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The oxygen isotope signature of water is a powerful tracer of water movement from plants to the global scale. However, little is known about the short-term variability of oxygen iso- topes leaving the ecosystem via transpiration, as high-frequency measurements are lacking. A laser spectrometer was coupled to a gas-exchange chamber directly estimating branch- level fluxes in order to evaluate the short-term variability of the isotopic composition of transpiration (dE) and to investigate the role of isotopic non-steady-state transpiration under natural conditions in cork-oak trees (Quercus suber) during distinct Mediterranean seasons. The measured d18O of transpiration (dE) deviated from isotopic steady state throughout most of the day even when leaf water at the evaporating sites was near isotopic steady state. High agreement was found between estimated and modeled dE values assuming non-steady- state enrichment of leaf water. Isoforcing, that is, the influence of the transpirational d18O flux on atmospheric values, deviated from steady-state calculations but daily means were similar between steady state and non-steady state. However, strong daytime isoforcing on the atmosphere implies that short-term variations in dE are likely to have consequences for large-scale applications, for example, partitioning of ecosystem fluxes or satellite-based applications.

Metabolic flux analysis (MFA) is an increasingly important tool to study metabolism quantitatively. Unlike the concentrations of metabolites, the fluxes, which are the rates at which intracellular metabolites interconvert, are not directly measurable. MFA uses stable isotope labeled tracers to reveal information related to the fluxes. The conceptual idea of MFA is that in tracer experiments the isotope labeling patterns of intracellular metabolites are determined by the fluxes, therefore by measuring the labeling patterns we can infer the fluxes in the network. In this review, we will discuss the basic concept of MFA using a simplified upper glycolysis network as an example. We will show how the fluxes are reflected in the isotope labeling patterns. The central idea we wish to deliver is that under metabolic and isotopic steady-state the labeling pattern of a metabolite is the flux-weighted average of the substrates’ labeling patterns. As a result, MFA can tell the relative contributions of converging metabolic pathways only when these pathways make substrates in different labeling patterns for the shared product. This is the fundamental principle guiding the design of isotope labeling experiment for MFA including tracer selection. In addition, we will also discuss the basic biochemical assumptions of MFA, and we will show the flux-solving procedure and result evaluation. Finally, we will highlight the link between isotopically stationary and nonstationary flux analysis.

Severe rheological failure of extremely soft rocks poses a significant threat to the safety and long-term stability of roadways. Herein, four long-term triaxial creep tests were conducted under low confinements and deviatoric stresses. The results show that greater deviatoric stress leads to more obvious creep deformation, while the confining pressure can delay the occurrence of accelerated creep and restrain the creep rate and lateral deformation. The total axial strain reached 4.03% under 0.6-MPa confinement, and the creep strain of the extremely soft coal rock was much larger than that of hard rocks. Additionally, two important features distinguish extremely soft coal rocks from common rocks, namely, the creep rate did not converge in the steady-state creep stage under each applied stress level and a “gradual” squeezing deformation instability occurred in the accelerated creep stage. Furthermore, the steady-state creep rate increased exponentially with an increase in deviatoric stress and decreased following a power function with confining pressure. Then, a modified Burgers model with a nonstationary viscous coefficient was proposed to reflect the dual and nonlinear influence of confining pressure on steady-state creep rate. Moreover, several principles and suggestions for the long-term stability control of extremely soft rock roadway are discussed. Finally, a novel nonlinear creep constitutive model was established by connecting a nonlinear viscoplastic element considering both creep time and applied stress with the modified Burgers model in series. The findings are essential for creep behavior prediction and stability control in extremely soft rock engineering.

We revisit the question of the existence of a potential function, the Cole–Hopf transform of the stationary measure, for nonequilibrium steady states, in particular those found in active matter systems. This has been the subject of ongoing research for more than fifty years, but continues to be relevant. In particular, we want to make a connection to some recent work on the theory of Helmholtz–Hodge decompositions and address the recently suggested notion of typical trajectories in such systems.

We continue the investigation of kinetic models of a system in contact via stochastic interactions with several spatially homogeneous thermal reservoirs at different temperatures. Considering models different from those investigated in Carlen et al. (Braz J Probab Stat 29:372–386, 2015), we explicitly compute the unique spatially uniform non-equilibrium steady state (NESS) and prove that it is approached exponentially fast from any uniform initial state. This leaves open the question of whether there exist NESS that are not spatially uniform. Making a further simplification of our models, we then prove non-existence of such NESS and exponential approach to the unique spatially uniform NESS (with a computably boundable rate). The method of proof relies on refined Doeblin estimates and other probabilistic techniques, and is quite different form the analysis in Carlen et al. (Braz J Probab Stat 29:372–386, 2015) that was based on contraction mapping methods.

A general time-delay reaction–diffusion–advection system with the Dirichlet boundary condition and spatial heterogeneity is investigated in this paper. By using the implicit function theorem, we obtain the existence and asymptotic expression of the spatially non-homogeneous positive steady-state solution. This is the steady-state bifurcation from zero equilibrium. Via analyzing the corresponding characteristic equation, the stability of the spatially non-homogeneous positive steady-state solution and the occurrence of Hopf bifurcation at the positive steady-state solution are obtained, and the spatially non-homogeneous periodic solution is derived from Hopf bifurcation, this is the secondary bifurcation behavior of the system. Utilizing the normal form method and center manifold theory, we prove that the direction of Hopf bifurcation is supercritical and the bifurcating spatially non-homogeneous periodic solution is stable. Furthermore, We show that there exist two sequences Hopf bifurcation values and the orders of two sequences Hopf bifurcation values are given. Moreover, theoretical and numerical results are applied to competition and cooperation systems, respectively. Finally, the effect of the advection rate and spatial heterogeneity are discussed.

Understanding and accurately modeling the creep behavior of rock salt is of great interest for its relevance to geological storage of nuclear wastes, oil, and gases. Many experimental studies on the creep of salt samples are performed at a deviatoric stress above 5 MPa. The creep rates at smaller stress levels are usually estimated by extrapolating from data at higher stress levels. However, recent low-stress creep tests conducted at below 1 MPa suggest that such extrapolation can significantly underestimate the creep rate of rock salt, as the controlling micro-mechanisms are very different in low- and high-stress regimes. Meanwhile, field observations suggest that salt creep is accelerated under higher ambient relative humidity (i.e., the so-called Joffe effect). The effect of humidity on salt creep in the pressure-solution dominating low-stress regime is even less understood at present. In this context, we conducted a series of long-term creep tests at intermediate–low uniaxial stresses of 1, 3, and 5 MPa on Avery Island salt samples. In order to quantify the effect of moisture on salt creep, a combined triaxial cell and air circulation system is designed to permit control over the environmental humidity. Three relative humidity levels (33%, 55% and 77%) are selected and are achieved through the vapor equilibrium technique. Our study confirmed that the creep rate at low stress level is indeed higher than those extrapolated from high-stress creep tests. For the same deviatoric stress, higher ambient humidity produces faster steady-state creep rate of salt samples. Finally, a modified creep law that incorporates the humidity dependency is proposed and validated against the new experimental data.HighlightsThe influence of ambient humidity on creep behavior of rock salt at intermediate–low stress regime was experimentally investigated.A novel experimental setup was developed to provide stable humidity- and stress-control during long-term uniaxial creep tests.Humidity-dependent scaling functions inspired by existing water retention and adsorption models were introduced in the steady-state creep model for rock salt.

$\\bullet$The aims of the study were to determine group specificity in microbial utilization of root-exudate compounds and whole rhizodeposition; quantify the proportions of carbon acquired by microbial groups from soil organic matter and rhizodeposition, respectively; and assess the importance of root-derived C as a driver of soil microbial community structure.$\\bullet$Additions of$^{13}C-labelled$root-exudate compounds to organic soil and steady-state labelling of Lolium perenne, coupled to compound-specific isotope ratio mass spectrometry, were used to quantify group-specific microbial utilization of rhizodeposition.$\\bullet$Microbial utilization of glucose and fumaric acid was widespread through the microbial community, but glycine was utilized by a narrower range of populations, as indicated by the enrichment of phospholipid fatty acid (PLFA) analysis fractions. In L. perenne rhizospheres, high rates of rhizodeposit utilization by microbial groups showed good correspondence with increased abundance of these groups in the rhizosphere.$\\bullet$Although rhizodeposition was not the quantitatively dominant C source for microbes in L. perenne rhizospheres, relative utilization of this C source was an important driver of microbial group abundance in organic soil.

In the realm of daily life, ensuring the safety of building structures and civil engineering projects remains a paramount research focus. The creep properties of materials significantly influence their long-term loading process. Specifically, creep load and creep time are pivotal factors that impact material creep damage, thereby playing a crucial role in assessing the safety of engineering endeavors and estimating aspects such as housing construction. This study undertakes creep damage tests on cement-based materials, subjecting them to varying creep loads and creep times, and subsequently conducts uniaxial compression tests on the specimens post-creep damage. The refined Nishihara model is employed for data fitting, facilitating the construction of a creep damage time-stress model. Concurrently, a Neural Network model is utilized to validate the experimental data. The findings indicate that both steady-state creep strain and steady-state creep rate exhibit discernible trends relative to creep load and creep time, effectively mirroring the alterations in creep damage experienced by the specimens. The refined Nishihara model proves adept at predicting and equating creep damage under diverse creep loads and creep times. Similarly, the trained Neural Network model demonstrates capability in measuring and estimating various creep damages. The study successfully explored the correlation between creep time and creep load, enabling the simulation of long-term creep damage within a shorter creep time and facilitating an analysis of its physical and mechanical properties, which is pivotal in predicting the safety of large-scale engineering projects. Concurrently, it advances research on material damage equivalence, offering insights and theoretical groundwork for developing a system to assess material damage equivalence under various damage conditions.

Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time decoupled from the spatial position at the resetting moment. However, in our world, getting from one place to another always takes time and places that are further away take more time to be reached. We thus set off to extend the theory of stochastic resetting such that it would account for this inherent spatio-temporal coupling. We consider a particle that starts at the origin and follows a certain law of stochastic motion until it is interrupted at some random time. The particle then returns to the origin via a prescribed protocol. We study this model and surprisingly discover that the shape of the steady-state distribution which governs the stochastic motion phase does not depend on the return protocol. This shape invariance then gives rise to a simple, and generic, recipe for the computation of the full steady state distribution. Several case studies are analyzed and a class of processes whose steady state is completely invariant with respect to the speed of return is highlighted. For processes in this class we recover the same steady-state obtained for resetting with instantaneous returns-irrespective of whether the actual return speed is high or low. Our work significantly extends previous results on motion with stochastic resetting and is expected to find various applications in statistical, chemical, and biological physics.