Showing papers on "Magnetic field published in 1990"
TL;DR: In this article, a least-squares program was developed to fit magnetic field data within a cloud, while estimating such cloud properties as its size, maximum field strength, and axis inclination.
Abstract: Interplanetary magnetic clouds emerge as a feature of the solar wind at 1 AU, exhibiting enhanced field strength and lower plasma temperature and density than the surrounding plasma. A least-squares program has been developed which fits magnetic field data within a cloud, while estimating such cloud properties as its size, maximum field strength, and axis inclination. The results obtained from a study of 12 clouds observed at 1 AU point to a probable cloud axis direction within 15 deg of the ecliptic plane and about 100 deg from the sun's direction, when projected into the ecliptic plane. A wide variety of orientations is observed; some extend to 80 deg from the ecliptic.
844 citations
TL;DR: The eigenstates of electrons interacting in quantum dots in a magnetic field are studied and their effects on the magnetic-field dependence of the energy spectrum are illustrated with the calculations of the electronic heat capacity.
Abstract: The eigenstates of electrons interacting in quantum dots in a magnetic field are studied. The interaction has important effects on the magnetic-field dependence of the energy spectrum. However, when the confinement potential is quadratic, the optical excitation energies of the many-body system are exactly the same as those of a single electron. This makes the interaction effects difficult to observe directly but they could be seen by measuring the thermodynamic properties of the electrons. This is illustrated with the calculations of the electronic heat capacity.
759 citations
TL;DR: In this paper, the authors used the ac detection method which senses the force gradient acting on a small magnetic tip due to fields emanating from the domain structure in the sample, and showed that the final 20 μm is essentially single domain with magnetization approximately parallel with the tip axis.
Abstract: This paper discusses the principles of magnetic force microscopy (MFM) and its application to magnetic recording studies. We use the ac detection method which senses the force gradient acting on a small magnetic tip due to fields emanating from the domain structure in the sample. Tip fabrication procedures are described for two types of magnetic tips: etched tungsten wires with a sputter‐deposited magnetic coating and etched nickel wires. The etched nickel wires are shown to have an apex radius on the order of 30 nm and a taper half‐angle of approximately 3°. Lorentz‐mode transmission electron microscopy of the nickel tips reveals that the final 20 μm is essentially single domain with magnetization approximately parallel with the tip axis. Images of written bit transitions are presented for several types of magnetic media, including CoPtCr, CoSm, and CoCr thin films, as well as γ‐Fe2O3 particulate media. In general, the written magnetization patterns are seen with high contrast and with resolution better ...
606 citations
TL;DR: In this paper, an efficient method is given for self-consistent reconstruction of the tokamak current profiles and their associated magnetic topology using the magnetohydrodynamic (MHD) equilibrium constraint from external magnetic measurements, kinetic profile measurements, internal poloidal magnetic field measurements, and topological information from soft X-ray (SXR) measurements.
Abstract: An efficient method is given for self-consistent reconstruction of the tokamak current profiles and their associated magnetic topology using the magnetohydrodynamic (MHD) equilibrium constraint from external magnetic measurements, kinetic profile measurements, internal poloidal magnetic field measurements, and topological information from soft X-ray (SXR) measurements. Illustrative examples for beam heated H-mode divertor discharges in the DIII-D tokamak are presented, using the experimentally measured kinetic profile information and external magnetic data from the existing diagnostics. Comparative reconstructions of the current profile using various combinations of diagnostics are given. Also presented is an alternative magnetic analysis method in which the MHD equilibrium is reconstructed using external magnetic data and a constraint on the edge pressure gradient. The results of a sensitivity study are given which show that the axial safety factor q(0) can be more accurately determined when additional information from internal poloidal magnetic measurements is used in conjunction with the external magnetic, kinetic and SXR topological data.
584 citations
TL;DR: This model explains recent experiments which have questioned the driving mechanism for dissipation in the superconducting phase of the high-temperature oxide superconductors.
Abstract: In layered superconductors with very weak coupling between the layers the concept of a flux-line lattice breaks down when the field is oriented parallel to the superconducting planes. For an arbitrary field orientation we propose that the formation of an Abrikosov lattice is only related to the perpendicular field component. The parallel field component penetrates as if the superconducting planes were completely decoupled. This model explains recent experiments which have questioned the driving mechanism for dissipation in the superconducting phase of the high-temperature oxide superconductors.
392 citations
TL;DR: The theory of nuclear magnetic resonance (NMR) on a solid sample containing pairs of coupled homonuclear spins 1/2, rotating in a large magnetic field, is presented in this paper, where the time dependence introduced by the sample rotation, in conjunction with the spin-spin coupling, makes it appear that each of the central two levels in the four level system split into a pair of virtual states.
Abstract: The theory of nuclear magnetic resonance (NMR) on a solid sample containing pairs of coupled homonuclear spins‐1/2, rotating in a large magnetic field, is presented. The time dependence introduced by the sample rotation, in conjunction with the spin–spin coupling, makes it appear that each of the central two levels in the four‐level system split into a pair of ‘‘virtual states.’’ Each of the eight possible single‐quantum coherences between the virtual states and the two outer levels in general contribute to the spectrum, although four of these contributions are forbidden unless a rotational resonance occurs (matching of an integer multiple of the spinning speed with the difference in isotropic shifts). Analytical line shapes for the case of vanishing shift anisotropy are given and techniques for numerical simulation in the general case demonstrated. The theory of Zeeman magnetization exchange in the presence of zero‐quantum dephasing is presented.
380 citations
TL;DR: A magnetic field is used to tune through a new superconducting-insulating transition of amorphous-composite indium oxide films at various stages of disorder and scaling behavior of the resistance over a wide range of temperatures and magnetic fields is found.
Abstract: A magnetic field is used to tune through a new superconducting-insulating transition of amorphous-composite indium oxide films at various stages of disorder. The results are in accord with scaling theory which identifies a universal sheet resistance separating a superconducting phase of localized vortices and Bose-condensed electron pairs from an insulating phase of Bose-condensed vortices and localized electron pairs. A unity dynamical exponent is confirmed and scaling behavior of the resistance over a wide range of temperatures and magnetic fields is found.
361 citations
TL;DR: In this article, the voltage-current characteristics of YBa2Cu3O7−δ epitaxial films within the flux creep model were described in a manner consistent with the resistive transition behavior.
Abstract: We describe the voltage‐current characteristics of YBa2Cu3O7−δ epitaxial films within the flux creep model in a manner consistent with the resistive transition behavior. The magnitude of the activation energy, and its temperature and magnetic field dependences, are readily derived from the experimentally observed power law characteristics and show a (1−T/Tc)3/2 type of behavior near Tc. The activation energy is a nonlinear function of the current density and it enables the determination of the shape of the flux line potential well.
331 citations
TL;DR: Self-consistent numerical solutions of the Poisson and Schrodinger equations have been obtained for electron states in a GaAs/Al heterostructure with confinement in all three spatial dimensions, indicating that the confining potential has nearly circular symmetry despite the square geometry of the gate, that the energy levels are quite insensitive to the charge in the quantum dot at a fixed gate voltage, and that the evolution of levels with increasing magnetic field is similar to that found for a parabolic potential.
Abstract: Self-consistent numerical solutions of the Poisson and Schr\"odinger equations have been obtained for electron states in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure with confinement in all three spatial dimensions. The equations are solved in the Hartree approximation, omitting exchange and correlation effects. Potential profiles, energy levels, and the charge in the quantum dot are obtained as functions of the applied gate voltage and magnetic field. First, the zero-magnetic-field case is considered, and the quantum-dot charge is allowed to vary continuously as the gate voltage is swept. Then, in connection with the phenomenon of Coulomb blockade, the number of electrons in the quantum dot is constrained to integer values. Finally, the calculation is extended to examine the evolution of levels in a magnetic field applied perpendicular to the heterojunction. Our results indicate that the confining potential has nearly circular symmetry despite the square geometry of the gate, that the energy levels are quite insensitive to the charge in the quantum dot at a fixed gate voltage, and that the evolution of levels with increasing magnetic field is similar to that found for a parabolic potential.
317 citations
TL;DR: The authors identify eight areas of potential safety concern during clinical magnetic resonance (MR) imaging, including biologic effects of the static magnetic field, and psychological effects, such as claustrophobia and anxiety induced because of the examination.
Abstract: The authors identify eight areas of potential safety concern during clinical magnetic resonance (MR) imaging. These include (a) biologic effects of the static magnetic field; (b) ferromagnetic attractive "projectile" effects of the static magnetic field; (c) potential effects of the relatively slowly time-varying magnetic field gradients; (d) effects of the rapidly varying radio-frequency (RF) magnetic fields, including RF power deposition concerns; (e) auditory considerations from noise caused by the rapidly pulsed magnetic field gradients; (f) safety considerations concerning superconductive systems, including quenches, use of cryogens, and cryogen storage and handling; (g) psychological effects, such as claustrophobia and anxiety induced because of the examination; and (h) possible effects of the intravenous use of the MR contrast agent gadopentetate dimeglumine. The concerns in each of these categories are elaborated upon, and the available data are presented to clarify their status.
307 citations
TL;DR: Very small quantum-dot structures containing 210 to 25 electrons per dot have been prepared starting from modulation-doped AlGaAs/GaAs heterostructures, induced by nonlocal interaction which becomes important at small dimensions.
Abstract: Very small quantum-dot structures containing 210 to 25 electrons per dot have been prepared starting from modulation-doped AlGaAs/GaAs heterostructures. The far-infrared response consists of a set of resonances which split, in a magnetic field B, into branches with negative and positive B dispersion. The intersection of these resonances, in classical analogy edge magnetoplasmons, leads to an anticrossing of the dispersions. This resonant coupling is induced by nonlocal interaction which becomes important at small dimensions.
TL;DR: In this paper, a class of nonlinear force-free magnetic fields is presented, described in terms of the solutions to a second-order, nonlinear ordinary differential equation, filling the infinite half-space above a plane where the lines of force are anchored.
Abstract: A class of nonlinear force-free magnetic fields is presented, described in terms of the solutions to a second-order, nonlinear ordinary differential equation. These magnetic fields are three-dimensional, filling the infinite half-space above a plane where the lines of force are anchored. They model the magnetic fields of the sun over active regions with a striking geometric realism. The total energy and the free energy associated with the electric current are finite and can be calculated directly from the magnetic field at the plane boundary using the virial theorem. In the study of solar magnetic fields with data from vector magnetographs, there is a long-standing interest in devising algorithms to extrapolate for the force-free magnetic field in a given domain from prescribed field values at the boundary. The closed-form magnetic fields of this paper open up an opportunity for testing the reliability and accuracy of algorithms that claim the capability of performing this extrapolation. The extrapolation procedure as an ill-posed mathematical problem is discussed. 22 refs.
TL;DR: The Madison Symmetric Torus (MST) is the largest reversed field pinch currently in operation as discussed by the authors, and it incorporates a number of design features that set it apart from other pinches.
Abstract: The Madison Symmetric Torus (MST) is the newest and largest reversed-field pinch (RFP) currently in operation. It incorporates a number of design features that set it apart from other pinches, incl...
TL;DR: In this paper, the y-component of the plasma flow within the low latitude boundary layer and magnetopause current layer was oppositely directed to that in the adjacent magnetosheath.
Abstract: Events observed in a fast plasma experiment, where the y-component of the plasma flow within the low latitude boundary layer and magnetopause current layer was oppositely directed to that in the adjacent magnetosheath, are examined. The observations are shown to be qualitatively and quantitatively consistent with previous observations of accelerated flows at the magnetopause and with models of magnetic reconnection, with reconnection occurring at low latitudes near the GSE XY plane, independently of the magnitude or the sign of the y-component ot the local magnetosheath magnetic field. Local magnetic shears at the magnetopause for these events (in 60-180 deg range) and the fact that these events occur at low latitudes do not support the antiparallel merging hypothesis. The observations of B(y)-dependent flow reversals demonstrate how the asymmetric polar cap convection and related phenomena, such as the Svalgaard-Mansurov effect, originate in magnetic reconnection at the dayside magnetopause.
TL;DR: Stern-Gerlach deflections of cold iron clusters, with from 15 to 650 atoms per cluster, have been measured, indicating spin relaxation within the isolated clusters.
Abstract: Stern-Gerlach deflections of cold iron clusters in a molecular beam, with from 15 to 650 atoms per cluster, have been measured. It is found that the clusters deflect uniquely in the direction of the increasing field, indicating spin relaxation within the isolated clusters. The measured average magnetic moments increase with increasing cluster temperature and with increasing field, and in all cases they are found to be below the bulk value.
TL;DR: In this article, the authors measured the transverse relaxation rates of a number of water-filled porous rock samples as a function of static magnetic field strength and Carr-Purcell pulse spacing.
TL;DR: In this article, multilayers consisting of two magnetic components with different anisotropies were prepared by successively depositing Co, Cu, Ni 80 Fe 20 and Cu layers.
Abstract: Multilayers consisting of two magnetic components with different anisotropies were prepared by successively depositing Co, Cu, Ni 80 Fe 20 and Cu layers. By applying a moderate field, the two magnetizations are oriented antiparallel with each other, and then the electric resistance significantly increases due to spin-dependent electron scattering. A large magnetoresistance change, 9.9% at 300 K, was observed in [Co(30 A)/Cu(50 A)/NiFe(30 A)/Cu(50 A)]×15.
TL;DR: A review of the theoretical concepts and models describing the acceleration of auroral particles can be found in this article, where the dynamics of the particles are described, beginning with the adiabatic motions of particles in the converging geomagnetic field in the presence of parallel potential drops.
Abstract: The auroral zone ionosphere is coupled to the outer magnetosphere by means of field-aligned currents. Parallel electric fields associated with these currents are now widely accepted to be responsible for the acceleration of auroral particles. This paper will review the theoretical concepts and models describing this coupling. The dynamics of auroral zone particles will be described, beginning with the adiabatic motions of particles in the converging geomagnetic field in the presence of parallel potential drops and then considering the modifications to these adiabatic trajectories due to wave-particle interactions. The formation of parallel electric fields can be viewed both from microscopic and macroscopic viewpoints. The presence of a current carrying plasma can give rise to plasma instabilities which in a weakly turbulent situation can affect the particle motions, giving rise to an effective resistivity in the plasma. Recent satellite observations, however, indicate that the parallel electric field is organized into discrete potential jumps, known as double layers. From a macroscopic viewpoint, the response of the particles to a parallel potential drop leads to an approximately linear relationship between the current density and the potential drop. The currents flowing in the auroral circuit must close in the ionosphere. To a first approximation, the ionospheric conductivity can be considered to be constant, and in this case combining the ionospheric Ohm's Law with the linear current-voltage relation for parallel currents leads to an outer scale length, above which electric fields can map down to the ionosphere and below which parallel electric fields become important. The effects of particle precipitation make the picture more complex, leading to enhanced ionization in upward current regions and to the possibility of feedback interactions with the magnetosphere. Determining adiabatic particle orbits in steady-state electric and magnetic fields can be used to determine the self-consistent particle and field distributions on auroral field lines. However, it is difficult to pursue this approach when the fields are varying with time. Magnetohydrodynamic (MHD) models deal with these time-dependent situations by treating the particles as a fluid. This class of model, however, cannot treat kinetic effects in detail. Such effects can in some cases be modeled by effective transport coefficients inserted into the MHD equations. Intrinsically time-dependent processes such as the development of magnetic micropulsations and the response of the magnetosphere to ionospheric fluctuations can be readily treated in this framework. The response of the lower altitude auroral zone depends in part on how the system is driven. Currents are generated in the outer parts of the magnetosphere as a result of the plasma convection. The dynamics of this region is in turn affected by the coupling to the ionosphere. Since dissipation rates are very low in the outer magnetosphere, the convection may become turbulent, implying that nonlinear effects such as spectral transfer of energy to different scales become important. MHD turbulence theory, modified by the ionospheric coupling, can describe the dynamics of the boundary-layer region. Turbulent MHD fluids can give rise to the generation of field-aligned currents through the so-called α-effect, which is utilized in the theory of the generation of the Earth's magnetic field. It is suggested that similar processes acting in the boundary-layer plasma may be ultimately responsible for the generation of auroral currents.
TL;DR: Observations of an electric-field threshold conduction and of related ac voltage (broad-band noise) generation in low-disorder two-dimensional electron systems in the extreme magnetic quantum limit are reported.
Abstract: We report observations of an electric-field threshold conduction and of related ac voltage (broad-band noise) generation in low-disorder two-dimensioanl electron systems in the extreme magnetic quantum limit. We interpret these phenomena as definitive evidence for formation of a pinned quantum Wigner crystal and determine its melting phase diagram from the disappearance of threshold and noise behavior at higher temperatures.
TL;DR: The magnetocaloric effect and magnetic permeability in annealed and quenched samples of Fe 49 Rh 51 alloys have been investigated in this article, where giant negative temperature changes about 13 K by applying a magnetic field at B = 2 T to the quencher sample of Fe 48 Rh 51 alloy have been observed.
TL;DR: In this article, it is pointed out that for a closed cavity, the problem should not be solved by the "vectorial" analog of the classical finite-element method (that is, with node-based finite elements).
Abstract: It is pointed out that for a closed cavity should not be solved by the 'vectorial' analog of the classical finite-element method (that is, with node-based finite elements). It is suggested that there are good reasons to use edge-elements instead. Such elements (whose degrees of freedom correspond to the edges of the mesh, not its nodes) not only guarantee the right kind of continuity for fields like h and e, but also prevent the appearance of unwanted, unphysical divergent solutions in the problem of eigenmodes, the so-called spurious modes. >
TL;DR: In this article, a new model of neutron-star magnetic moments is proposed, by which the fields are generated as the neutron star is born, and follow the evolution of the field over a Hubble time.
Abstract: STRONGLY magnetized neutron stars are believed to be at the heart of a number of astrophysical systems, notably pulsars and X-ray binaries. Although the magnetic field is an important determinant in the behaviour of such systems, the origin and stability of the field is the subject of conflicting observational and theoretical evidence. Here I describe a new model of neutron-star magnetic moments, by which the fields are generated as the neutron star is born, and follow the evolution of the field over a Hubble time. With realistic thermal evolution and conductivities, isolated neutron stars will maintain large magnetic fields for more than 1010 years. In addition, I show how mass accretion on to neutron stars can reduce the field strength1,2. This model of field generation and decay can explain a wide variety of observed systems.
TL;DR: Berry's Phase and Persistent Charge and Spin Currents in Textured Mesoscopic Rings
Abstract: We consider the motion of electrons through a mesoscopic ring in the presence of a classical, static, inhomogeneous, magnetic field. Zeeman interaction between the electron spin and this texture couples spin and orbital motion, and results in a Berry phase. As a consequence, the system supports persistent equilibrium spin and charge currents, even in the absence of conventional electromagnetic flux through the ring. We mention the possibility of analogous persistent mass and spin currents in normal $^{3}\mathrm{He}$.
TL;DR: In this article, the evolution of H II regions in spherical clouds with small, constant-density cores and power-law density distributions r exp -w outside the core is described analytically.
Abstract: The evolution of H II regions in spherical clouds with small, constant-density cores and power-law density distributions r exp -w outside the core is described analytically. It is found that there is a critical exponent above which the cloud becomes completely ionized. Its value in the formation phase depends on the initial conditions, but it has a well-defined value w(crit) = 3/2 during the expansion phase. For w less than w(crit), the radius of the H II region grows at a given rate, while neutral mass accumulates in the interphase between the ionization and shock fronts. For w = w(crit), the fronts move together without mass accumulation. Cases with w greater than w(crit) lead to the champagne phase: once the cloud is fully ionized, the expansion becomes supersonic. For self-gravitating disks without magnetic fields, the main features include a new 'variable-size' stage. The initial shape of the H II region has a critical point beyond which the disk becomes completely ionized.
TL;DR: Electrophysiological recordings from the ophthalmic nerve and the trigeminal ganglion of the bobolink indicate the presence of units (14% of the spontaneously active cells) that are sensitive to small changes in the magnetic field.
TL;DR: In this article, the authors have observed multiple spin echoes using an NMR microscopy system which has a field of 11.7 T. They have shown that the cause of the MSE is the dipolar demagnetizing field.
TL;DR: Presentation des mesures des correlations angulaires bidimensionnelles a spins polarises, du rayonnement d'annihilation dans NiMnSb, compares aux distributions calculees.
Abstract: Spin-polarized measurements of the two-dimensional angular correlation of annihilation radiation in NiMnSb are presented. By making use of the inherent partial polarization of the positron beam and the alignment of the magnetic domains with the aid of an external magnetic field, the sum and difference of the spin-dependent contributions to the angular correlation have been obtained for integration directions 〈100〉, 〈110〉, and 〈111〉. The results are compared with calculated distributions. A least-squares analysis of the data yields a value of (-8.4\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ for the three-photon difference effect in NiMnSb and establishes the half-metallic character of the band structure with an accuracy of ${\mathrm{\ensuremath{\sim}}}_{\mathrm{\ensuremath{-}}0.02}^{+0.01}$ electrons per formula unit.
TL;DR: SIMion as discussed by the authors is a personal computer program for designing and analyzing charged particle (ions and electrons) lenses, ion transport systems, and various types of mass spectrometers and surface probes that utilize charged particles.
Abstract: SIMION PC/PS2 4.02 is a personal computer program for designing and analyzing charged particle (ions and electrons) lenses, ion transport systems, and various types of mass spectrometers and surface probes that utilize charged particles. The modification of an existing design or the generation of a completely new one is performed interactively with a graphics screen and mouse. Once the geometry has been defined, the operating conditions (electrode voltages and magnetic field configuration) can be quickly changed and the resultant fields viewed in several different 2D and 3D modes. The trajectories of charged particles moving in these fields are calculated utilizing sophisticated ‘‘look‐ahead’’ algorithms that dynamically control the time step to optimize speed and accuracy. A unique graphics display of the electrostatic fields and ion trajectories gives the user an intuitive, easily understood view of the performance characteristics. simion also includes a totally integrated capability for users to easily...
TL;DR: Comparison with experimental data shows that Rashba term is the dominant spin-splitting mechanism in these samples and g factors that lie between -2 and -3 are deduced from the perpendicular-field data.
Abstract: The spin splitting in zero magnetic field which was recently reported in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{In}}_{0.52}$${\mathrm{Al}}_{0.48}$As heterostructures is analyzed with use of the inversion-asymmetry, or ${\mathit{k}}^{3}$, term and the interface spin orbit or Rashba term. Comparison with experimental data shows that Rashba term is the dominant spin-splitting mechanism in these samples. Zero-field spin splittings of 2.5--2.75 meV are deduced from the perpendicular-field data. Analysis of tilted-magnetic-field data gives g factors that lie between -2 and -3.
TL;DR: In this paper, the authors suggest a different value of KJ 483 594 GHz/volt (maintained) to the Josephson constant KJ presumed equal to 2e/h, based on the premise that the SI value of the quantum Hall resistance is RK = 25 812,8092 ± 0,0014 Ω.
Abstract: Mechanical and electrical power in SI units have been equated by measurements made on a coil part of which is in a strong magnetic field The force due to a current I flowing in the coil, is weighed by opposing it with a mass M subject to the earth's gravitational acceleration g This is combined with a separate measurement in which a voltage V is generated in the coil when it is moved vertically with velocity u through the relationship IV = M g u If the current produces a voltage V across a resistor whose value R is known in SI units, then V = (M g u R)1/2 Hence the voltage V and the current I are known in SI units and can be used to express the value of the NPL working standards in SI units The working standard of voltage has hitherto been maintained in terms of a Josephson effect apparatus by ascribing the value 483 594 GHz/volt (maintained) to the Josephson constant KJ presumed equal to 2e/h The measurements reported here suggest a different value of KJ 483 597,903 ± 0,035 ought to be used, based on the premise that the SI value of the quantum Hall resistance is RK = 25 812,8092 ± 0,0014 Ω If one presumed also that RK = h/e2 exactly, the values of elementary charge e and the Planck constant, h, which may be deduced from these measurements are e = 1,602 176 35 ± 0,000 000 14 × 10-19 C, h = 6,626 068 21 ± 0,000 000 90 × 10-34 J s, which may be compared with the values recommended by the CODATA Task Group on Fundamental Constants which are e = 1,602 177 33 ± 0,000 000 14 × 10-19 C, h = 6,626 075 5 ± 0,000 004 0 × 10-34 J s