Field Splitting Research Articles

Overlapping multiplicative Schwarz preconditioning for linear and nonlinear systems

For linear and nonlinear systems arising from the discretization of PDEs, multiplicative Schwarz preconditioners can be defined based on subsets of the unknowns that derive from domain decomposition, field splitting, or other collections of conveniently solved subproblems, and are well established theoretically for nonoverlapping subsets. For overlapping subsets, establishing the equivalence of the preconditioned and original iterations is less trivial. We derive herein an explicit formulation for a variety of multiplicative Schwarz preconditioners including overlaps representative of interfacial and bulk coupling in multiphysics systems, thus extending theoretical support for the nonlinear multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm to these classes. For nonlinear multiplicative Schwarz preconditioners with overlaps, we illustrate the performance through numerical experiments involving applications such as a shocked duct flow and a natural convection cavity flow. We begin with a broad introduction to nonlinear preconditioning to set the context for those new to the technique.

Multilevel field-split preconditioners with domain decomposition for steady and unsteady flow problems

With the incremental applications of Newton–Krylov methods for solving large sparse nonlinear systems of equations, the design of robust and scalable linear preconditioners plays an essential role for the whole solver. In this paper, we investigate the family of field-split (FS) preconditioners with different combinations of physics-based and domain decomposition methods, applied to the two typical fluid problems, i.e., the unsteady flow through fractured porous media and the steady buoyancy driven flow. In the implementation, several new versions of FS preconditioners are considered under the framework of the domain decomposition technique: additive FS, multiplicative FS, Schur-complement FS, and the constrained pressure residual (CPR) method, where the inverse of corresponding matrices is approximated by using the restricted additive Schwarz (RAS) algorithm. Rigorous eigenvalue analysis for various FS preconditioners is also provided for facilitating the design of algorithms. In particular, our approach further enhances the numerical performance by presenting a family of multilevel field-split methods for efficiently preconditioning. Numerical experiments are presented to demonstrate the robustness and parallel scalability of the proposed preconditioning strategies for both standard benchmarks as well as realistic flow problems on a supercomputer.

Key Role of Deep Orbitals in the dx2-y2-d3z2-r2 Gap in Tetragonal Complexes and 10Dq.

Using first-principles calculations, we show that the origin of the intrinsic a1g(∼3z2 – r2)–b1g(∼x2 – y2) splitting, Δint, in tetragonal transition-metal complexes and the variations of the cubic field splitting, 10Dq, with the metal–ligand distance, R, are much more subtle than commonly thought. As a main novelty, the key role played by covalent bonding with deep valence ligand levels and thus the inadequacy of too simple models often used for the present goal is stressed. Taking as a guide the isolated D4h CuF64– complex, it is proved that Δint essentially arises from bonding with deep 2s(F) orbitals despite them lying ∼23 eV below 2p(F) orbitals. This conclusion, although surprising, is also supported by results on octahedral fluoride complexes where the contribution to 10Dq splitting from bonding with 2s(F) orbitals is behind its strong R dependence, stressing that explanations based on the crystal-field approach are simply meaningless.

Exogeneity in climate econometrics

Human activity affects the Earth's climate while itself being affected by climate change. To empirically estimate the impact of humanity onto climate and vice versa, climate econometrics has emerged as a field split into two strands: one side focusing on conditional models of the economic impact of climate change, taking climate as given. The other side empirically models climate, taking economic and human activity as given. However, economic and environmental systems are determined with feedback in both directions. Here I examine one way to reconcile the two strands of climate-econometric research by considering a full (albeit simple) empirical climate-economic system and the conditions under which the system can be studied by only looking at the conditional economic or climate side alone. Weak exogeneity is necessary for valid conditioning, strong exogeneity – required for conditional forecasting – lends itself to the concept of climate-takers and climate-setters (countries measurably affecting local climate), while super-exogeneity can be interpreted as policy invariance for the economic impact side, and as a ‘no-tipping point’ condition on the physical side. An application to a stylised climate-economic system using temperatures, SO2 emissions, and global forcing highlights how these concepts can be applied in practice. A system analysis in climate econometrics allows us to move towards fully-coupled empirical climate-economic models accounting for the necessary feedback to obtain empirical estimates of the impact of climate on humanity and vice versa.

Novel splitting of excitation and emission spectra of K2TiF6:Mn4+ phosphors induced by graphene quantum dots

A series of K2TiF6:0.03Mn4+@GQDsymg/mol (KTF:0.03Mn4+@GQDsymg/mol, GQDs: Graphene quantum dots) was prepared by a simple coating method. Multiple enhanced effects on excitation (PLE) & emission (PL) spectra inducing by coating of GQDs are observed: (a) The intensities of PLE&PL are greatly enhanced, (b) PLE&PL spectra have large split, (c) Emission peaks of as-v4, as-v6, s-v4 and s-v3 are selectively enhanced to produce four strong peaks with almost the same intensity. Furthermore, the experimental results indicate that the appearance of the strong as-v4 and as-v6 helps to improve the red light quality of the sample. The mechanism of the enhanced effects is proposed: the coordination of GQDs with Ti4+ and Mn4+ ions leads to the splitting of the crystal field, which further results to enhancement and the large splitting of PLE and PL spectra. Prototype white light-emitting diodes (WLEDs) with low correlated color temperature and high color-rendering index are obtained using the optimal sample.

Influence of phase transitions on the temperature behavior of photoluminescence spectra in a (N(CH3)4)2MnCl4 crystal

Monocrystals (N(CH 3 ) 4 ) 2 MnCl 4 were grown from an aqueous solution of salts by slow evaporation at room temperature. The effect of phase transitions on the behavior of photoluminescence spectra, as well as excitation spectra and time of attenuation of the glow band of 539 nm is studied in the temperature range of 4.5‒300 K. Based on the studies of the spectra of photoluminescence of the (N(CH 3 ) 4 ) 2 MnCl 4 , the glow bands, which are caused by the glow of the Mn 2+ ion and correspond to the 4 Т 1 → 6 А 1 transition, were determined. The temperature evolution of photoluminescence spectra (4.5–300 K) of the (N(CH 3 ) 4 ) 2 MnCl 4 crystal demonstrates anomalies of their parameters at the points of phase transitions. Temperature dependences of crystal photoluminescence spectra of the (N(CH 3 ) 4 ) 2 MnCl 4 crystal prove the existence of phase transitions in the temperature intervals from 100 to 300 K. The excitation spectra for the luminescence band of 539 nm and their temperature evolution (4.5–300 K) are shown. The bands of around 2.93 and 2.96 eV are quickly damped with temperature, so at the temperatures above 170 K and 270 K, the bands of 2.96 and 2.93 eV are not observed, respectively. Peaks in the excitation spectrum correspond to electron transitions from the basic state of 6 A 1 Mn 2+ to various excited states (T d ). Their excitation energies are explained by a model of crystals using the Tanabe-Sugano diagrams. The Racah B and C parameters, as well as the splitting of crystal field Δ, were calculated based on the Tanabe-Sugano diagrams for d 5 of electronic configuration. The temperature behavior of the time of attenuation of the photoluminescence band of 539 µm was studied. The resulting time of attenuation of the photoluminescence band increases at an increase in temperature. The kinetics of attenuation of the photoluminescence band of 539 µm of a crystal is well described by an exponential function

A field-split preconditioning technique for fluid-structure interaction problems with applications in biomechanics.

We present a novel preconditioning technique for Krylov subspace algorithms to solve fluid-structure interaction (FSI) linearized systems arising from finite element discretizations. An outer Krylov subspace solver preconditioned with a geometric multigrid (GMG) algorithm is used, where for the multigrid level subsolvers, a field-split (FS) preconditioner is proposed. The block structure of the FS preconditioner is derived using the physical variables as splitting strategy. To solve the subsystems originated by the FS preconditioning, an additive Schwarz (AS) block strategy is employed. The proposed FS preconditioner is tested on biomedical FSI applications. Both 2D and 3D simulations are carried out considering aneurysm and venous valve geometries. The performance of the FS preconditioner is compared with that of a second preconditioner of pure domain decomposition type.

Scale effects of runoff generation under reduced and conventional tillage

Review studies indicate that conservation tillage effectively reduces runoff generation measured on large plots, but less so on smaller plots. These tillage and scale effects have never been measured in a single study for temperate mechanized agriculture. With the objective to study how runoff production changes with scale as influenced by tillage we set up rainfall-runoff plots of 5 m2, 30 m2 and 180 m2 size, on a field split into a reduced tillage (RT) and a conventionally ploughed field (CT) during two crop seasons (maize and wheat). In addition, we conducted rainfall simulations on small plots (0.7 m2) and measured soil surface properties. Average scale effects, defined as reduction of runoff coefficients with increasing plot size, were 57% (RT) and 37% (CT) between 5 m2 and 30 m2, and − 24% (reversed) (RT) and 27% (CT) between 30 m2 and 180 m2. Tillage effects, defined as the reduction in runoff coefficients of RT compared to CT were 65% at 5 m2, 86% at 30 m2 and 31% at 180 m2. On average, scale effects were 15% stronger on RT compared to CT. The overall level of runoff coefficient was most clearly affected by crop type, with winter wheat having 1.7–30 times lower runoff coefficients than maize. Crop development and soil moisture negatively affected runoff coefficients on Wheat, while rainfall intensity affected runoff coefficients positively on Maize. No evidence for interactions of these variables with either scale or tillage were found. Runoff coefficients of CT and RT diverged with scale (i.e. runoff accumulation) between 5 m2 and 30 m2, which was expected and can be explained with higher residue cover and macropore density on reduced tillage than conventional tillage slowing down runoff and increasing infiltration opportunities. Unexpectedly, between 30 m2 and 180 m2, on Maize, runoff coefficients converged strongly, which was interpreted with erosion of sealing on conventional tillage. In summary, this study confirms previous findings on the effects of tillage on runoff coefficients, but finds indications that important process transitions take place at the field scale that are affected differently by tillage, and that are not yet sufficiently studied or accounted for in models.

Manipulating longitudinal photonic spin Hall effect based on dynamic and Pancharatnam-Berry phase

Photonic spin Hall effect is generally described as a spin-dependent splitting. Previous studies have focused on the transverse spin-dependent splitting of light field. In this work, a method of manipulating the longitudinal photonic spin Hall effect which is based on dynamic and Pancharatnam-Berry phase is proposed. The theoretical analysis demonstrates that the lens group consisting of a Pancharatnam-Berry phase lens and a dynamic lens has two spin-dependent foci. Firstly, because Pancharatnam-Berry phase is spin-dependent, the left- and right-handed circularly polarized component can respectively acquire a Pancharatnam-Berry phase with opposite sign when a linearly polarized light beam passes through the Pancharatnam-Berry phase lens with phase retardation <inline-formula><tex-math id="M90">\begin{document}${\text{π}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182004_M90.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182004_M90.png"/></alternatives></inline-formula>. It leads one circularly polarized component to be focused and the other diverged. This is essentially the spin-dependent splitting of light field in momentum space, which is caused by Pancharatnam-Berry phase. And then, an ordinary lens is inserted behind the Pancharatnam-Berry phase lens to introduce a dynamic phase modulation. Due to dynamic phase being spin-independent, the constructed lens group can focus the photons with different spin states at different focal points longitudinally under the appropriate conditions. In other words, the lens group has two spin-dependent focal points. The two focal points split the photons with different spin states in the longitudinal direction. The longitudinal spin-dependent splitting is dependent on the focal lengths of the two lens and the distance between the two lenses. By changing the three parameters, arbitrary longitudinal spin-dependent splitting can be obtained. Lastly, an experimental system is set up to verify the theoretical results. The relationship between the spin-dependent splitting and the distance between the two lenses is measured. By introducing a Glan laser polarizer and a quarter wave-plate, the circularly polarized chirality of the light field at the focal point is also measured. These experimental results are all in good agreement with the theoretical analyses. These results are helpful in understanding the physical origin of photonic spin Hall effect and developing novel photonic devices based on photonic spin Hall effect.

New preconditioning techniques for the steady and unsteady buoyancy driven flow problems

In this paper we study the performances of generalized minimal residual method (GMRES) preconditioned with geometric multigrid (GMG), applied to steady and unsteady buoyancy driven flow problems, discretized with the finite element method. For the unsteady case, the second order Crank–Nicolson method is used for the temporal discretization. At each geometric multigrid level, we use Richardson iterative solvers preconditioned with different combinations of physics-based and domain decomposition preconditioners. Three different preconditioners are considered: incomplete LU decomposition (ILU), overlapping Vanka-type domain decomposition for additive Schwarz method (ASM), and field split (FS) physics-based decomposition. We also analyze the effect on the smoother of how the variables are ordered, and in particular whether the leading variable is the velocity or the temperature, resulting in six classes of preconditioners: ILU_VT, ILU_TV, ASM_VT, ASM_TV, FS_VT and FS_TV. The eigenvalue analysis for the six preconditioners is conducted to study the rate of GMRES convergence under several Prandtl numbers. The numerical performances of nested combinations of the above preconditioners are compared. Numerical results show that the pair of FS_VT and FS_TV preconditioners works better than the other two pairs, and that the FS_TV preconditioner always performs the best in terms of the computational time for all the steady and unsteady cases.

Minimizing the number of apertures in multileaf collimator sequencing with field splitting

In this paper we consider the problem of decomposing a given integer matrix A into an integer conic combination of consecutive-ones matrices with a bound on the number of columns per matrix. This problem is of relevance in the realization stage of intensity modulated radiation therapy (IMRT) using linear accelerators and multileaf collimators with limited width. Constrained and unconstrained versions of the problem with the objectives of minimizing beam-on time and decomposition cardinality are considered. We introduce a new approach which can be used to find the minimum beam-on time for both constrained and unconstrained versions of the problem. The decomposition cardinality problem is shown to be NP-hard and an approach is proposed to solve the lexicographic decomposition problem of minimizing the decomposition cardinality subject to optimal beam-on time.

Evaluation of Spin Hamiltonian Parameters and Local Structure of Cu2+-doped Ion in xK2SO4–(50 – x)Na2SO4–50ZnSO4 Glasses with Various K2SO4 Concentrations

The spin Hamiltonian parameters (SHPs), i.e., g factors and hyperfine structure constants, and local structures are theoretically studied by analyzing tetragonally elongated 3d9 clusters for Cu2+ in xK2SO4–(50 – x)Na2SO4–50ZnSO4 glasses with various K2SO4 concentrations x. The concentration dependences of the SHPs are attributed to the parabolic decreases of the cubic field parameter Dq, orbital reduction factor k, relative tetragonal elongation ratio τ, and core polarization constant κ with x. The [CuO6]10– clusters are found to undergo significant elongations of about 17% due to the Jahn–Teller effect. The calculated cubic field splittings and the SHPs at various concentrations agree well with the experimental data.

Investigation of a Polariton Condensate in Micropillars in a High Magnetic Field

The photoluminescence of a nonequilibrium polariton condensate in cylindrical and rectangular micropillars etched on the surface of a high-Q GaAs microcavity is investigated in magnetic fields of up to 12 T. The measurements are carried out under different levels of nonresonant optical pumping with nanosecond laser pulses for a wide range of cavity detuning. As far as nonresonant excitation produces a high density of excitons in a reservoir, it should be expected that the exciton–polariton interaction, which depends on the pump level, has a considerable effect on the Zeeman splitting and polarization of the condensate. However, measurements of the Zeeman splitting and polarization in high magnetic fields demonstrate that only minor changes take place up to the highest available pump levels. This means that, in the case under study, the effect of exciton–polariton interaction on the polariton system is insignificant. At the same time, the data obtained provide an estimate for the exciton density in the reservoir. In contrast to cylindrical micropillars, the photoluminescence of the condensate in rectangular micropillars consists of two perpendicularly linearly polarized lines which retain a high degree of linear polarization even in a field as high as 12 T. The Zeeman splitting in this case is nearly independent of the pump power. The degrees of both circular and linear polarization change with pump power, but these changes are noticeably smaller than the ones predicted theoretically. This indicates that the system of polaritons in micropillars deviates considerably from thermodynamic equilibrium.

Behavior of temperature-dependent dc-photoconductivity in hot-wall deposited CaAl2Se4 layers

The dc-photoconductive characteristic on the hot-wall grown CaAl2Se4 (CAS) layers was explored as a function of temperature. From the photocurrent (PC) measurement, three PC peaks A, B, and C corresponded to the intrinsic transitions, which represent the band-to-band transitions from the valence-band states of Γ2(A), Γ3 + Γ4(B), and Γ3 + Γ4(C) to the conduction-band state of Γ1, respectively. Based on these PC results, the optical band-gap energy was well matched by E g (T) = E g (0) − 4.94 × 10−3 T 2/(T + 552), where E g (0) is found to be 3.8239, 3.8716, and 3.8801 eV for three peaks A, B, and C, respectively. Thus, the effect of the crystal field and spin-orbit splitting (These values were extracted out to be 47.7 and 8.5 meV, respectively.) was observed and calculated by means of the PC spectroscopy. However, PC intensity gradually decreased with decreasing temperature unlike an ordinary behavior. In the log J ph vs 1/T plot, two dominant traplevels were observed to be 20.81 meV at temperatures of 300 - 70 K and 1.18 meV at temperatures below 70 K. Consequently, we extract out that these trapping centers caused by native defects in CAS confine the PC intensity as temperature decreases.

Exogeneity in Climate Econometrics

Human activity affects the Earth's climate while itself being affected by climate change - from rising sea levels to productivity effects of temperatures, natural disasters and climate-driven conflict. To empirically estimate the impact of humanity onto climate and vice versa, climate econometrics has emerged as a field split into two strands: one side focusing on conditional models of the economy taking climate as given, the other side modelling and predicting climate taking economic activity as given. However, economic and environmental systems are determined with feedbacks in both directions. Conditional modelling of one side can be informative about the underlying parameters of interest (e.g. climate impacts onto the economy, or climate sensitivity) if conditions on weak, strong, and super exogeneity are met. Here I attempt to reconcile the two strands of the climate-econometric literature by considering a full (albeit simple) empirical climate-economic system and the conditions under which the system can be studied by only looking at the conditional economic or the climate side. Weak exogeneity is required for valid conditioning, strong exogeneity - required for conditional forecasting - lends itself to the concept of climate-takers and climate-setters (countries measurably affecting climate), while super-exogeneity can be interpreted as policy invariance for the economic impact side, and as a `no-tipping point' condition on the physical side. An application to a simple bivariate climate-economic system using US SO2 emissions and temperatures highlights how these concepts can be applied in practice. A system analysis in climate econometrics allows us to move towards fully-coupled empirical climate-economic models consistent with the underlying physics and fully accounting for the necessary feedbacks, to obtain estimated impacts in both directions. While far from trivial in large systems, this is necessary to obtain rigorous empirical estimates of the impact of climate on humanity and vice versa.

Uncertainty Principles for Three-Dimensional Inverse Source Problems

Novel uncertainty principles for far fields of time-harmonic acoustic or electromagnetic waves radiated by collections of well-separated localized sources in two-dimensional free space have recently been established in [R. Griesmaier and J. Sylvester, SIAM J. Appl. Math., 77 (2017), pp. 154--180]. These uncertainty principles have been utilized to develop stability estimates and reconstruction algorithms for the recovery of the far field radiated by each of the individual sources, and the simultaneous restoration of missing data segments. In this paper, we present generalizations of these uncertainty principles for a relevant three-dimensional setting. We consider extensions of the reconstruction schemes for far field splitting and data completion, including their stability analysis, and we discuss the sharpness of our results in the three-dimensional case. We briefly comment on the numerical implementation of the reconstruction algorithms and include a numerical example.

Antiferromagnetism in a Family of S = 1 Square Lattice Coordination Polymers NiX2(pyz)2 (X = Cl, Br, I, NCS; pyz = Pyrazine).

The crystal structures of NiX2(pyz)2 (X = Cl (1), Br (2), I (3), and NCS (4)) were determined by synchrotron X-ray powder diffraction. All four compounds consist of two-dimensional (2D) square arrays self-assembled from octahedral NiN4X2 units that are bridged by pyz ligands. The 2D layered motifs displayed by 1-4 are relevant to bifluoride-bridged [Ni(HF2)(pyz)2]EF6 (E = P, Sb), which also possess the same 2D layers. In contrast, terminal X ligands occupy axial positions in 1-4 and cause a staggered packing of adjacent layers. Long-range antiferromagnetic (AFM) order occurs below 1.5 (Cl), 1.9 (Br and NCS), and 2.5 K (I) as determined by heat capacity and muon-spin relaxation. The single-ion anisotropy and g factor of 2, 3, and 4 were measured by electron-spin resonance with no evidence for zero-field splitting (ZFS) being observed. The magnetism of 1-4 spans the spectrum from quasi-two-dimensional (2D) to three-dimensional (3D) antiferromagnetism. Nearly identical results and thermodynamic features were obtained for 2 and 4 as shown by pulsed-field magnetization, magnetic susceptibility, as well as their Néel temperatures. Magnetization curves for 2 and 4 calculated by quantum Monte Carlo simulation also show excellent agreement with the pulsed-field data. Compound 3 is characterized as a 3D AFM with the interlayer interaction (J⊥) being slightly stronger than the intralayer interaction along Ni-pyz-Ni segments (J(pyz)) within the two-dimensional [Ni(pyz)2](2+) square planes. Regardless of X, J(pyz) is similar for the four compounds and is roughly 1 K.

On the natural magnetization of ideal quantum dots and the possibility of detection of terahertz radiation in the magnetic field

A wave function is constructed and the binding energy of electron localized at an ideal quantum dot in the external magnetic field is calculated. It is shown that the energy of the Zeeman splitting in moderate magnetic fields corresponds to photons from the terahertz band, i.e., processes with the electron spin flip lead to radiation or absorption of terahertz radiation. It is established that external terahertz radiation changes the spin equilibrium distribution and, as a result, the magnetization of the system, thus creating the possibility of detection of this radiation by measuring the magnetization of the system of quantum dots.

Pr- and La-doping effects on the magnetic anisotropy in the antiferromagnetic phase of Kondo semiconductorCeRu2Al10

We have studied the Pr- and La-doping effects on the magnetic anisotropy in the antiferro-magnetic (AFM) phase of ${\mathrm{CeRu}}_{2}{\mathrm{Al}}_{10}$. The crystalline electric field (CEF) splitting in ${\mathrm{PrRu}}_{2}{\mathrm{Al}}_{10}$ was found to be as large as $\ensuremath{\sim}800$ K with a singlet ground state. In ${\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{Pr}}_{x}{\mathrm{Ru}}_{2}{\mathrm{Al}}_{10}$, the CEF level scheme of the Pr ion is not changed with $x$. The AFM moment (${m}_{\mathrm{AF}}$) is rotated from $c$ to $b$ axis in both systems at ${x}_{c}^{\mathrm{sr}}\ensuremath{\sim}0.03$ and $\ensuremath{\sim}0.07$ for Ln=Pr and La, respectively. As the ionic radius of La and Pr is larger and smaller than that of Ce, respectively, these results indicate that the chemical pressure effect is not associated with the rotation of ${m}_{\mathrm{AF}}$, but is caused by the suppression of the $c\ensuremath{-}f$ hybridization originating from the decrease of $4f$ electrons of Ce ions by Ce-site substitution. Since a small amount of Pr or La doping changes easily the magnetization easy axis of all the moments on Ce sites, the origin of the magnetic anisotropy is not the local single ion effect but the bandlike effect through the anisotropic $c\ensuremath{-}f$ hybridization. The magnetic phase diagrams of ${\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{Ln}}_{x}{\mathrm{Ru}}_{2}{\mathrm{Al}}_{10}$ indicate that above ${x}_{c}^{\mathrm{sr}}$, the AFM order with ${m}_{\mathrm{AF}}\ensuremath{\parallel}b$ continues to exist up to ${x}_{c}$, which is $\ensuremath{\sim}0.4$ and $\ensuremath{\sim}0.6$ in Ln=Pr and Ln=La, respectively. This indicates that even in the sample with an AFM transition temperature (${T}_{0}$) near ${x}_{c}$, the anisotropic $c\ensuremath{-}f$ hybridization dominates the AFM order. A large positive transverse magnetoresistance is seen below ${T}_{0}$, but a very small one above ${T}_{0}$. Together with the results of Hall resistivity and the observation of Shubnikov--de Haas oscillation, we propose that there exist large Fermi surfaces above ${T}_{0}$ and small ones below ${T}_{0}$. A gap is opened by the AFM order on almost the area of the large Fermi surface, and small Fermi surfaces are constructed below ${T}_{0}$, although we do not know the mechanism, which might be specific to the AFM order in Kondo semiconductors. The largest suppression of the magnetic scattering below ${T}_{0}$ is observed for the current $I\ensuremath{\parallel}a$ and the smallest one for $I\ensuremath{\parallel}b$. This anisotropy may be associated with the anisotropic $c\ensuremath{-}f$ hybridization, which may contribute to the anisotropic magnetic scattering of the conduction electron below ${T}_{0}$.

CSCW and Social Computing

Research on IT support for collaborative work has a long history. Researchers have approached the topic from many directions using many perspectives. The field split into multiple subfields, each focused on different goals, and each with its own terminology. One subfield is Computer-Supported Collaborative Work (CSCW). The origins of CSCW trace back to a workshop organized by Irene Greif and Paul Cashman in 1984, where researchers from different disciplines met to exchange ideas, share results, and to join forces to better understand how IT could be used to improve and enhance group outcomes. A variety of definitions for CSCW have flowered, but they converge to similar concepts: ‘‘In its most general form, CSCW examines the possibilities and effects of technological support for humans involved in collaborative group communication and work processes’’ (Bowers and Benford 1991, p. 5). By studying work processes, and by developing and testing tools to support them, numerous technologies and tools have been developed and tested, and groundbreaking insights into understanding the process of collaboration and the process of introducing tools for supporting communication and collaboration have been obtained. For example, the utility of coexistence and awareness for some kinds of cooperative work is now well understood, and technological support for those items have been prototyped, tested, and diffused into the field (Dourish and Belotti 1992; Koch and Gross 2006). The concept of coordination has been researched, and support for coordination is now ubiquitous in the workplace (Malone and Crowston 1992). A variety of models for understanding the role of communication have been advanced, e.g. the context-oriented communication model by Misch (2001) or the Cooperative Work Framework by Dix et al. (1993, pp. 465 f), and each provides valuable insights for practitioners and researcher. CSCW research also helped to promulgate useful methodological points-of-view and methods to the information sciences. CSCW researchers were leaders in the diffusion of ethnographic studies in the IS discipline, and contributed to the growing perspective that people are not just ‘‘end-users’’ of information systems, but are an integral part of these systems, and so should be active participants in the processes by which systems are designed and deployed (Brenner et al. 2014). A different stream of research, now called Group Support Systems (GSS), emerged in the early 1970s in response to the need for very large numbers of stakeholders to converge on a single, validated set of computer system requirements. Daniel Teichroew, Jay Nunamaker, and others PSL/PSA, a system where users would write their requirements in a structured-English format akin to Pseudcode, and then feed the requirements into an Prof. Dr. M. Koch (&) Cooperation Systems Center Munich, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany e-mail: michael.koch@unibw.de URL: http://www.kooperationssysteme.de