The performance requirements of fusion reactors based on FRC adiabatic compression with a D- ^3 He fuel are discussed. Assuming thermonuclear reaction rates, confinement times exceeding 10 ms are required for peak magnetic fields below 25 T. The typical thermodynamic cycle of such reactors in current/flux variables is computed. The fact that most magnetic energy is channeled to vacuum magnetic energy, instead of heating the plasma, translates into a very elongated thermodynamical cycle. The consequences for the viability of this type of reactors are discussed.

In a previous work, a complete methodology for monitoring the growth of a filamentous fungus was introduced, allowing the automated extraction of its graph structure and of its key statistics. In parallel, a stochastic growth-fragmentation model for the dynamics of such mycelial networks was introduced and studied. This simple model depends on three parameters: the elongation speed v of a single filament, the branching rate b1 of a filament at its open end, and the per unit length rate b2 at which a budding event happens and creates a new filament branching off from an existing one. Leaving aside the spatial structure of the mycelium and describing its structure essentially through the empirical measure of the lengths of its filament segments, the three parameters of the growth dynamics encoded in the model summarise the local balance between mass creation and regulation through non-linear mechanisms such as anastomosis or density-dependent growth modulation. In this work, we develop a generic statistical inference method based on the large-time behaviour of the stochastic model, and on the high-resolution pictures of the mycelial network obtained using the methodology for fungal growth monitoring, to reconstruct the effective growth parameters v, b1 and b2 from a single panorama of the filament network pictured after several hours of development and an empirical measurement of the exponential rate of increase of the number of branch points and apexes. We use this method to analyse the growth dynamics of Podospora anserina mycelia observed under standard conditions and when several forms of stress are applied, in order to quantify the effect of these stresses on the different mechanisms of fungal growth. By comparing the reconstructed effective parameters with the hyphal elongation speed and branching rates estimated from the much more complex dynamical tracking of individual filaments, we find that the effective branching rates we infer are in close agreement with the individual branching rates estimated from the dynamical tracking procedure. This suggests that, in this application at least, the effects of non-linear local regulation mechanisms on branching are well encoded by an effective Markovian rate during the exponential growth phase of the mycelium. By contrast, the effective elongation speed reconstructed with our model-based approach is approximately twice as low as the hyphal elongation speed estimated from the dynamical tracking procedure, a bias that may be explained by a mismatch between the definitions of "elongation speed" used in the two approaches. Nevertheless, our results show that the three parameters of our growth-fragmentation model, combined with experimental data that are now readily available, enable us to quantify different components of the exponential growth dynamics of an expanding mycelial network.

The mycelium of a filamentous fungus is a growing, branching network of numerous entangled hyphae exhibiting polarised apical growth. Expansion occurs during the vegetative phase from a single ascospore, driven by the need to explore and occupy surrounding space-limiting competitors, enhancing nutrient uptake, and promoting spore dispersal. Radial, rapid, and rectilinear growth combined with frequent branching appears adaptive. However, passive growth without interactions or feedback may produce suboptimal networks, as neither local density nor potential connectivity is considered. Reorientations of the apex near existing hyphae suggest apex-hypha feedback. Yet, the diversity of behaviours, spontaneous fluctuations, and limited apical trajectories studied leave open the question of active regulation. To investigate possible apex-hypha interactions, we analyse a dataset of Podospora anserina thallus growth by reconstructing all apical trajectories post-branching and fitting them with a classical Langevin model that incorporates potential interactions. Comparing isolated and non-isolated hyphae trajectories allows to identify a clear signature of interaction composed of abrupt deceleration and reorientation. This work opens the path towards a systematic exploration of hyphal interactions.

In their natural environment, fungi are subjected to a wide variety of environmental stresses which they must cope with by constantly adapting the architecture of their growing network. In this work, our objective was to finely characterize the thallus development of the filamentous fungus Podospora anserina subjected to different constraints that are simple to implement in vitro and that can be considered as relevant environmental stresses, such as a nutrient-poor environment or non-optimal temperatures. At the Petri dish scale, the observations showed that the fungal thallus is differentially affected (thallus diameter, mycelium aspect) according to the stresses but these observations remain qualitative. At the hyphal scale, we showed that the extraction of the usual quantities (i.e. apex, node, length) does not allow to distinguish the different thallus under stress, these quantities being globally affected by the application of a stress in comparison with a thallus having grown under optimal conditions. Thanks to an original geomatics-based approach based on the use of automatized Geographic Information System (GIS) tools, we were able to produce maps and metrics characterizing the growth dynamics of the networks and then to highlight some very different dynamics of network densification according to the applied stresses. The fungal thallus is then considered as a map and we are no longer interested in the quantity of material (hyphae) produced but in the empty spaces between the hyphae, the intra-thallus surfaces. This study contributes to a better understanding of how filamentous fungi adapt the growth and densification of their network to potentially adverse environmental changes.

Experimentally monitoring the kinematics of branching network growth is a tricky task, given the complexity of the structures generated in three dimensions. One option is to drive the network in such a way as to obtain two-dimensional growth, enabling a collection of independent images to be obtained. The density of the network generates ambiguous structures, such as overlaps and meetings, which hinder the reconstruction of the chronology of connections. In this paper, we propose a general method for global network reconstruction. Each network connection is defined by a unique label, enabling it to be tracked in time and space. In this work, we distinguish between lateral and apical branches on the one hand, and extremities on the other. Finally, we reconstruct the network after identifying and eliminating overlaps. This method is then applied to the model filamentous fungus Podospora anserina to reconstruct its growing thallus. We derive criteria for differentiating between apical and lateral branches. We find that the outer ring is favorably composed of apical branches, while densification within the network comes from lateral branches. From this, we derive the specific dynamics of each of the two types. Finally, in the absence of any latency phase during growth initiation, we can reconstruct a time based on the equality of apical and lateral branching collections. This makes it possible to directly compare the growth dynamics of different thalli.

ABSTRACT The growth of the network of a filamentous fungus is monotonous, showing an ever increasing complexity with time. The components of network growth are very simple and based on two mechanisms, the elongation of each hyphae and their multiplication by successive branching. These two mechanisms are sufficient to produce a complex network, and could only be localized at the tips of the hyphae. However, branching can be of two types, apical or lateral, depending on its location on the hyphae, imposing the redistribution of the necessary material in the whole network. From an evolutionary point of view, maintaining different branching processes, with its associated cost, is intriguing. We propose in this work to discuss the advantages of each of the two branching types using a new observable for the network growth allowing to compare growth configurations. For this purpose, we build on experimental observations of the Podospora anserina thallus growth, allowing us to feed and constrain a lattice-free modeling of this network based on a binary tree. First, we report the set of statistics related to the branches of P. anserina that we have implemented in the model. Then, we build the density observable, allowing us to discuss the growth phases. We predict that the evolution of the density is not monotonic but presents a marked stationary phase, clearly separating two other phases of growth. The location of this stable region appears to be driven solely by the growth rate. Finally, we show that the density is a good observable for stress differentiation.

This paper presents a conceptual model describing the medium and long term co-evolution of natural and socio-economic subsystems of Earth. An economy is viewed as an out-of-equilibrium dissipative structure that can only be maintained with a flow of energy and matter. The distinctive approach emphasized here consists in capturing the economic impact of natural ecosystems’ depletion by human activities via a pinch of thermodynamic potentials. This viewpoint allows: ( i ) the full-blown integration of a limited quantity of primary resources into a non-linear macrodynamics that is stock-flow consistent both in terms of matter-energy and economic transactions; ( ii ) the inclusion of natural and forced recycling; ( iii ) the inclusion of a friction term which reflects the impossibility to produce (and recycle)goods and services without exuding energy and matter wastes, and ( iv ) the computation of the anthropically produced entropy as a function of metabolizing intensity and frictions. Analysis and numerical computations confirm the role played by intensity and frictions as key factors for sustainability by contrast with real gdp growth—as well as the interplay between resource scarcity, income inequality, and inflation. A more egalitarian society with moderate inflation turns out to be more sustainable than an unequal society with low inflation. Our approach is flexible enough to allow for various economic models to be embedded into our thermodynamic framework. Finally, we propose the open source E co D yco software as a first complete realization implementing economic dynamics in a multi-resource environment.

Like all current industrial systems, agriculture overwhelmingly relies on energy supply from controllable sources, mainly fossil fuels and grid electricity. Power supply from these sources can be adapted to perfectly match the timing of power requirements of demand systems. The energy transition largely consists in substituting renewable power-which is intermittent by nature-to controllable sources, leading to disconnection between instantaneous power production and demand. Energy storage is a potential solution for balancing production and demand and safeguarding the operating conditions of the demand system. In this paper we quantify the effects of renewable power supply (solar and wind) on the operation of a standard poultry farm. We model the balance of power generation and demand considering the growth conditions of poultry and local weather data including temperatures, wind speed and solar radiation. We assess scenarios of renewable power supply in function of the size of the power plant, the wind-to-solar power generation mix and energy storage, and assess the impact of power supply patterns on the operating intensity (productivity) of the demand system. We show that, with a limited storage capacity, it is possible to achieve non-negligible shares of renewable power penetration without major loss in farm productivity. However, a full transition to renewable power would require the combination of i)-large energy storage compared to the annual demand, ii)- significant oversizing of the power production plant, and iii)-the exclusion of power generation combinations (wind/solar) that deviate from the timing of demand. Storage and power plant oversizing is all the more critical as production and demand are uncorrelated over the year. The ratio of useful to unused energy storage by the end of the year varies with the energy mix and operating intensity (productivity) of the farm. We discuss the implications of different energy configurations on the performance of the demand system.

Under ideal conditions, the growth of the mycelial network of a filamentous fungus is monotonous, showing an ever increasing complexity with time. The components of the network growth are very simple and based on two mechanisms: the elongation of each hypha, and their multiplication by successive branching. These two mechanisms are sufficient to produce a complex network, and could be localized only at the tips of hyphae. However, branching can be of two types, apical or lateral, depending on its location on the hyphae, therefore imposing the redistribution of the necessary material in the whole mycelium. From an evolutionary point of view, maintaining different branching processes, with additional energy needs for structure and metabolism, is intriguing. We propose in this work to discuss the advantages of each branching type using a new observable for the network growth, allowing us to compare growth configurations. For this purpose, we build on experimental observations of the Podospora anserina mycelium growth, enabling us to feed and constrain a lattice-free modeling of this network based on a binary tree. First, we report the set of statistics related to the branches of P. anserina that we have implemented into the model. Then, we build the density observable, allowing us to discuss the succession of growth phases. We predict that density over time is not monotonic, but shows a decay growth phase, clearly separated from an other one by a stationary phase. The time of appearance of this stable region appears to be driven solely by the growth rate. Finally, we show that density is an appropriate observable to differentiate growth stress.

Based upon apical growth and hyphal branching, the two main processes that drive the growth pattern of a fungal network, we propose here a two-dimensions simulation based on a binary-tree modelling allowing us to extract the main characteristics of a generic thallus growth. In particular, we showed that, in a homogeneous environment, the fungal growth can be optimized for exploration and exploitation of its surroundings with a specific angular distribution of apical branching. Two complementary methods of extracting angle values have been used to confront the result of the simulation with experimental data obtained from the thallus growth of the saprophytic filamentous fungus Podospora anserina . Finally, we propose here a validated model that, while being computationally low-cost, is powerful enough to test quickly multiple conditions and constraints. It will allow in future works to deepen the characterization of the growth dynamic of fungal network, in addition to laboratory experiments, that could be sometimes expensive, tedious or of limited scope.

Muscles are biological actuators extensively studied in the frame of Hill's classic empirical model as isolated biomechanical entities, which hardly applies to a living organism subjected to physiological and environmental constraints. Here we elucidate the overarching principle of a living muscle action for locomotion, considering it from the thermodynamic viewpoint as an assembly of actuators (muscle units) connected in parallel, operating via chemical-to-mechanical energy conversion under mixed (potential and flux) boundary conditions. Introducing the energy cost of effort as the generalization of the well-known oxygen cost of transport in the frame of our compact locally linear nonequilibrium thermodynamics model, we analyze oxygen consumption measurement data from a documented experiment on energy cost management and optimization by horses moving at three different gaits. Horses adapt to a particular gait by mobilizing a nearly constant number of muscle units minimizing waste production per unit distance covered; this number significantly changes during transition between gaits. The mechanical function of the animal is therefore determined both by its own thermodynamic characteristics and by the metabolic operating point of the locomotor system.

Under the current global energy crisis the interests in developing a third generation of biofuels produced from non-food feedstock such as microalgae and cyanobacteria have clearly increased. Hydrodynamic stress, always present in cultivation process of these microorganisms, is an essential factor to ensure mixing inside bioreactors; however the importance of its intensity is usually ignored by applying a random agitation (energy consumption) which is unnecessarily overestimated. In this work, two types of agitation, stirring in agitated photobioreactors (APBR) and bubbling air in draft tube airlift photobioreactors (DPBR), are applied to study the effects of hydrodynamic stress on the growth and pigment content evolution of the cyanobacteria Synechocystis sp. PCC 6803, a self-propelled microorganism. The range of applied shear stress was between 0 and 400 mPa. Similar results are obtained for both agitation mechanisms, indicating that the effects of shear stress are limited to the breakdown of the cell colonies; once they are broken down any further increase in shear stress has no significant effect on their growth rate. Moreover, the variation in pigments concentration appeared to be linear with the cellular concentration and independent from shear intensity.

Adaptable or adapted? Whether it is a question of physical, biological, or even economic systems, this problem arises when all these systems are the location of matter and energy conversion. To this interdisciplinary question, we propose a theoretical framework based on the two principles of thermodynamics. Considering a finite time linear thermodynamic approach, we show that non-equilibrium systems operating in a quasi-static regime are quite deterministic as long as boundary conditions are correctly defined. The Novikov–Curzon–Ahlborn derivation applied to non-endoreversible systems then makes it possible to precisely determine the conditions for obtaining characteristic operating points. As a result, power maximization principle (MPP), entropy minimization principle (mEP), efficiency maximization, or waste minimization states are only specific modalities of system operation. We show that boundary conditions play a major role in defining operating points because they define the intensity of the feedback that ultimately characterizes the operation. Armed with these thermodynamic foundations, we show that the intrinsically most efficient systems are also the most constrained in terms of controlling the entropy and dissipation production. In particular, we show that the best figure of merit necessarily leads to a vanishing production of power. On the other hand, a class of systems emerges, which, although they do not offer extreme efficiency or power, have a wide range of use and therefore marked robustness. It therefore appears that the number of degrees of freedom of the system leads to an optimization of the allocation of entropy production.

The success of filamentous fungi in colonizing most natural environments can be largely attributed to their ability to form an expanding interconnected network, the mycelium, or thallus, constituted by a collection of hyphal apexes in motion producing hyphae and subject to branching and fusion. In this work, we characterize the hyphal network expansion and the structure of the fungus Podospora anserina under controlled culture conditions. To this end, temporal series of pictures of the network dynamics are produced, starting from germinating ascospores and ending when the network reaches a few centimeters width, with a typical image resolution of several micrometers. The completely automated image reconstruction steps allow an easy post-processing and a quantitative analysis of the dynamics. The main features of the evolution of the hyphal network, such as the total length L of the mycelium, the number of “nodes” (or crossing points) N and the number of apexes A, can then be precisely quantified. Beyond these main features, the determination of the distribution of the intra-thallus surfaces (Si) and the statistical analysis of some local measures of N, A and L give new insights on the dynamics of expanding fungal networks. Based on these results, we now aim at developing robust and versatile discrete/continuous mathematical models to further understand the key mechanisms driving the development of the fungus thallus.

The metabolic processes complexity is at the heart of energy conversion in living organisms and forms a huge obstacle to develop tractable thermodynamic metabolism models. By raising our analysis to a higher level of abstraction, we develop a compact-i.e. relying on a reduced set of parameters- thermodynamic model of metabolism, in order to analyse the chemical-to-mechanical energy conversion under muscle load, and give a thermodynamic ground to Hill's seminal muscular operational response model. Living organisms are viewed as dynamical systems experiencing a feedback loop in the sense that they can be considered as thermodynamic systems subjected to mixed boundary conditions, coupling both potentials and fluxes. Starting from a rigorous derivation of generalized thermoelastic and transport coefficients, leading to the definition of a metabolic figure of merit, we establish the expression of the chemical-mechanical coupling, and specify the nature of the dissipative mechanism and the so-called figure of merit. The particular nature of the boundary conditions of such a system reveals the presence of a feedback resistance, representing an active parameter, which is crucial for the proper interpretation of the muscle response under effort in the framework of Hill's model. We also develop an exergy analysis of the so-called maximum power principle, here understood as a particular configuration of an out-of-equilibrium system, with no supplemental extremal principle involved.