Stable Arrangement Research Articles

Arched foot based on conformal complex neural network testing

Complex-Valued Neural Networks (CNNs) are the most successful extension of the real-valued neural networks. They play a significant role in deep learning. Following this great fact, CNNs are utilized in computer vision and its critical field Image analysis (IA). Symmetry vision is a theory closely related to assembly and uniformity. More accurately, symmetrical rallies can be categorized as covering self-similarities. In 2D images, the self-similarity comes from rigid transformations (such as operators, polynomials and differential and integral equations) that map one part onto another (in calculus is called an injective map and in the conformal analysis is called a univalent map). In this paper, we define a new style of CNNs called Conformal Neural Networks (CoNNs) based on the concept of conformal theory in the open unit disk. Moreover, we introduce a general symmetric 2D-parameter Beltrami equation (SBE) in a complex domain. The dominant idea is to map the external and inner of the domain conformally to unit disks, using a symmetric differential operator (which is suggested to be the solution of SBE). As an application, we present a new algorithm to obtain the arches of the foot from their marks by training CoNNs. The results prove that the effectiveness of our suggested procedure is a stable form arrangement.

Structure, Stability, and Mechanical Properties of Boron-Rich Mo-B Phases: A Computational Study.

Molybdenum borides were studied theoretically using first-principles calculations, parameterized lattice model, and global optimization techniques to determine stable crystal structures. Our calculations reveal the structures of known Mo-B phases, attaining close agreement with experiment. Following our developed lattice model, we describe in detail the crystal structure of boron-rich MoBx phases with 3 ≤ x ≤ 9 as the hexagonal P63/mmc-MoB3 structure with Mo atoms partially replaced by triangular boron units. The most energetically stable arrangement of these B3 units corresponds to their uniform distribution in the bulk, which leads to the formation of a disordered nonstoichiometric phase, with ordering arising at compositions close to x = 5 because of a strong repulsive interaction between neighboring B3 units. The most energetically favorable structures of MoBx correspond to the compositions 4 ≲ x ≤ 5, with MoB5 being the boron-richest stable phase. The estimated hardness of MoB5 is 37-39 GPa, suggesting that the boron-rich phases are potentially superhard.

Charge reduction in ions in the ionic liquid 1-ethy-2,3-dimethylimidazolium bis(trifluoromethanesulfonyl)imide on the Au(111) surface

Room-temperature ionic liquids (RTILs) are one type of electrolytes which have promising applications in batteries, catalysts, supercapacitors, etc. Computational simulations have played an essential role in elucidating many of the RTILs’ properties. Because Coulomb interactions dominate in RTILs, it is important to understand charge fluctuations, i.e., when ions’ charges are significantly less than unity. In this work, we perform calculations from density functional theory methods and the Bader charge analysis to examine ionic charges of 1-ethy-2,3-dimethylimidazolium bis(trifluoromethanesulfonyl)imide ([EMMIM]+[TFSI]−) thin film on the gold (111) surface. For cation and anion of similar sizes, we first identify the most stable ionic arrangement on Au(111) to be a checkerboard pattern. We build the thin film with up to four layers of ions in the most stable configuration and analyze the charge of each ion. In addition to cases of equal numbers of cations and anions, we also study systems where there is one more cation or anion but no net charge. We find that ions mostly maintain a near unity charge. However, when the ion numbers are not equal, and therefore the system is kept neutral by accruing counter charge on the gold, the counter charge is much less than unity, indicating charge reduction in ions. We further find that the charge deviation mostly occurs on the ion in the top layer and the reduction increases with the number of layers. We explain the results through a model of state mixing that includes charge transfer between the gold and ions.

Nuclear structure is governed by the fundamental laws of electromagnetism

Contradicting interpretations of the nuclear force as given by two contrasted approaches like the meson theory and the quantum chromodynamics, are overcome here by reviving the basic electromagnetic laws which are applicable on the existing charged subconstituents in nucléons. On this basis, considerable charge distributions in nucleons are determined after a careful analysis of the magnetic moments and the results of the deep inelastic scattering. Basic equations derived from the distributed charges of oriented spins of nucléons give strong and short ranged forces leading exactly to the binding energies of the deuteron and other nuclei. According to these interactions, p-p and n-n systems repel and only the p-n bonds form rectangles and closely packed parallelepipeds. Such contrary forces create structures of saturation and of finite number of nucléons. They also invalidate the charge independence hypothesis and differ fundamentally from the central potential and the effects of the Pauli principle of the electronic configurations responsible for the development of the models of the Fermi gas and nuclear shell. There are two kinds of p-n bonds, which imply anisotropy, leading often to elongated shapes of vibrational and rotational modes of excitation, while the surface tension contributes to the creation of non elongated shapes of stable arrangements. Finally, for A>40 a type of shell structure provides new rules for understanding the structure of magic nuclei for N>Z and the increasing ratio N/Z with A.

Copts and the Security State: Violence, Coercion, and Sectarianism in Contemporary Egypt

Copts and the Security State: Violence, Coercion, and Sectarianism in Contemporary Egypt

Jammed hard-sphere hcp crystals permeated with trivacancy tunnels

Supported by simple table-top experiments involving stackings of ball bearings and theoretical analysis, we have discovered crystal packings of identical hard spheres that are permeated by a high concentration of large tunnels and yet are jammed (mechanically stable). We show that starting with a strictly jammed hexagonal close-packed (hcp) crystal of identical hard spheres, removal of certain subsets of those spheres can produce mechanically stable vacancy arrangements involving compact (equilateral triangle) trivacancies such that they produce linear trivacancy tunnels. These tunnels can extend over the entire macroscopic length of the hcp medium, and their width is sufficient to allow contained “test” hard spheres with diameters less than 5−1=1.23606… to migrate over that entire length without contacting the static tunnel-wall spheres. A search for the stable (strictly jammed) periodic framework that hosts the highest density of parallel trivacancy tunnels has identified a structure exhibiting a packing fraction ϕ=π/32=0.55536…, which is equal to 3/4 of the maximum monovalent sphere packing fraction ϕmax=π/18=0.74048…. In that periodic arrangement, filling the interior of the contained tunnels with movable unit-diameter spheres may approach the greatest possible “rattler” density within jammed monovalent sphere systems subject to periodic boundary conditions. It will be of interest to study the physical and chemical properties of these anisotropic porous crystal structures. Our findings may have practical implications for engineered separation and catalytic processes.

The structural organization of Giardia intestinalis cytoskeleton.

Giardia intestinalis, the causative agent of giardiasis, has complex cytoskeleton organization with structures involved in motility, adhesion, cell division, and cell differentiation. Microtubules are key components of the cytoskeleton and are the main elements of the ventral disc, median body, funis, in addition to four pairs of flagella. These cytoskeletal elements are basically stable microtubule arrangements. Although tubulins are the main proteins of these elements, molecular and biochemical analyses of Giardia trophozoites have revealed the presence of several new and not yet characterized proteins in these structures, which may contribute to their nanoarchitecture (mainly in the ventral disc). Despite these findings, morphological data are still required for understanding the organization and biogenesis of the cytoskeletal structures. In the study of this complex and specialized network of filaments in Giardia, two distinct and complementary approaches have been used in recent years: (a) transmission electron microscopy tomography of conventionally processed as well as cryo-fixed samples and (b) high-resolution scanning electron microscopy and helium ion microscopy in combination with new plasma membrane extraction protocols. In this review we include the most recent studies that have allowed better understanding of new Giardia components and their association with other filamentous structures of this parasite, thus providing new insights in the role of the cytoskeletal structures and their function in Giardia trophozoites.

The Coase Theorem, the Nonempty Core, and the Legal Neutrality Principle

AbstractThe Coase theorem states that where there are externalities and no transaction costs resource allocation is Pareto-optimal and independent of the stakeholders’ legal position. This result has been challenged many times. In the cooperative game approach to resource allocation, the refutation is made by constructing a three-person game which has an empty core under one set of liability rules—which implies that optimal allocations are coalitionally unstable–and a nonempty core under another set. In this example, however, the probability that the core is non-empty is rather high (5/6). Yet, even if coalitionally stable Pareto-optimal arrangements are likely, to establish the plain validity of the Coase theorem it must be shown that the legal neutrality statement also holds. We show that for the three-person cooperative game example mentioned above, the probability that the two assertions of the Coase theorem hold can be as low as 3/8.

Resonant excitation and all-optical switching of femtosecond soliton molecules

The emergence of confined structures and pattern formation are exceptional manifestations of concurring nonlinear interactions found in a variety of physical, chemical and biological systems[1]. Optical solitons are a hallmark of extreme spatial or temporal confinement enabled by a variety of nonlinearities. Such particle-like structures can assemble in complex stable arrangements, forming "soliton molecules"[2,3]. Recent works revealed oscillatory internal motions of these bound states, akin to molecular vibrations[4-8]. These observations beg the question as to how far the "molecular" analogy reaches, whether further concepts from molecular spectroscopy apply in this scenario, and if such intra-molecular dynamics can be externally driven or manipulated. Here, we probe and control such ultrashort bound-states in an optical oscillator, utilizing real-time spectroscopy and time-dependent external perturbations. We introduce two-dimensional spectroscopy of the linear and nonlinear bound-state response and resolve anharmonicities in the soliton interaction leading to overtone and sub-harmonic generation. Employing a non-perturbative interaction, we demonstrate all-optical switching between distinct states with different binding separation, opening up novel schemes of ultrafast spectroscopy, optical logic operations and all-optical memory.

ON THE NA’T GHAZALS OF ABDURAHMAN JAMI AND ALISHER NAVAI

The article deals with a comparative study of na’t ghazals of the great figures of the Persian and Turkic poetry – Abdurahman Jami and Alisher Navois’ Devans. The ghasals play an important role for the evaluation of the XV century’s religious-philosophical and artistic thinking. In Alisher Navoi's ‘Khazoyin ul-maoni’, which consists of four devan and n’at ghazals of A. Jami’s three devans, which deals with the subject-matters about Muhammad (s.a.v)’s lifestyle, khadises, miracles sent to him and his role in the life of a human being have been stated. Author analyzes the na’ts by both poets’ ghazals, in particular the subject of the artistic knowledge of several images and concepts: Mecca, Batho, Ka'ba, Medina, Yasrib, Zamzam, Prophethood, Adam, Khatam al-Anbiya, Hadisand others. According to the placement of na’t ghazals of A. Navai’s devan, the author emphasizes that they have a stable arrangement in the composition of devons, unlike of A. Jami’s ghazals, which is linked with ‘Shawahid un- Nubuwat’, the life-style of the Prophet Muhammad.

Folded graphene nanoribbon as a sensitive and selective gas sensor: first principles study

In recent years, graphene nanoribbon (GNR) has emerged as a promising new semiconducting substance due to its potential applications in nanoelectronics. Two types of GNRs; zigzag (ZGNR) and armchair (AGNR) have been investigated recently, where the latter is suitable for sensor applications due to its semiconducting properties. Moreover, a new configuration of AGNR, which is constructed by folding an AGNR over its width (FAGNR), has attracted significant attention due to its unique electrical properties. The potential applications of AGNR and FAGNR as gas sensors have been investigated in detail. In order to achieve stable atomic arrangement, each structure is relaxed up to a minimum energy construction. Using density functional theory, it is found that the interactions of CO, O2 and CO2 molecules with FAGNR are more than those with AGNR. Furthermore, based on non-equilibrium Green’s function (NEGF), the current–voltage characteristics of the two aforementioned gas sensors are calculated and compared. It is demonstrated that FAGNR shows more resistive sensitivity and selectivity to CO2 gas molecule even under normal atmospheric conditions, where FAGNR has already adsorbed O2 gas molecules from ambiance. Consequently, it is deduced that FAGNR would open a new window for developing a selective and more efficient CO2 resistive gas nanosensor.

Molecular scale modeling approach to evaluate stability and dissociation of methane and carbon dioxide hydrates

A comprehensive knowledge and precise estimation of the dynamic, structural, and thermodynamic characteristics of hydrates are needed to assess the stability of gas hydrates. Thermodynamic model and experimental studies can be utilized to compute the physical and dynamic properties of hydrate structures. The use of molecular dynamic (MD) simulation is a well-established approach in gas hydrate studies at the atomic level where the properties of interest are obtained from the numerical solution of Newtonian equations. The present work uses MD simulations by employing the constant temperature-constant pressure (NPT), constant temperature-constant volume (NVT) conditions, and the consistent valence force field (CVFF) to monitor the stability and decomposition of methane and carbon dioxide gas hydrates with different compositions. The effects of temperature and composition on the hydrate stability are investigated. In this study, we also compute the radial distribution function, mean square displacement, diffusion coefficient, lattice parameter, potential energy, dissociation enthalpy as well as the density of methane and carbon dioxide under various thermodynamic and process conditions. The formation of methane and carbon dioxide bubbles is studied to investigate bubble evolution during hydrate dissociation. The sizes of methane and carbon dioxide bubbles are not the same due to different solubility conditions of methane and carbon dioxide in liquid water. In addition, the influences of pressure and temperature on the lattice parameter and density of clathrate hydrates are discussed. The obtained results are consistent with previous theoretical and experimental findings, implying that the methodology followed in this work is reliable. The most stable arrangement of methane and carbon dioxide molecules in the gas hydrate is found. The insights/findings of this study might be useful to further understand detailed transport phenomena (e.g., molecular interactions, gas production rate, carbon dioxide replacement, and carbon dioxide capture) involved in the process of carbon dioxide injection into gas hydrate reservoirs.

Host-guest inclusion systems of tetra(alkyl)resorcin [4]arenes with choline in DMSO: Dynamic NMR studies and X-ray structural characterization of the 1:1 inclusion complex

The host-guest complex of C-tetra(methyl)calix[4]resorcinarene (1), C-tetra(pentyl)calix[4]resorcinarene (2), and C-tetra(nonyl)calix[4]resorcinarene (3) with choline in DMSO was examined via dynamic NMR. Under these conditions, only C-tetra(methyl)calix[4]resorcinarene formed a complex with choline. In order to establish the role of DMSO during the solubilization/complexation process, titration was carried out with resorcinarenes and DMSO in CDCl3. Our careful NMR analysis was based on the assignment of 1H NMR signals of the resorcinarenes in CDCl3 after the addition of variable amounts of DMSO, which showed an interesting host-guest interaction with C-tetra(pentyl)calix[4]resorcinarene. With both solvents, it is possible to define stable cone conformational arrangements based on the signals shown in the spectra of all the experiments. The results show the formation of a 1:1 inclusion complex between DMSO and C-tetra(pentyl)calix[4]resorcinarene. Suitable crystals of C-tetra(pentyl)resorcinarene in DMSO were characterized through an X-ray crystal structure determination and showed the inclusion of a molecule of DMSO in the cavity of the resorcinarene. The asymmetric unit contains one molecule of water and five molecules of DMSO, and analysis indicated that resorcinarene prefers a cone configuration (rccc conformation) in the solid state. In the crystal array, classical hydrogen bond O–H⋯O interactions and intermolecular contacts were observed.

DNA segregation under Par protein control.

The spatial organization of DNA is mediated by the Par protein system in some bacteria. ParB binds specifically to the parS sequence on DNA and orchestrates its motion by interacting with ParA bound to the nucleoid. In the case of plasmids, a single ParB bound plasmid is observed to execute oscillations between cell poles while multiple plasmids eventually settle at equal distances from each other along the cell’s length. While the potential mechanism underlying the ParA-ParB interaction has been discussed, it remains unclear whether ParB-complex oscillations are stable limit cycles or merely decaying transients to a fixed point. How are dynamics affected by substrate length and the number of complexes? We present a deterministic model for ParA-ParB driven DNA segregation where the transition between stable arrangements and oscillatory behaviour depends only on five parameters: ParB-complex number, substrate length, ParA concentration, ParA hydrolysis rate and the ratio of the lengthscale over which the ParB complex stimulates ParA hydrolysis to the lengthscale over which ParA interacts with the ParB complex. When the system is buffered and the ParA rebinding rate is constant we find that ParB-complex dynamics is independent of substrate length and complex number above a minimum system size. Conversely, when ParA resources are limited, we find that changing substrate length and increasing complex number leads to counteracting mechanisms that can both generate or subdue oscillatory dynamics. We argue that cells may be poised near a critical level of ParA so that they can transition from oscillatory to fixed point dynamics as the cell cycle progresses so that they can both measure their size and faithfully partition their genetic material. Lastly, we show that by modifying the availability of ParA or depletion zone size, we can capture some of the observed differences in ParB-complex positioning between replicating chromosomes in B. subtilis cells and low-copy plasmids in E. coli cells.

Structure and spectrum of the hydrated electron. A combined quantum chemical statistical mechanical simulation

In the current work, in order to model a free electron solvated in water, we have implemented a method to represent the molecular charge distribution as a set of Slater-type functions within the framework of a QM/MM method called QMSTAT. Also, it has been introduced in this method a new approach to calculate the intermolecular induction energy in the presence of very strong electric fields. Unlike most previous potentials, our method uses the ab initio energies of the electron-water complex as reference to obtain the few fitted parameters that the model needs, instead of the ab initio potential of the electron.A Metropolis-Monte Carlo simulation of 15 million steps has been carried out in a system that consists of an electron solvated in 200 water molecules explicitly described. The obtained results predict a vertical electron detachment energy of 3.30 eV and a radius of gyration of 2.38 Å, which are in very good agreement with the experimental data of 3.27 ± 0.10 eV and 2.45 Å, respectively. We have also obtained the absorption spectrum of the hydrated electron from our simulation. The maximum of the spectrum agrees very well with the experimental result and the experimental width at half-maximum is only 0.11 eV wider than the calculated curve. The calculations predict the same blue tail as the experimental result but with a less smooth shape. Also, our results indicate that the transfer of intensity from the transition arriving to the highest of the three p states to transitions arriving to higher-lying states contributes to the intensity enhancement of the blue tail of the spectrum. Regarding the solvated structure of the free electron, we have found that if the basis center is used as the electron site to calculate the correlation functions, the results predict a structure where the electron places itself on top of a central water molecule surrounded by the remaining water molecules in a very organized and stable arrangement. However, if the maximum of the electron density is used as electron site the obtained picture shows an electron located in a very fluctuating cavity that collapses and reforms continuously.

Intestinal Gel-Forming Mucins Polymerize by Disulfide-Mediated Dimerization of D3 Domains

The mucin 2 glycoprotein assembles into a complex hydrogel that protects intestinal epithelia and houses the gut microbiome. A major step in mucin 2 assembly is further multimerization of preformed mucin dimers, thought to produce a honeycomb-like arrangement upon hydrogel expansion. Important open questions are how multiple mucin 2 dimers become covalently linked to one another and how mucin 2 multimerization compares with analogous processes in related polymers such as respiratory tract mucins and the hemostasis protein von Willebrand factor. Here we report the x-ray crystal structure of the mucin 2 multimerization module, found to form a dimer linked by two intersubunit disulfide bonds. The dimer structure calls into question the current model for intestinal mucin assembly, which proposes disulfide-mediated trimerization of the same module. Key residues making interactions across the dimer interface are highly conserved in intestinal mucin orthologs, supporting the physiological relevance of the observed quaternary structure. With knowledge of the interface residues, it can be demonstrated that many of these amino acids are also present in other mucins and in von Willebrand factor, further indicating that the stable dimer arrangement reported herein is likely to be shared across this functionally broad protein family. The mucin 2 module structure thus reveals the manner by which both mucins and von Willebrand factor polymerize, drawing deep structural parallels between macromolecular assemblies critical to mucosal epithelia and the vasculature.

Partnering against Insecurity? A Comparison of Markets, Institutions and Worker Risk in Canadian and Swedish Retail

AbstractThis article provides insights on how union power influences the outcomes of labour‐management partnerships, with a focus on insecurity. It examines matched pairs of food retailers in Canada and Sweden. Trends in wages, scheduling and union coverage from 1980 to 2016 are compared. Actors in both contexts adopted partnering strategies in response to intensified price competition. However, the Swedish partnerships produced stable work arrangements, while working conditions eroded considerably in Canada. Bargaining structures, union security and identity are examined to explain the variations. As market competition intensified, the Swedish union gained leverage by using partnerships to fight unfair competition and promote sectoral well‐being in the process. Meanwhile, the Canadian union lost leverage, instead using partnerships to align employment practices with those of low‐cost market entrants and enhancing store‐level performance at all costs. The argument is that markets can be a resource for unions, even in low‐skilled service sectors, but only under inclusive institutions.

From 3D to 2D: Structural, Spectroscopic and Theoretical Investigations of the Dimensionality Reduction in the [PtAl2 ]δ- Polyanions of the Isotypic MPtAl2 Series (M=Ca-Ba, Eu).

Four new MPtAl2 (M=Ca, Sr, Ba, Eu) compounds, adopting the orthorhombic MgCuAl2 -type structure, have been synthesized from the elements using tantalum ampoules. All compounds are obtained as platelet-shaped crystallites and exhibit an increasing moisture sensitivity with increasing size of the formal M cation. Structural investigations indicate a pronounced elongation of the crystallographic b-axis, which results in a significant distortion of the [PtAl2 ]δ- polyanion. Within the polyanion, layer-like arrangements can be found with bonding Pt-Al interactions within the slab; the increase of the b-axis can be attributed to increasing Al-Al distances and therefore decreasing interactions between the slabs, caused by the differently-sized formal M cations. While the alkaline earth (M=Ca, Sr) representatives exhibit Pauli paramagnetism, BaPtAl2 shows diamagnetic behavior, finally EuPtAl2 is ferromagnetic with TC =54.0(5) K. The effective magnetic moment indicates that the Eu atoms are in a divalent oxidation state, which is confirmed by 151 Eu Mössbauer spectroscopic investigations. Measurements below the Curie-temperature show a full magnetic hyperfine field splitting with Bhf =21.7(1) T. 27 Al and 195 Pt magic-angle spinning NMR spectroscopy corroborates the presence of single crystallographic sites for the Pt and Al atoms. The large 27 Al nuclear electric quadrupolar coupling constants confirm unusually strong electric field gradients, in agreement with the structural distortions and the respective theoretical calculations. X-ray photoelectron spectroscopy has been utilized to investigate the charge transfer within the polyanion. The Pt 4f binding energy decreases with decreasing electronegativity / ionization energy of the alkaline earth elements, suggesting an increasing electron density at the Pt atoms. Theoretical investigations underline the platinide character of the investigated compounds by Bader charge calculations. The analysis of the integrated crystal orbital Hamilton population (ICOHP) values, electron localization function (ELF) and isosurface analyses lead to a consistent structural picture, indicating stable layer-like arrangements of the [PtAl2 ]δ- polyanion.

The plus-tip tracking and microtubule stabilizing activities of Javelin-like regulate microtubule organization and cell polarity.

Cell polarity is essential for building cell asymmetry in all eukaryotic cells. Drosophila oocyte and bristle development require the newly characterized Spn-F protein complex, which includes Spn-F, IKKε, and Javelin-like (Jvl), to establish polarity. Jvl is a novel microtubule (MT)-associated protein; however, the mechanism by which it regulates MT organization is still unknown. We found that overexpression of Jvl stabilizes MTs and that jvl is needed for stable MT arrangement at the bristle tip and organization of the dynamic MT throughout the bristle shaft. At low levels of expression in cultured cells, Jvl behaved as a microtubule plus-end tracking protein. We demonstrated that Jvl physically interacts with the highly conserved MT end-binding protein 1 (EB1) using yeast two-hybrid and GST pull-down assays. This interaction is, however, dispensable for Jvl function in oocyte and bristle development. In addition, using a MT-binding assay, we saw that Jvl-C terminus directly binds to MTs. We also revealed that oocyte developmental arrest caused by Jvl overexpression in the germline can be rescued by mutations in its partners, spn-F and ikkε, suggesting that complex formation with Spn-F and IKKε is required for Jvl function invivo. In summary, our results show that the microtubule plus-end tracking and stabilizing activities of Jvl are central for controlling cell polarity of oocytes and bristles.

Analysis of dislocation microstructure characteristics of surface grains under cyclic loading by discrete dislocation dynamics

The dislocation structure formation under low-amplitude fatigue in fcc metals for multislip loading conditions is investigated using three-dimensional discrete dislocation dynamics. Tools based on graph analysis, a statistical description of stable dislocation arrangements such as dislocation dipoles and prismatic loops are developed and applied. Upon decreasing the loading amplitude one order of magnitude below the persistent slip band threshold, although qualitative microstructural differences are seen, the elementary features of the investigated defects are the same. A critical number of cycles is required to produce sessile Lomer junctions that stabilize the structure and result in dislocation clustering around them. The crystallographic orientation of the crystal with respect to the loading axis results in different patterns strongly linked to sessile junctions, which are analyzed using spatial correlation functions. The increase in irreversible bulk dislocation arrangements results in roughening of the free surface and increase in surface step heights. Furthermore the crystallographic orientation with respect to the free surface is shown to control the dislocation density evolution combined with the macroscopic Schmid factor.