Description Of Flow Research Articles

Analysis of mathematical methods for describing financial flows: dynamic modeling of an innovative company

Purpose. Development of a dynamic mathematical model of an innovative company operating in accordance with Ukrainian legislation, allowing for the analysis and adjustment of its financial activities. Methodology. When developing a model and description of financial flows, a factor analysis of the necessary indicators of the financial condition of the enterprise in question was carried out, which were used in the calculations of the presented mathematical modeling. A mathematical apparatus has been developed for calculating financial indicators depending on time. Using inductive, deductive and logical methods, an analysis of the financial situation for the year was carried out. Findings. The main methods and tools for describing financial flows have been analyzed. Mathematical modeling of the innovative company is carried out, which allows analyzing the costs of the enterprise and determining the size of its free funds. The calculation of financial indicators of the enterprise, which are demonstrated in the form of tables, is performed and the dynamics is shown in charts and graphs. All calculations were made on the basis of existing Ukrainian legislation using modern information technologies. Originality. A mathematical dynamic model of changes in financial flows at the enterprise has been developed and implemented. The proposed model takes into account various items of expenses and profits in accordance with the state legislation. Calculations allow for dynamic analysis and determination of the impact of various indicators on the financial condition of the enterprise, which allows for faster adoption and implementation of decisions in managing financial flows. This dynamic model is a convenient tool for any enterprise in Ukraine. Practical value. The results that were obtained during the study can become the basis for creating the necessary digital tools for researching, analyzing and adjusting the financial flows of a particular enterprise. Now methods are available that allow analyzing and describing financial flows more accurately and forecasting their changes in the future. The methodology presented allows the creation of dynamic models that can account for complex dependencies between different indicators and forecast the behavior of financial flows in real time. The financial model allows the simulation of cash flows of planned activities and the evaluation of financial planning in advance, taking into account the conducted research. It is straightforward to use and allows the analysis of different scenarios of business development, significantly reducing the time required.

Extending the Asteroseismic Calibration of the Stellar Rossby Number

The stellar Rossby number (Ro) is a dimensionless quantity that is used in the description of fluid flows. It characterizes the relative importance of Coriolis forces on convective motions, which is central to understanding magnetic stellar evolution. Here we present an expanded sample of Kepler asteroseismic targets to help calibrate the relation between Ro and Gaia color, and we extend the relation to redder colors using observations of the mean activity levels and rotation periods for a sample of brighter stars from the Mount Wilson survey. Our quadratic fit to the combined sample is nearly linear between 0.55 < G BP − G RP < 1.2, and can be used to estimate Ro for stars with spectral types between F5 and K3. The strong deviation from linearity in the original calibration may reflect an observational bias against the detection of solar-like oscillations at higher activity levels for the coolest stars.

Effect of the flow-force relationships used in two parameter modelling of freezing and vitrification protocols for bovine embryos

Cells may become damaged by strong volume changes and related intracellular changes during slow freezing or vitrification. These osmotic events can be modelled mathematically, using descriptions of transmembrane flow of solute and water. We compared different variants of an often used 2-parameter (2P) formalism in fitting of an empirical shrink-swell curve of a bovine embryo in 5 vol% glycerol, and in simulations of CPA loading and removal in a vitrification protocol. In its original form, the 2P model uses a flow-force relationship for the flux of CPA that is not analogous to that for water (asymmetrical), but in the other variants used, the flow-force relationships for water and CPA are analogous to each other (symmetrical). The effect of used model on estimated values for Lp and Ps in 5 vol% glycerol was small. Also the effect on shrinking and swelling in vitrification media was small, but the original 2P model predicted stronger swelling of embryos during one-step CPA removal. One variant that we compared simply assumes Raoult's law, i.e. M = m, even in very concentrated solutions We conclude that this simple model is easy and appropriate for simulating osmotic events of embryos. But if a method for correcting for the deviation from Raoult's law is used, a symmetrical model seems more appropriate than the original (asymmetrical) 2P model.

Influence of concentration on thermophoresis of spherical aerosol particles within a Brinkman medium

Abstract We are examining the thermophoretic movement of a uniform mixture of spherical aerosol particles, all with the same properties, as they are situated within a porous material. These particles can have various thermal conductivity and surface characteristics. This analysis focuses on situations where the Péclet and Reynolds numbers are small. The influence of particle interactions is carefully considered by using a unit cell model, a well-established method known for its accurate predictions in the context of sedimentation for monodisperse suspensions of spherical particles. The porous medium is represented as a Brinkman fluid characterized by a Darcy permeability, which can be determined directly from experimental observations. This medium is considered to be uniform and isotropic, and the solid matrix is in thermal equilibrium with the fluid flowing through the voids of the medium. The Knudsen number is assumed to be low, enabling the description of fluid flow through the porous medium using a continuum model that includes temperature jump, thermal creep, frictional slip, and thermal stress slip at the aerosol particle’s surface. The conservation equations for energy and momentum are individually tackled within each cell. In this model, each cell represents a spherical particle enclosed by a concentric shell of surrounding fluid. The thermophoretic particle migration velocity is determined across different cases. We derive analytical expressions for this average particle velocity, expressing it in terms of the particle volume fraction. It is observed that different cell models yield somewhat varied results for particle velocity. Generally, with a fixed permeability parameter characterizing the porous medium, an increase in the thermal stress slip coefficient tends to decrease the normalized thermophoretic velocity across the different cell models. The results are in good agreement with the available data as documented in the existing literature. Additionally, a parallel examination of aerosol sphere sedimentation is provided.

Development and testing of hybrid (PNM–CFD) mathematical model and numerical algorithm for description of fluid flows in three-dimensional digital core models

Numerical simulation of fluid flow in porous and fractured rocks is an important task for many industrial applications. The most common approaches to constructing such models are direct (CFD or lattice Boltzmann) and porous network (PNM) modeling. Each approach has its own advantages and disadvantages. This paper presents a hybrid mathematical PNM–CFD model for describing fluid flows in three-dimensional digital core models, which has the high speed performance of PNM approaches and high accuracy of CFD models. Numerical technique has been developed for describing fluid flows in three-dimensional digital core models using a hybrid PNM–CFD model. The numerical technique links a one-dimensional pore network solver and a three-dimensional CFD solver into a combined model in original way by constructing a single pressure field for the entire computation domain. To validate the model, several tests were performed, including flow in straight channels and numerical simulation of fluid flow in a microfluidic chip. The test results have shown the adequacy of the hybrid model performance. The hybrid model for determining pressure drop in a branched network with three-dimensional chambers has an error of no more than 5 % when compared to experimental data. Similarly, the error in calculating velocity does not exceed 7 % when compared to the full three-dimensional calculation. The hybrid model has shown an almost twofold increase in calculation speed compared to the full three-dimensional model.

A geometric-tension-dynamics model of epithelial convergent extension

Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer under actively generated internal tension. To resolve this apparent paradox, we formulate a model in which tissue flow in the tension-dominated regime occurs through adiabatic remodeling of force balance in the network of adherens junctions. We propose that the slow dynamics within the manifold of force-balanced configurations is driven by positive feedback on myosin-generated cytoskeletal tension. Shifting force balance within a tension network causes active cell rearrangements (T1 transitions) resulting in net tissue deformation oriented by initial tension anisotropy. Strikingly, we find that the total extent of tissue deformation depends on the initial cellular packing order. T1s degrade this order so that tissue flow is self-limiting. We explain these findings by showing that coordination of T1s depends on coherence in local tension configurations, quantified by a geometric order parameter in tension space. Our model reproduces the salient tissue- and cell-scale features of germ band elongation during Drosophila gastrulation, in particular the slowdown of tissue flow after approximately twofold elongation concomitant with a loss of order in tension configurations. This suggests local cell geometry contains morphogenetic information and yields experimentally testable predictions. Defining biologically controlled active tension dynamics on the manifold of force-balanced states may provide a general approach to the description of morphogenetic flow.

Two‐phase flows simulations in a space‐time framework for injection molding applications: Comparison with experimental results

AbstractHigh‐resolution numerical simulations of the injection molding process are crucial for precise process and part behavior prediction and tool fabrication. However, the complex flow behavior with high shear rates, rapid cooling as well as the nonlinear material properties post many challenges, and efficient high‐resolution numerical analysis is still subject to research. This study presents a simplified numerical description of the polymer flow and cooling during the injection phase, aiming for efficient and yet accurate simulations of the process. The in‐house finite‐element solver XNS is used to simulate the polymer and air flows, as a two‐phase flow, using the level‐set method. The injected polymer is characterized as a shear‐thinning flow using the non‐Newtonian Cross‐Williams‐Landel‐Ferry rheology model. To reduce the computational time, other polymer model effects such as a precise crystallization kinetics model during the injection phase have been neglected as a result of the findings of a previous study. Heading towards more efficient computations, we use a space‐time discretization, which has a higher convergence rate than commonly used time discretizations and can allow future mesh refinement in time, particularly convenient for our application. The results of the simulation are compared to the propagation of the flow front in an injection molding process of a plate part. The flow front is traced in‐situ by three aligned infrared sensors that detect the temperature increase from the mold wall. The time of flow front propagation between two sensors is in good agreement with experimental results. The peak temperature is calculated lower as compared to the experiment; however the temperature gradients are in good agreement validating the numerical model presented here.

Generalized grain boundary constitutive description implemented in a strain-gradient large-strain FFT-based formulation: Application to nano-metallic laminates

This paper presents a general treatment of grain boundary constitutive behavior in the context of strain-gradient (SG) plasticity, and its numerical implementation in a large-strain (LS) elasto-viscoplastic (EVP) fast Fourier transform (FFT)-based micromechanical model. Two novel grain boundary constitutive equations are proposed, allowing for more accurate description of the Burgers vector flow at the grain boundary. The capabilities of the generalized SG-LS-EVPFFT formulation are illustrated for the case of kink-band formation during layer-parallel compression of nano-metallic laminates (NMLs), requiring consideration of the interaction between dislocations and interfaces.

Kernel-Based Minimal Distributed Charges: A Conformationally Dependent ESP-Model for Molecular Simulations.

A kernel-based method (kernelized minimal distributed charge model (kMDCM)) to represent the molecular electrostatic potential (ESP) in terms of off-center point charges is introduced. The positions of the charges adapt to the molecular geometry and allow the description of intramolecular charge flow. Using Gaussian kernels and atom-atom distances as the features, the ESPs for water and methanol are shown to improve by at least a factor of 2 compared with point charge models fit to an ensemble of structures. The conformationally fluctuating molecular dipole moment of water is reproduced almost twice as accurately using kMDCM compared with static PCs, despite not fitting to the dipole directly. The role of hyperparameters in the kernelization is investigated and their implication on model performance and simulation stability is discussed. Combining kMDCM for the electrostatics and reproducing kernels for the bonded terms allows energy-conserving simulations of 2000 water molecules with periodic boundary conditions on the nanosecond time scale. These MD simulations sample geometries outside the training set but remain stable, which demonstrates the robustness of the model and its implementation.

Lattice Boltzmann modeling of natural circulation loop with emphasis on non-Boussinesq mechanism

The natural circulation loop is crucial for the safe and stable operation of nuclear reactors and other applications. Traditional numerical algorithms, based on the Boussinesq approximation, have limitations when dealing with large temperature differences and density disparity, and they do not fully address fluid compressibility. This paper adopts the decoupled and stabilized lattice Boltzmann method (DSLBM) with a non-Boussinesq algorithm to study the natural circulation loop. The DSLBM provides a detailed flow description under large temperature and density differences, incorporating the pseudopotential multiphase model, temperature equation, and state equation, without relying on assumptions. The study examines the loop's performance under various temperature differences, central height differences, and heating source lengths, focusing on mass flow rate, driving head, and heating power. It reveals the energy performance, flow characteristics, and heat transfer properties of the loop, highlighting the physical mechanisms involved. Comparison with the empirical formulation of the incompressible equation from the theoretical aspect shows that when the temperature difference coefficient is lower than 0.15, the two methods are not much different from each other. When the temperature difference coefficient reaches 0.2, 0.3, and 0.4, the difference between the two methods is 9.47%, 19.11%, and 42.64%, respectively. Consequently, the Boussinesq approximation can be compensated by DSLBM, which proves the value of the application of the algorithm in exploiting the compressibility of fluids. The dimensionless fitting correlation with greater universality is obtained, which helps to predict the properties of the natural circulation loop with varying temperature differences, friction coefficients, and geometric structures. The research in this paper will lay the foundation for optimizing the system design of the natural circulation loop and improving energy utilization efficiency.

Linearity of the Co-moving Velocity

The co-moving velocity is a new variable in the description of immiscible two-phase flow in porous media. It is the saturation-weighted average over the derivatives of the seepage velocities of the two immiscible fluids with respect to saturation. Based on analysis of relative permeability data and computational modeling, it has been proposed that the co-moving velocity is linear when plotted against the derivative of the average seepage velocity with respect to the saturation, the flow derivative. I show here that it is enough to demand that the co-moving velocity is characterized by an additive parameter in addition to the flow derivative to be linear. This has profound consequences for relative permeability theory as it leads to a differential equation relating the two relative permeabilities describing the flow. I present this equation together with two solutions.

Inferring pattern-driving intercellular flows from single-cell and spatial transcriptomics.

From single-cell RNA-sequencing (scRNA-seq) and spatial transcriptomics (ST), one can extract high-dimensional gene expression patterns that can be described by intercellular communication networks or decoupled gene modules. These two descriptions of information flow are often assumed to occur independently. However, intercellular communication drives directed flows of information that are mediated by intracellular gene modules, in turn triggering outflows of other signals. Methodologies to describe such intercellular flows are lacking. We present FlowSig, a method that infers communication-driven intercellular flows from scRNA-seq or ST data using graphical causal modeling and conditional independence. We benchmark FlowSig using newly generated experimental cortical organoid data and synthetic data generated from mathematical modeling. We demonstrate FlowSig's utility by applying it to various studies, showing that FlowSig can capture stimulation-induced changes to paracrine signaling in pancreatic islets, demonstrate shifts in intercellular flows due to increasing COVID-19 severity and reconstruct morphogen-driven activator-inhibitor patterns in mouse embryogenesis.

Towards bit threads in general gravitational spacetimes

The concept of the generalized entanglement wedge was recently proposed by Bousso and Penington, which states that any bulk gravitational region a possesses an associated generalized entanglement wedge E(a) ⊃ a on a static Cauchy surface M in general gravitational spacetimes, where E(a) may contain an entanglement island I(a). It suggests that the fine-grained entropy for bulk region a is given by the generalized entropy Sgen(E(a)). Motivated by this proposal, we extend the quantum bit thread description to general gravitational spacetimes, no longer limited to the AdS spacetime. By utilizing the convex optimization techniques, a dual flow description for the generalized entropy Sgen(E(a)) of a bulk gravitational region a is established on the static Cauchy surface M, such that Sgen(E(a)) is equal to the maximum flux of any flow that starts from the boundary ∂M and ends at bulk region a, or equivalently, the maximum number of bit threads that connect the boundary ∂M to the bulk region a. In addition, the nesting property of flows is also proved. Thus the basic properties of the entropy for bulk regions, i.e. the monotonicity, subadditivity, Araki-Lieb inequality and strong subadditivity, can be verified from flow perspectives by using properties of flows, such as the nesting property. Moreover, in max thread configurations, we find that there exists some lower bounds on the bulk entanglement entropy of matter fields in the region E(a) \\ a, particularly on an entanglement island region I(a) ⊂ (E(a) \\ a), as required by the existence of a nontrivial generalized entanglement wedge. Our quantum bit thread formulation may provide a way to investigate more fine-grained entanglement structures in general spacetimes.

Experimental and Statistical Determination of Convective Heat and Mass Transfer Coefficients for Eucalyptus nitens Sawn Wood Drying

This study aimed to develop a model using experimentally obtained convective heat and mass transfer coefficients to predict the effect of temperature, humidity, and drying rate on wood drying. Tangential wood samples of Eucalyptus nitens (H. Deane &amp; Maiden) were used in the investigation. The experimental design consisted of two temperature levels (40 °C and 55 °C), two relative humidity levels (55% and 75%), and two air velocity settings (2 m·s−1 and 3 m·s−1). The experiments were conducted under a constant evaporation rate, spanning the maximum and critical moisture content in the wood. A statistical model using multivariate regression was created to predict the convective heat and mass transfer coefficients. The results indicated that the experimental data and empirical correlations exhibited an error margin of 37.77% and 37.86%, respectively. A significant positive correlation was found between the convective heat transfer coefficient and air velocity, temperature, and relative humidity, while the convective mass transfer coefficient showed a significant positive correlation only with air velocity and temperature. The model predicted the convective heat and mass transfer coefficients with high accuracy and statistical significance. Using the proposed method, we successfully obtained both convective coefficients, which enable accurate description of heat and mass flow during the convective drying of Eucalyptus nitens wood.

Heat flow analysis and description of the cooperation of the heat exchange station with heat exchange substations located in apartments

Heat flow analysis and description of the cooperation of the heat exchange station with heat exchange substations located in apartments

Theoretical analysis of using multiple borehole heat exchangers for production of heating and cooling energy in shallow geothermal reservoirs with underground water flow

In this work the feasibility of using the double-U borehole heat exchangers (BHE) in multiple arrangements for production of heating and cooling energy has been investigated.Theoretical case studies are given for a few hypothetical lithological cases corresponding to the lithology that can be found in City of Zagreb. The results show interference between the borehole heat exchangers and limits of use of shallow reservoir with respect to slow convection and loss of accumulated energy in the reservoir. Special emphasis is placed on the description of the groundwater flow determined by the parameters of the shallow geothermal reservoir, such as permeability, water saturation, thermal conductivity, specific heat capacity and soil density, topography, precipitation, etc. Simulations have been performed in FeFlow coupled with Python user-scripts for individual control of the BHE’s, and the surface equipment is modelled using RES2GEO. To assess the accuracy of numerical predictions in simulating thermal responses, FeFlow software was utilized to conduct Thermal Response Tests (TRT) for individual Borehole Heat Exchangers (BHEs). These numerical results were then juxtaposed with empirical TRT data collected from a site near Velika Gorica, a town within the City of Zagreb. For each case simulation is done for one year with one hour resolution. The temperature distribution analysis highlights notable differences between scenarios, where the temperature field with lower permeability experiences significant variations, particularly near the BHE. Here, temperatures can soar to 20 °C during cooling periods and plummet to 4 °C in heating seasons. These fluctuations cause overheating and subcooling of the reservoir, impairing the heat pump’s efficiency and necessitating increased electricity consumption. By using Multivariate linear regression and Multi-layer perceptron regressor method, the main parameter for determination of COP of ground source heat pump. The analysis reveals that the majority of errors fall within the range of ± 5 %, although the MLA prediction method exhibits slightly more frequent errors. Additionally, the R2 scores demonstrate strong performance: the MLA procedure achieves 0.95 for heating and 0.99 for cooling, while the MLP procedure attains 0.99 for both heating and cooling phases.

An integrated method and tool for telescopic beams design in extendable undercarriages

Earth-moving machine builders require innovative design methods and tool to optimize structural performance while reducing production and design costs, particularly in crucial phases like undercarriage frame design and structural verification. After an in-depth description of the design flow normally followed in industry, the paper presents a computationally efficient method and tool to aid designers in dimensioning extendable tracked undercarriages, aiming to drastically reduce design time and efforts to optimize resources. The proposed tool is based on an analytical model established from in-depth analyses of the undercarriage Computer Aided Design (CAD) assembly and the expertise of the industrial partner. To address the 3D structural problem, a planar system is employed with proper corrective coefficients. These coefficients are meticulously evaluated through direct comparison with Finite Element Method (FEM) models by seamlessly integrating SolidWorks and ANSYS Workbench. The tool accepts as inputs geometric and material data, as well as specific user-defined load scenarios, providing outputs in the form of the deflected configuration of the undercarriage and stress levels. Direct comparison with the results obtained from FEM for three industrial undercarriage models demonstrates the validity of the approach, with errors consistently within the 10% range in almost all cases. This enables designers with no advanced skills in FEM to efficiently validate diverse design variants with minimal effort. Once validated, the tool is integrated with an optimizer in Matlab to conduct computationally efficient design optimization studies. The optimization problem, focused on minimizing the beam’s vertical size while maintaining structural integrity and limiting deflections, has been successfully resolved within a limited computational time, showcasing the benefits of the proposed approach for undercarriage design.

Basal Force Fluctuations and Granular Rheology: Linking Macroscopic Descriptions of Granular Flows to Bed Forces With Implications for Monitoring Signals

AbstractGranular flows are ubiquitous in nature with single flows traversing a wide range of dynamic conditions from initiation to deposition. Many of these flows are responsible for significant hazards and can generate remotely detectable seismic signals. These signals provide a potential for real‐time flow measurements from a safe distance. To fully realize the benefit of seismic measurements, basal‐granular forces must be linked to macroscopic internal flow dynamics across a wide range of flow conditions. We utilize discrete element simulations to observe dry and submerged granular flows under plane‐shear and inclined‐flow configurations, relating bulk kinematics to basal‐force distributions. We find that the power and frequency of force fluctuations scale with non‐dimensional shear rate (I). This scaling tracks three pre‐established regimes that are described by μ(I) rheology: (a) an intermittent particle rearrangement regime, where basal forces are dominated by low frequencies; (b) an intermediate regime where basal forces start to increase in frequency while showing correlations in space and (c) a fully collisional regime where the signal is nearly flat up to a cutoff frequency. We further identify a newly defined fourth regime that marks a “phase change” from the intermediate to collisional regime where increases in basal force fluctuations with increasing shear rates stalls as the granular bed dilates, partially destroying the contact network. This effort suggests that basal forces can be used to interpret complex granular processes in geophysical flows.

A historical overview of experimental hydrology in China

AbstractThe history of experimental hydrology in China is important but poorly documented. Here we review 94 papers (86 of these in Chinese) from the CNKI and Web of Science websites to chronicle the history of experimental studies in China before 2000. Professor Wei‐Zu Gu—the focus of this Special Issue—factors heavily into this history. Perhaps more than any country, the experimental hydrology history of China is influenced by socioeconomic development and political change. Our analysis shows 4 main periods of development associated with (1) an early development stage before 1949, the founding year of People's Republic of China (PRC), (2) an initial period of rapid transition in experimental studies in China (1949–1965), (3) a struggling and recovering stage for during and shortly after the Cultural Revolution, from 1965 to 1978, and (4) significant progress associated with new policies for reform and opening up in China from 1978 to 2000, that included contributions of Wei‐Zu Gu and other scientists. In terms of experimental hydrological findings, two notable contributions are a mathematical description of saturation overland flow derived from streamflow and precipitation data and calculated water storage deficit in the unsaturated zone by Zhao and Zhuang (1963), several years before its process‐based ‘discovery’ in the USA (and elsewhere) and the ‘interface runoff generation law’ of Yu (1985) which was ahead of its time in understanding linking the notion of the commonality of all runoff forms. In terms of model development stemming from experimental studies, the development of the Xinanjiang Model of Zhao (1980) was a significant achievement, later partly adopted into the VIC model in the USA and the ARNO model in Europe. Finally, the Hydrohill catchment developed by Wei‐Zu Gu led the way for the rapid rise in process studies and internationalization of experimental hydrology in China. Overall, the experimental hydrological studies from 1949 to 2000 had a strong engineering focus, with many links to water conservation construction and management.

Improving the sustainability of arable cropping systems by modifying root traits: A modelling study for winter wheat

AbstractModifying root systems by crop breeding has been attracting increasing attention as a potentially effective strategy to enhance the sustainability of agriculture by increasing soil organic matter (SOM) stocks and soil quality, whilst maintaining or even improving yields. We used the new soil‐crop model USSF (Uppsala model of Soil Structure and Function) to investigate the potential of this management strategy using winter wheat as a model crop. USSF combines a simple (generic) crop growth model with physics‐based descriptions of soil water flow, water uptake and transpiration by plants. It also includes a model of the interactions between soil structure dynamics and organic matter turnover that considers the effects of physical protection and microbial priming on the decomposition of SOM. The model was first calibrated against field data on soil water contents and both above‐ground and root biomass of winter wheat measured during one growing season in a clay soil in Uppsala, Sweden using the GLUE method to identify five ‘acceptable’ parameter sets. We created four model crops (ideotypes) by modifying root‐related parameters to mimic winter wheat phenotypes with improved root traits. Long‐term (30‐year) simulations of a conventionally tilled monoculture of winter wheat were then performed to evaluate the potential effects of cultivating these ideotypes on the soil water balance, soil organic matter stocks and grain yields. Our results showed that ideotypes with deeper root systems or root systems that are more effective for water uptake increased grain yields by 3% and SOM stocks in the soil profile by ca. 0.4%–0.5% in a 30‐year perspective (as an average of the five parameter sets). An ideotype in which below‐ground allocation of dry matter was increased at the expense of stem growth gave even larger increases in SOM stocks (ca. 1.4%). An ideotype combining all three modifications (deeper and more effective root systems and greater root production) showed even more promising results: compared with the baseline scenario, surface runoff decreased while yields were predicted to increase by ca. 7% and SOM stocks in the soil profile by ca. 2%, which is roughly equivalent to ca. 20% of the 4‐per‐mille target (https://4p1000.org/).