rate of the reactor can be used to tune selectivity toward the middle distillates, in addition to the molecular mechanism of catalysis. We anticipate that two-phase reactor models will be important in many polymer upcycling processes and that reactive separation strategies will provide ways to boost the yield of the desired products in these cases.

Effect of multiply excited states to the EUV emission from yttrium-like tin

The spectral emission rate of yttrium-like tin (Sn11+) is investigated as the typical ion, which has a strong emission of extreme ultra-violet (EUV) light near the wavelength of 13.5 nm. The energy level structure of the tin ion is investigated using the non-relativesitic configuration average model to calculate the population in the local thermodynamic equilibrium, and the spectral structure of the unresolved transition array that has EUV emission is investigated based on the calculated atomic data using the HULLAC code. It is shown that the broad main peak is accompanied by the tail structure for shorter and longer wavelengths, which arises from multiply and inner-shell excited levels. The emission channels that significantly contribute to the spectrum are determined from a convergence analysis. The excited states below the ionization limit with a large population are shown to have a significant contribution to the emission.

Efficient enumeration and visualization of helix-coil ensembles

Helix-coil models are routinely used to interpret circular dichroism data of helical peptides or predict the helicity of naturally-occurring and designed polypeptides. However, a helix-coil model contains significantly more information than mean helicity alone, as it defines the entire ensemble—the equilibrium population of every possible helix-coil configuration—for a given sequence. Many desirable quantities of this ensemble are either not obtained as ensemble averages or are not available using standard helicity-averaging calculations. Enumeration of the entire ensemble can allow calculation of a wider set of ensemble properties, but the exponential size of the configuration space typically renders this intractable. We present an algorithm that efficiently approximates the helix-coil ensemble to arbitrary accuracy by sequentially generating a list of the M highest populated configurations in descending order of population. Truncating this list of (configuration, population) pairs at a desired accuracy provides an approximating sub-ensemble. We demonstrate several uses of this approach for providing insight into helix-coil ensembles and folding mechanisms, including landscape visualization.

Multi-strategy ratiometric luminescent thermometry based on Dy doped CaWO4 phosphors independent of excitation wavelength

This paper explores the detailed photoluminescence (PL) behaviors of Dy3+ doped CaWO4 (Dy:CaWO4) phosphors under multi-ultraviolet wavelength excitation. Moreover, it proposes multi-strategy ratiometric thermometry based on luminescence intensity ratio (LIR) from the transitions of thermally coupled energy levels (TCLs) of Dy3+. Under excitation of multiple ultraviolet wavelengths, the Dy:CaWO4 phosphors exhibited multi-wavelength responsive PL characteristics of Dy3+ with strong blue and yellow emissions from Dy3+ TCLs transitions. The temperature-dependent PL properties of Dy:CaWO4 phosphors were investigated over a temperature range of 300∼650 K. Multi-strategy ratiometric luminescent thermometry was examined under various excitation wavelengths by the thermal equilibrium population of Dy3+ TCLs. The proposed six LIR schemes based on the PL emissions of Dy3+ exhibited a good quantitative relationship with temperature. They showed well-luminescent thermometric behaviors with high absolute and relative sensitivities due to the largest energy gap of TCLs and a relatively larger LIR value. The thermometry properties of the multiple LIR schemes were independent of excitation wavelength, attributed to the stable site symmetry of Dy3+ and the thermal equilibrium population of TCLs under different excitation wavelengths. The multi-strategy ratiometric thermometry of Dy3+ demonstrated the merit of high sensitivity, excellent stability, and repeatability, indicating the potential luminescent thermometric application of Dy:CaWO4 phosphors.

The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory, and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated. Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer–resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density‐regulation functions are usually non‐linear and may exhibit convex or concave curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the Schoener model. More complex consumer dynamics show similarities to a Maynard Smith–Slatkin model. We show how population‐level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. We propose simple relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer–resource systems. Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time‐series from microbial food chains to fit population growth models as a test case for our theoretical predictions. Our results show that density‐regulation functions need to be chosen carefully as their shapes will depend on the study system's biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

Energy-Conserving and Thermally Corrected Neglect of Back-Reaction Approximation Method for Nonadiabatic Molecular Dynamics.

In this work, the energy-conserving and thermally corrected neglect of the back-reaction approximation approach for nonadiabatic molecular dynamics in extended atomistic systems is developed. The new approach introduces three key corrections to the original method: (1) it enforces the total energy conservation, (2) it introduces an explicit coupling of the system to its environment, and (3) it introduces a renormalization of nonadiabatic couplings to account for a difference between the instantaneous nuclear kinetic energy and the kinetic energy of guiding trajectories. In the new approach, an auxiliary kinetic energy variable is introduced as an independent dynamical variable. The new approach produces nonzero equilibrium populations, whereas the original neglect of the back-reaction approximation method does not. It yields population relaxation time scales that are favorably comparable to the reference values, and it introduces an explicit and controllable way of dissipating energy into a bath without an assumption of the bath being at equilibrium.

Modeling the Mg I from the NUV to MIR

Context. Reliable atomic data are mandatory ingredients to obtain a realistic semiempirical model of any stellar atmosphere. Due to their importance, we further improved our recently published Mg I atomic model. Aims. We tested the new atomic model using atmospheric models of stars of different spectral types: the Sun (dG2), HD 22049 (dK2, Epsilon Eridani), GJ 832 (dM2), and GJ 581 (dM3). Methods. Significant improvements have been included in the atomic model, mainly to the electron impact excitation (ϒij) values. We used new Breit-Pauli distorted-wave (DW) multiconfiguration calculations, which proved to be relevant for many transitions in the mid-infrared (MIR) range. The new atomic model of Mg I includes the following: (i) recomputed (ϒij) data through the DW method, including the superlevels. (ii) For the nonlocal thermodynamic equilibrium (NLTE) population calculations, 5676 theoretical transitions were added (3001 term-to-term). (iii) All of these improvements were studied in the Sun and the stars listed above. Comparisons for the distribution of magnesium among the first ionization states and the formation of molecules, as well as for the population of the different energy levels and atmospheric heights, were carried out. Several lines, representative of the spectral ranges, were selected to analyze the changes that were produced. In particular, we exemplify these results with the problematic line 2853.0 Å, a transition between the third level and the ground state. Results. The magnesium distribution between ionization states for stars with different effective temperatures was compared. For the Sun and Epsilon Eridani, Mg II predominates with more than 95%, while for GJ 832 and GJ 581, Mg I represents more than 72% of the population. Moreover, in the latter stars, the amount of magnesium forming molecules in their atmosphere is at least two orders of magnitude higher. Regarding the NLTE population, a noticeable lower variability in the departure coefficients was found, indicating a better population coupling for the new model. Comparing the synthetic spectrum calculated with the older and new Mg I atomic model, these results show minimal differences in the visible range but they are stronger in the infrared (IR) for all of the stars. This aspect should be considered when using lines from this region as indicators. Nevertheless, some changes in the spectral type were found, also emphasizing the need to test the atomic models in different atmospheric conditions. The most noticeable changes occurred in the far-ultraviolet (FUV) and near-ultraviolet (NUV), obtaining a higher flux for the new atomic model regardless of the spectral type. The new model did not prevent the formation of the core emission in the synthetic NUV line 2853.0 Å. However, by including other observations, we could note that the emission indeed exists, although with a much lower intensity. Further tests have shown that to reduce the emission, the population of its upper level (3s3p 1P) should be reduced by a factor of about 100.

Calculated Equilibrium Populations of Ti2C2@C82 Isomers

High-temperature equilibrium relative populations of two Ti2C2@C82 isomers isolated recently are treated by quantum-chemical calculations, viz. endohedrals with the C s (c);6-C82 and C 3v (b);8-C82 IPR (isolated-pentagon-rule) cages. The calculations are carried out using the Gibbs energy based on the MP2=FU/6-31+G*∼SDD energetics and B3LYP/6-31G*∼SDD entropy. The observed ratio Ti2C2@C s (c);6-C82 : Ti2C2@C 3v (b);8-C82=1.6:1 is in the computations obtained at a temperature of 1543 K, i.e., in the supposed synthetic temperature region. Before that point, the two isomers reach their equimolarity at a temperature of 983 K. This fine theory-experiment agreement represents another example of a good performance of the Gibbs-energy based quantum-chemical evaluations of the fullerenic equilibrium compositions under the high-temperature synthetic conditions.

Pr@C82 Metallofullerene: Calculated Isomeric Populations

Relative equilibrium populations of the five lowest-energy isolated-pentagon-rule (IPR) isomeric structures of Pr@C82 under high-temperature fullerene synthesis conditions were calculated with the Gibbs energy terms based on molecular characteristics derived using density functional theory (DFT) treatments (B3LYP/6-31+G*∼SDD energetics and B3LYP/6-31G*∼SDD entropy). Two leading isomers were identified, major Pr@C2v;9-C82 and minor Pr@Cs;6-C82. The calculated isomeric relative equilibrium populations agreed with observations.

Tracking Isomerizations of High-Energy Adenine Cation Radicals by UV-Vis Action Spectroscopy and Cyclic Ion Mobility Mass Spectrometry.

We report experimental and computational studies of protonated adenine C-8 σ-radicals that are presumed yet elusive reactive intermediates of oxidative damage to nucleic acids. The radicals were generated in the gas phase by the collision-induced dissociation of C-8-Br and C-8-I bonds in protonated 8-bromo- and 8-iodoadenine as well as by 8-bromo- and 8-iodo-9-methyladenine. Protonation by electrospray of 8-bromo- and 8-iodoadenine was shown by cyclic-ion mobility mass spectrometry (c-IMS) to form the N-1-H, N-9-H and N-3-H, N-7-H protomers in 85:15 and 81:19 ratios, respectively, in accordance with the equilibrium populations of these protomers in water-solvated ions that were calculated by density functional theory (DFT). Protonation of 8-halogenated 9-methyladenines yielded single N-1-H protomers, which was consistent with their thermodynamic stability. The radicals produced from the 8-bromo and 8-iodo adenine cations were characterized by UV-vis photodissociation action spectroscopy (UVPD) and c-IMS. UVPD revealed the formation of C-8 σ-radicals along with N-3-H, N-7-H-adenine π-radicals that arose as secondary products by hydrogen atom migrations. The isomers were identified by matching their action spectra against the calculated vibronic absorption spectra. Deuterium isotope effects were found to slow the isomerization and increase the population of C-8 σ-radicals. The adenine cation radicals were separated by c-IMS and identified by their collision cross sections, which were measured relative to the canonical N-9-H adenine cation radical that was cogenerated in situ as an internal standard. Ab initio CCSD(T)/CBS calculations of isomer energies showed that the adenine C-8 σ-radicals were local energy minima with relative energies at 76-79 kJ mol-1 above that of the canonical adenine cation radical. Rice-Ramsperger-Kassel-Marcus calculations of unimolecular rate constants for hydrogen and deuterium migrations resulting in exergonic isomerizations showed kinetic shifts of 10-17 kJ mol-1, stabilizing the C-8 σ-radicals. C-8 σ-radicals derived from N-1-protonated 9-methyladenine were also thermodynamically unstable and readily isomerized upon formation.

Nonlinear diffusion in multi-patch logistic model.

We examine a multi-patch model of a population connected by nonlinear asymmetrical migration, where the population grows logistically on each patch. Utilizing the theory of cooperative differential systems, we prove the global stability of the model. In cases of perfect mixing, where migration rates approach infinity, the total population follows a logistic law with a carrying capacity that is distinct from the sum of carrying capacities and is influenced by migration terms. Furthermore, we establish conditions under which fragmentation and nonlinear asymmetrical migration can lead to a total equilibrium population that is either greater or smaller than the sum of carrying capacities. Finally, for the two-patch model, we classify the model parameter space to determine if nonlinear dispersal is beneficial or detrimental to the sum of two carrying capacities.

Victorians and Numbers: Statistics and Society in Nineteenth Century Britain by Lawrence Goldman

<i>Victorians and Numbers: Statistics and Society in Nineteenth Century Britain</i> by Lawrence Goldman

Characterization of local non-equilibrium phonons in bulk MoS2 probed by temperature-dependent Raman scattering

This study presents an experimental implementation to determine the temperature dependence of Raman spectra of bulk 2H-MoS2 in the temperature range of 300–650 K. In addition, we have measured according to the anti-Stokes to Stokes integrated intensity ratio (). The results indicate that Raman shift of both the vibration modes and exhibits a linear temperature-dependent behavior in the heating and cooling processes. It is confirmed that the sample did not deteriorate by oxidization and decomposition at high temperatures. However, above 500 K, the measured phonon temperature deviated from the heat bath temperature. It is suggested that the does not correspond to the equilibrium population of optical phonons, thus indicating that the measurement was not in thermal equilibrium but in a thermal steady state under laser irradiation. We conclude that this is caused by the difference in relaxation times in the thermal steady state.

Evolutionary rescue in a fluctuating environment: periodic versus quasi-periodic environmental changes.

No environment is constant over time, and environmental fluctuations impact the outcome of evolutionary dynamics. Survival of a population not adapted to some environmental conditions is threatened unless, for example, a mutation rescues it, an eco-evolutionary process termed evolutionary rescue. We here investigate evolutionary rescue in an environment that fluctuates between a favourable state, in which the population grows, and a harsh state, in which the population declines. We develop a stochastic model that includes both population dynamics and genetics. We derive analytical predictions for the mean extinction time of a non-adapted population given that it is not rescued, the probability of rescue by a mutation, and the mean appearance time of a rescue mutant, which we validate using numerical simulations. We find that stochastic environmental fluctuations, resulting in quasi-periodic environmental changes, accelerate extinction and hinder evolutionary rescue compared with deterministic environmental fluctuations, resulting in periodic environmental changes. We demonstrate that high equilibrium population sizes and per capita growth rates maximize the chances of evolutionary rescue. We show that an imperfectly harsh environment, which does not fully prevent births but makes the death rate to birth rate ratio much greater than unity, has almost the same rescue probability as a perfectly harsh environment, which fully prevents births. Finally, we put our results in the context of antimicrobial resistance and conservation biology.