Magnetic field effects on TcT_c and the pseudogap onset temperature in cuprate superconductors

We study the sensitivity of $T_c$ and the pseudogap onset temperature, $T^*$, to low fields, $H$, for cuprate superconductors, using a BCS-based approach extended to arbitrary coupling. We find that $T^*$ and $T_c$, which are of the same superconducting origin, have very different $H$ dependences. The small coherence length makes $T^*$ rather insensitive to the field. However, the presence of the pseudogap at $T_c$ makes $T_c$ more sensitive to $H$. Our results for the coherence length $\xi$ fit well with existing experiments. We predict that very near the insulator $\xi$ will rapidly increase.Comment: 4 pages, 1 figure, contribution to the PPHMF-IV conference, Oct. 200

Magnetic Field Effects in the Pseudogap Phase: A Precursor Superconductivity Scenario

We demonstrate that the observed dependences of $T_c$ and $T^*$ on small magnetic fields can be readily understood in a precursor superconductivity approach to the pseudogap phase. In this approach, the presence of a pseudogap at $T_c$ (but not at $T^*$) and the associated suppression of the density of states lead to very different sensitivities to pair-breaking perturbations for the two temperatures. Our semi-quantitative results address the puzzling experimental observation that the coherence length $\xi$ is weakly dependent on hole concentration $x$ throughout most of the phase diagram. We present our results in a form which can be compared with the recent experiments of Shibauchi et al, and argue that orbital effects contribute in an important way to the $H$ dependence of $T^*$.Comment: 6 pages, 1 figure, elsart.cls included. Submitted to the proceeding of SNS 2001, Chicag

TEMHD Effects on Solidification Under Microgravity Conditions

An unexplored potential exists to control microstructure evolution through the use of external DC magnetic fields. Thermoelectric currents form during solidification and interact with this external field to drive microscopic fluid dynamics within the inter-dendritic region. The convective heat and mass transport can lead to profound changes on the dendritic structure. In this paper the effect of high magnetic fields is demonstrated through the use of both 3-dimensional and 2-dimensional numerical models. The results show that the application of a magnetic field causes significant disruption to the dendritic morphology. Investigation into the underlying mechanism gives initial indicators of how external magnetic fields can either lead to unexpected growth behaviour, or alternatively can be used to control the evolution of microstructure in undercooled melts as encountered in levitated droplet solidification

Dendritic growth velocities in undercooled melts under static magnetic fields

Dendritic growth in undercooled melts has been an interesting topic for metallurgists, physicists and mathematicians. In recent years, attention has been focused on the effects of melt flow on dendritic growth. Significant thermoelectric currents form in undercooled growth due to the presence of relatively large thermal gradients. Numerical simulations showed that the application of a static magnetic field exerts a complex influence on melt flow due to Lorentz force, damping and thermoelectrically driven convection, affecting growth kinetics in undercooled metallic melts. To verify the simulated results, bulk melts of high purity nickel were undercooled using the glass fluxing technique under static magnetic fields of up to 6 T. A high-speed camera was used for in situ monitoring of the recalescence process of the undercooled samples. The dendritic growth velocities at different melt undercoolings were calculated by simulating the recorded images of the recalescence process. The measured data confirms the predicted effect of heat and mass transport through thermoelectric magnetohydrodynamics flow on dendritic growth

Thermoelectric magnetohydrodynamics in dendritic solidification

The focus of this work is to investigate the effects of applying an external magnetic field to a solidifying liquid metal melt. The principle is that thermoelectric currents that are naturally inherent to solidification processes will interact with this magnetic field, resulting in a Lorentz force. This force will exist in a microscopic region in the vicinity of the solidification front, generating microscopic fluid flow in the liquid region which can significantly effect the mechanism of dendritic growth. The work contained in this thesis provides an initial insight into the complex behaviour of this process, through the use of numerical models. To model the soldification dynamics, an enthalpy based model for dendritic growth in a supercooled melt is used in 2-dimensions and extended into 3-dimensions. The dendrite is defined as being equiaxed in nature and, for purely diffusion driven growth, numerical calculations show a good agreement with other methods under similar growth parameters. To investigate the effects of fluid dynamics, dendritic growth is tested under forced convection conditions and significant morphological changes occur. The incident tip velocity is increased and the downstream tip velocity is decreased; in agreement with many other authors investigating similar situations. In the presence of a magnetic field the Lorentz force will form in planes perpendicular to the direction of the magnetic field. Due to the morphology and anisotropy of the surface temperature, the nature of the flow is dependent on the relative orientation of the magnetic field and the crystallographic orientation of the lattice. Using a low magnetic field strength approximation, thus removing the non-linear and resistive terms in Navier-Stokes equation, the resulting fluid velocity is arbitrarily small so that convective transport is negated. At some time, when the morphological features of a dendrite are apparent, steady state simulations show the flow fields that exist with different orientations of the magnetic field. The results are compared to an analytic solution for the Lorentz force, which is described by reducing the morphology of a dendrite to a sphere and assuming that the surface temperature is equivalent to the anisotropy in the surface energy. When the thermoelectric currents are large and the magnetic field strength is substantial the convective transport, non-linear and resistive terms become significant. The problem is purely 3-dimensional and it is shown that classical 2-dimensional boundary conditions lead to stagnant conditions. A 2-dimensional quasi 3-dimensional approximation is proposed and, with the magnetic field orientated in the (001) direction, the effect of heat and solute redistribution through convection on the crystal morphology is modelled. Two significant morphological changes occur; the first is a deflection of the dendrite tip and the second is the initiation of secondary branching into the incident flow. The deflection is caused by circulations at the tips of the dendrite; the circulations continuously provide a region of higher free energy on the incident side while lowering it on the other. The net effect is a bias of growth in the direction of incident flow. The increase in secondary branching, in a similar fashion to the deflection, is caused by both a circulation at the tip and also a global circulation around the entire dendrite, destabilising the incident interface and initiating secondary growth. To qualify the quasi 3-dimensional approximation, a moving mesh technique is developed that tracks a single tip of 3-dimensional growth and the similar morphological features are observed in comparison to the quasi 3-dimensional case. Finally a discussion into possible extensions of this work is proposed and preliminary results for grain growth in the presence of a magnetic field are given

The Multiplicity Scaling of the Fragmentation Function

The single-particle inclusive fragmentation function and the particle multiplicity are observables of fundamental importance in studying properties of quantum chromodynamics at colliders. It is well-known that at high energies, the multiplicity distribution satisfies KNO scaling in which all moments are proportional to powers of the mean multiplicity. We prove that, under weak assumptions, the leading dependence of the fragmentation function on multiplicity is itself a kind of KNO scaling in which all moments are inversely proportional to powers of the mean multiplicity. This scaling with multiplicity additionally accounts for the dominant dependence on collision energy in the fragmentation function. The proof relies crucially on properties of the fragmentation function conditioned on the total multiplicity and application of the Stieltjes moment problem. In the process, we construct a novel basis of the fragmentation function expressed as an overall exponential suppression times a series of Laguerre polynomials. We study this scaling of the fragmentation function in experimental electron-position collision data and observe that residual scale violations are significantly reduced.Comment: 5 + 2 pages, 2 + 2 figure

AI-tocracy

Can frontier innovation be sustained under autocracy? We argue that innovation and autocracy can be mutually reinforcing when: (i) the new technology bolsters the autocrat's power; and (ii) the autocrat's demand for the technology stimulates further innovation in applications beyond those benefiting it directly. We test for such a mutually reinforcing relationship in the context of facial recognition AI in China. To do so, we gather comprehensive data on AI firms and government procurement contracts, as well as on social unrest across China during the last decade. We first show that autocrats benefit from AI: local unrest leads to greater government procurement of facial recognition AI, and increased AI procurement suppresses subsequent unrest. We then show that AI innovation benefits from autocrats' suppression of unrest: the contracted AI firms innovate more both for the government and commercial markets. Taken together, these results suggest the possibility of sustained AI innovation under the Chinese regime: AI innovation entrenches the regime, and the regime's investment in AI for political control stimulates further frontier innovation