TY - JOUR
AB - Torque magnetization measurements on YBa2Cu3Oy (YBCO) at doping y=6.67 (p=0.12), in dc fields (B) up to 33 T and temperatures down to 4.5 K, show that weak diamagnetism persists above the extrapolated irreversibility field Hirr(T=0)≈24 T. The differential susceptibility dM/dB, however, is more rapidly suppressed for B≳16 T than expected from the properties of the low field superconducting state, and saturates at a low value for fields B≳24 T. In addition, torque measurements on a p=0.11 YBCO crystal in pulsed field up to 65 T and temperatures down to 8 K show similar behavior, with no additional features at higher fields. We offer two candidate scenarios to explain these observations: (a) superconductivity survives but is heavily suppressed at high field by competition with charge-density-wave (CDW) order; (b) static superconductivity disappears near 24 T and is followed by a region of fluctuating superconductivity, which causes dM/dB to saturate at high field. The diamagnetic signal observed above 50 T for the p=0.11 crystal at 40 K and below may be caused by changes in the normal state susceptibility rather than bulk or fluctuating superconductivity. There will be orbital (Landau) diamagnetism from electron pockets and possibly a reduction in spin susceptibility caused by the stronger three-dimensional ordered CDW.
AU - Yu, Jing Fei
AU - Ramshaw, B. J.
AU - Kokanović, I.
AU - Modic, Kimberly A
AU - Harrison, N.
AU - Day, James
AU - Liang, Ruixing
AU - Hardy, W. N.
AU - Bonn, D. A.
AU - McCollam, A.
AU - Julian, S. R.
AU - Cooper, J. R.
ID - 7070
IS - 18
JF - Physical Review B
SN - 1098-0121
TI - Magnetization of underdoped YBa2Cu3Oy above the irreversibility field
VL - 92
ER -
TY - JOUR
AB - In this paper, we develop an energy method to study finite speed of propagation and waiting time phenomena for the stochastic porous media equation with linear multiplicative noise in up to three spatial dimensions. Based on a novel iteration technique and on stochastic counterparts of weighted integral estimates used in the deterministic setting, we formulate a sufficient criterion on the growth of initial data which locally guarantees a waiting time phenomenon to occur almost surely. Up to a logarithmic factor, this criterion coincides with the optimal criterion known from the deterministic setting. Our technique can be modified to prove finite speed of propagation as well.
AU - Julian Fischer
AU - Grün, Günther
ID - 1311
IS - 1
JF - SIAM Journal on Mathematical Analysis
TI - Finite speed of propagation and waiting times for the stochastic porous medium equation: A unifying approach
VL - 47
ER -
TY - JOUR
AB - We present an algorithm for the derivation of lower bounds on support propagation for a certain class of nonlinear parabolic equations. We proceed by combining the ideas in some recent papers by the author with the algorithmic construction of entropies due to Jüngel and Matthes, reducing the problem to a quantifier elimination problem. Due to its complexity, the quantifier elimination problem cannot be solved by present exact algorithms. However, by tackling the quantifier elimination problem numerically, in the case of the thin-film equation we are able to improve recent results by the author in the regime of strong slippage n ∈ (1, 2). For certain second-order doubly nonlinear parabolic equations, we are able to extend the known lower bounds on free boundary propagation to the case of irregular oscillatory initial data. Finally, we apply our method to a sixth-order quantum drift-diffusion equation, resulting in an upper bound on the time which it takes for the support to reach every point in the domain.
AU - Julian Fischer
ID - 1313
IS - 1
JF - Interfaces and Free Boundaries
TI - Estimates on front propagation for nonlinear higher-order parabolic equations: An algorithmic approach
VL - 17
ER -
TY - JOUR
AB - We derive a posteriori estimates for the modeling error caused by the assumption of perfect incompressibility in the incompressible Navier-Stokes equation: Real fluids are never perfectly incompressible but always feature at least some low amount of compressibility. Thus, their behavior is described by the compressible Navier-Stokes equation, the pressure being a steep function of the density. We rigorously estimate the difference between an approximate solution to the incompressible Navier-Stokes equation and any weak solution to the compressible Navier-Stokes equation in the sense of Lions (without assuming any additional regularity of solutions). Heuristics and numerical results suggest that our error estimates are of optimal order in the case of "well-behaved" flows and divergence-free approximations of the velocity field. Thus, we expect our estimates to justify the idealization of fluids as perfectly incompressible also in practical situations.
AU - Fischer, Julian L
ID - 1314
IS - 5
JF - SIAM Journal on Numerical Analysis
TI - A posteriori modeling error estimates for the assumption of perfect incompressibility in the Navier-Stokes equation
VL - 53
ER -
TY - JOUR
AB - In the present work we introduce the notion of a renormalized solution for reaction–diffusion systems with entropy-dissipating reactions. We establish the global existence of renormalized solutions. In the case of integrable reaction terms our notion of a renormalized solution reduces to the usual notion of a weak solution. Our existence result in particular covers all reaction–diffusion systems involving a single reversible reaction with mass-action kinetics and (possibly species-dependent) Fick-law diffusion; more generally, it covers the case of systems of reversible reactions with mass-action kinetics which satisfy the detailed balance condition. For such equations the existence of any kind of solution in general was an open problem, thereby motivating the study of renormalized solutions.
AU - Julian Fischer
ID - 1316
IS - 1
JF - Archive for Rational Mechanics and Analysis
TI - Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems
VL - 218
ER -