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We deal with a Leslie-Gower predator–prey model with a generalist or alternating food for predator and linear functional response. Using a topological equivalent polynomial system we prove that the system is not Liouvillian (hence also not Darboux) integrable. In order to study the global dynamics of this model, we use the Poincaré compactification of R 2 to characterize all phase portraits in the Poincaré disc, obtaining two different topological phase portraits. [ABSTRACT FROM AUTHOR]

An extension of the use of the linear response function to interpret non-covalent interactions is put forward. Due to its computational intricacies, most applications until now have been done on isolated atoms or molecules using coupled perturbed Hartree–Fock or Kohn–Sham theory, thereby adopting the simplest level for the LRF evaluation, the independent particle approximation. The previously presented possibilities for extension (the random phase and the "full" expression) are scrutinised, thereby highlighting the intricacies in the evaluation of the exchange-correlation term in the case of meta-GGAs and hybrid functionals, and implemented. A set of 25 hydrogen bonded and 11 halogen bonded systems, selected from Hobza S66 and X 40 compilations, were used to investigate the correlation between the stabilisation energy due to these non-covalent interactions and the relevant atom–atom-condensed LRF matrix element. The lack of a relevant correlation in the case of hydrogen bonding is contrasted with the excellent result for the halogen bonds. The correlation between the full option and the IPA is high providing support for our previous work using the IPA as is also the case for the previously used iterative Hirshfeld condensation and the more advanced FOHI method making use of fractional occupation numbers. The fundamental difference between hydrogen and halogen bond behaviour and the retrieval of the stability sequence within the halogen bonds series are traced back to the nature of the LRF as a response function for perturbations in the external potential putting polarisation effects and the polarisability of the atoms of the donor–acceptor couple at the forefront. The extension to the use of the softness kernel is advocated and already invoked to rectify the behaviour of two deviating complexes involving S as second row halogen bond acceptor atom. [ABSTRACT FROM AUTHOR]

While a large latitudinal displacement of the westerly jet brings about disproportionate socioeconomic impacts over Northern Hemisphere midlatitude continents, it is not well understood as to whether the winter circulation will become wavier or less in response to climate change. Here, using observations and large ensembles of climate models, we show that changes in atmospheric waviness can be estimated from the optimal structures of the westerly jet for wavier circulation, which are obtained from an advection‐diffusion model. Thus, the changes in westerly jet structure in climate models under climate change provide a physical constraint on changes in atmospheric waviness, indicating that the North Atlantic wave activity will experience a robust decline in a warmer climate, while future North Pacific wave activity is obscured by model uncertainty rather than internal variability. These findings highlight the changes to jet stream structure as a constraint for regional circulation waviness in a changing climate. Plain Language Summary: A large latitudinal meandering of Northern Hemisphere winter circulation can induce stagnant weather that causes severe impacts on densely populated East Asia, Western North America, or Western Europe, yet whether the winter circulation will become wavier or less under climate change remains uncertain. Here we analyze observations and large ensembles of climate models and show that changes to atmospheric wave activity under climate change are largely constrained by changes to zonal advecting wind for the Lagrangian motion of air parcels in an advection‐diffusion model. This constraint further indicates a consistent decline in future waviness over the North Atlantic, while changes to future wave activity over the North Pacific are uncertain, due to model uncertainty rather than internal variability of the climate system. Key Points: Changes in atmospheric waviness can be roughly estimated by changes in zonal advecting wind in an advection‐diffusion modelChanges in the optimal structure of jet stream help constrain regional circulation waviness in a changing climateModel results suggest future waviness will robustly decline in North Atlantic but is less clear in North Pacific due to model uncertainty [ABSTRACT FROM AUTHOR]

Abstract While a large latitudinal displacement of the westerly jet brings about disproportionate socioeconomic impacts over Northern Hemisphere midlatitude continents, it is not well understood as to whether the winter circulation will become wavier or less in response to climate change. Here, using observations and large ensembles of climate models, we show that changes in atmospheric waviness can be estimated from the optimal structures of the westerly jet for wavier circulation, which are obtained from an advection‐diffusion model. Thus, the changes in westerly jet structure in climate models under climate change provide a physical constraint on changes in atmospheric waviness, indicating that the North Atlantic wave activity will experience a robust decline in a warmer climate, while future North Pacific wave activity is obscured by model uncertainty rather than internal variability. These findings highlight the changes to jet stream structure as a constraint for regional circulation waviness in a changing climate.

Abstract Convection is usually parameterized in global climate models, and there are often large discrepancies between results obtained with different convection schemes. Conventional methods of comparing convection schemes using observational cases or directly in three‐dimensional (3D) models do not always clearly identify parameterization strengths and weaknesses. In this paper we evaluate the response of parameterizations to various perturbations rather than their behavior under particular strong forcing. We use the linear response function method proposed by Kuang (2010) to compare 12 physical packages in five atmospheric models using single‐column model (SCM) simulations under idealized radiative‐convective equilibrium conditions. The models are forced with anomalous temperature and moisture tendencies. The temperature and moisture departures from equilibrium are compared with published results from a cloud‐resolving model (CRM). Results show that the procedure is capable of isolating the behavior of a convection scheme from other physics schemes. We identify areas of agreement but also substantial differences between convection schemes, some of which can be related to scheme design. Some aspects of the model linear responses are related to their RCE profiles (the relative humidity profile in particular), while others constitute independent diagnostics. All the SCMs show irregularities or discontinuities in behavior that are likely related to threshold‐related mechanisms used in the convection schemes, and which do not appear in the CRM. Our results highlight potential flaws in convection schemes and suggest possible new directions to explore for parameterization evaluation.

Some Mo‐oxo complexes bearing pyridine rings have the capability for dihydrogen production from water. However, energy barrier and overall energy vary depending on the effect exerted by several substituent groups located at different positions around one or more pyridine rings which are ligands of these compounds. Based on the Karunadasa and coworkers investigation where the para‐position was experimentally tested in compounds derivatised from the 2,6‐bis[1,1‐bis(2‐pyridil)ethyl]‐pyridine oxo‐molybdenum complex synthesized (Karunadasa et al., Nature, 2010, 464, 1329), we tested the combined effect of electron‐withdrawing and electron‐donating groups simulated as perturbations represented by point‐charges. Then, we used the density polarization concept, δρ(r), a local reactivity descriptor corresponding to the partially integrated linear response function, χ(r, r′) (a non‐local reactivity descriptor), which is able to reveal different displacements of π‐electrons on molecular structures. We perturbed the para‐positions in the pentadentate ligand 2,6‐bis[1,1‐bis(2‐pyridil)ethyl]‐pyridine in the Mo‐based complex by means of point‐charges. They were located in three different configurations of the organic ligand (trans, geminal, and cis) which could help to explain energy barriers and overall energy of reactions catalyzed by this type of Mo‐complexes. Our results indicate that the trans configuration of point‐charges induces the most amount of fraction of electron shifted on the complex. A Mo‐based complex bearing the same trans configuration for electron‐withdrawing and electron‐donating substituent groups (cyano and amino, respectively), leads to a kinetically more favorable H2 release than the cis or geminal configuration of the substituent groups aforementioned. [ABSTRACT FROM AUTHOR]

Convection is usually parameterized in global climate models, and there are often large discrepancies between results obtained with different convection schemes. Conventional methods of comparing convection schemes using observational cases or directly in three‐dimensional (3D) models do not always clearly identify parameterization strengths and weaknesses. In this paper we evaluate the response of parameterizations to various perturbations rather than their behavior under particular strong forcing. We use the linear response function method proposed by Kuang (2010) to compare 12 physical packages in five atmospheric models using single‐column model (SCM) simulations under idealized radiative‐convective equilibrium conditions. The models are forced with anomalous temperature and moisture tendencies. The temperature and moisture departures from equilibrium are compared with published results from a cloud‐resolving model (CRM). Results show that the procedure is capable of isolating the behavior of a convection scheme from other physics schemes. We identify areas of agreement but also substantial differences between convection schemes, some of which can be related to scheme design. Some aspects of the model linear responses are related to their RCE profiles (the relative humidity profile in particular), while others constitute independent diagnostics. All the SCMs show irregularities or discontinuities in behavior that are likely related to threshold‐related mechanisms used in the convection schemes, and which do not appear in the CRM. Our results highlight potential flaws in convection schemes and suggest possible new directions to explore for parameterization evaluation. Plain Language Summary: The transport of heat up and down the atmosphere, called atmospheric convection, is a complex process. To simplify the representation of convection in global climate models (GCMs) scientists use "parameterization," which is essentially mathematical equations of physical processes. However, there are many different ways to formulate these equations, and no agreement on which is better. In this work we aim to understand a few popular ways to parameterize convection. We extract one vertical column from five different GCMs and lightly tickle (perturb) it and then observe its responses. We found that different models respond very differently to the same tickling, and this tells us a lot about the model. Importantly, the specific perturbation that we used can single out the responses of convection‐related equations from equations of other processes. All the models in our study have one thing in common: They are quite jumpy when tickled, especially at the top of the boundary layer where clouds start to form. We suspect the culprits are thresholds placed in the models that sometimes lead to sudden changes in their response. Our work highlights potentially problematic behavior that can give clues on how to make climate models better. Key Points: The linear response function method is applied in single‐column model (SCM) simulations and is able to isolate the behavior of convection schemesLinear responses of the models are related to the mean state relative humidity in both shape and magnitudeAll SCMs show discontinuities in their responses which are likely related to thresholds used in convective parameterization [ABSTRACT FROM AUTHOR]

Plants depend on the signalling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signalling network involves a negative feedback on Aux/IAA proteins which mediate the influence of auxin (the signal) on the auxin response factor (ARF) transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signalling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative feedback allows the system to have a far larger sensitivity in its dynamical response to auxin and that this sensitivity does not prevent the system from being highly resilient. Given this insight, we build a new biomolecular signalling model for quantitatively describing such Aux/IAA and ARF responses.

We argue that when one divides a molecular property into atom‐in‐a‐molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms‐in‐a‐molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference‐free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecule's atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an “arbitrary” choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We examined nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function (LRF). From the computational results of a square-well model system, the behavior of responses obviously depends on the number of electrons (N): as N increases, LRF, δρ(r)/δv(r′), decays rapidly for the distance, |r−r′|. This exemplifies that the principle suggested by Kohn and Prodan holds even for finite systems: the cause of NEM is destructive interference among electron density amplitudes. In addition, we examined double-well model systems, which have low-lying degenerate levels. In this case, there are two types of LRF: the cases of the half-filled and of full-filled in low-lying degenerate levels. The response for the former is delocalized, while that of the later is localized. These behaviors of model systems are discussed in relation to the molecular systems’ counterparts, H2, He22+, and He2 systems. We also see that NEM holds for the dissociated limit of H2, of which the mechanism is similar to that of the insulating state of solids as suggested by Kohn. We also examined LRF of alanine tripeptide system as well as butane and butadiene molecules, showing that NEM of the polypeptide system is caused by sp3 junctions at Cα atoms that prevent propagation of amplitudes of LRF, which is critically different from that of NEM for finite and infinite homogeneous systems.

We applied our analysis, based on a linear response function of density and spin density, to two typical transition metal complex systems-the reaction centers of P450, and oxygen evolving center in Photosystem II, both of which contain open-shell transition metal ions. We discuss the relationship between LRF of electron density and spin density and the types of units and interactions of the systems. The computational results are discussed in relation to quantum mechanics (QM) cluster and quantum mechanics/molecular mechanics (QM/MM) modeling that are employed to compute the reaction centers of enzymes.

We present the linear response function of bond-orders (LRF-BO) based on a real space integration scheme for molecular systems. As in the case of the LRF of density, the LRF-BO is defined as the response of the bond order of the molecule for the virtual perturbation. Our calculations show that the LRF-BO enables us not only to detect inductive and resonating effects of conjugating systems, but also to predict pKa values on substitution groups via linear relationships between the Hammett constants and the LRF-BO values for meta- and para-substituted benzoic acids. More importantly, the LRF-BO values for the O-H bonds strongly depend on the sites to which the virtual perturbation is applied, implying that the LRF-BO values include essential information about reaction mechanism of the acid-dissociation of substituted benzoic acids. [ABSTRACT FROM AUTHOR]

The energy (E) versus number of electrons (N) and external potential (v) functional E = E[N, v], which has proved to be of fundamental importance in conceptual density functional theory through the response functions it generates, has been examined concentrating on the concavity of the E = E[v] functional as opposed to the convexity of the E = E(N) function. The concavity of the E = E[v] functional is reflected in negative values of the diagonal elements of the linear response function χ (r , r ′) comprising the second functional derivative of E with respect to v (r) , whereas no sign can be retrieved for the off-diagonal elements. These findings are in agreement with recent computational studies in extracting the chemical content of the linear response function. The results for the diagonal elements can easily be interpreted in terms of electron depletion from regions where the potential is increased and are easily retrieved via the independent particle model expression and in agreement with the diagonal elements of the most general expression for the linear response function. These concavity-related issues are put in contrast with the positive (∂ 2 E / ∂ N 2) v derivative, resulting from the convexity of the E(N) function, in line with the positivity of the chemical hardness as resulting from the I versus A (ionization vs. electron affinity) ratio. The first-order derivative (δ E / δ v (r)) N is discussed within an iso-electronic atom series for which it is shown in detail that the potentials can be ordered univocally, through their Z-dependence. The sign of the slope of the E = E[v] curve is in agreement with the positivity of ρ (r) . The result for the E = E[v] functional is put in contrast with the negative (∂ E / ∂ N) v derivative (identified as minus the electronegativity) for the E = E(N) function retrieved on the basis of experimental and theoretical data on ionization energies and electron affinities. [ABSTRACT FROM AUTHOR]

We have investigated nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function to examine theoretical foundation of contemporary computational chemistry such as quantum mechanics/molecular mechanics methods. In this study, we introduce several nearsightedness-related indices to assess the magnitude of localisability of responses for one-dimensional finite model systems. We started from two electrons' systems, which are beyond the scope of the original concept of NEM, and increased the number of electrons (N) to a hundred electrons to analyse dependency of such indices onN. In the process of construction of the indices, we analysed the factors, because of which the magnitude of nonlocal parts of linear response functions becomes small, into several ones, and extracted purely the magnitude of propagation of responses. [ABSTRACT FROM AUTHOR]

We here formulate and implement linear response function (LRF) of the Mayer bond order (MBO), which is expected to be a new indicator to describe intrinsic chemical reactivity of molecules. We calculate LRFs of the MBOs of para-substituted benzoic acids, and compare the results with the Hammett substituent constants and computational results of acid dissociation constants that were previously reported. The results are discussed from the viewpoint of the applicability of LRF of the MBO to estimate the relative reactivity of the substituted benzoic acids. [ABSTRACT FROM AUTHOR]

We examined nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function (LRF). From the computational results of a square-well model system, the behavior of responses obviously depends on the number of electrons (N): as N increases, LRF, δρ(r)/δv(r′), decays rapidly for the distance, ∣r−r′∣. This exemplifies that the principle suggested by Kohn and Prodan holds even for finite systems: the cause of NEM is destructive interference among electron density amplitudes. In addition, we examined double-well model systems, which have low-lying degenerate levels. In this case, there are two types of LRF: the cases of the half-filled and of full-filled in low-lying degenerate levels. The response for the former is delocalized, while that of the later is localized. These behaviors of model systems are discussed in relation to the molecular systems’ counterparts, H2, He22+, and He2 systems. We also see that NEM holds for the dissociated limit of H2, of which the mechanism is similar to that of the insulating state of solids as suggested by Kohn. We also examined LRF of alanine tripeptide system as well as butane and butadiene molecules, showing that NEM of the polypeptide system is caused by sp3 junctions at Cα atoms that prevent propagation of amplitudes of LRF, which is critically different from that of NEM for finite and infinite homogeneous systems. [ABSTRACT FROM AUTHOR]

Although it is widely known that trimethylamine N-oxide (TMAO), an osmolyte used by nature, stabilizes the folded state of proteins, the underlying mechanism of action is not entirely understood. To gain further insight into this important biological phenomenon, we use the C≡N stretching vibration of an unnatural amino acid, p-cyano-phenylalanine, to directly probe how TMAO affects the hydration and conformational dynamics of a model peptide and a small protein. By assessing how the lineshape and spectral diffusion properties of this vibration change with cosolvent conditions, we are able to show that TMAO achieves its protein-stabilizing ability through the combination of (at least) two mechanisms: (i) It decreases the hydrogen bonding ability of water and hence the stability of the unfolded state, and (ii) it acts as amolecular crowder, as suggested by a recent computational study, that can increase the stability of the folded state via the excluded volume effect. [ABSTRACT FROM AUTHOR]