We employ the Klemm-Clem transformations to map the equations of motion for the Green functions of a clean superconductor with a general ellipsoidal Fermi surface (FS) characterized by the effective masses m1, m2, and m3 in the presence of an arbitrarily directed magnetic induction B = B(sin θ cos φ, sin θ sin φ, cos θ) onto those of a spherical FS. We then obtain the transformed gap equation for a transformed pairing interactionṼ (k,k ′ ) appropriate for any orbital order parameter symmetry. We use these results to calculate the upper critical induction Bc2(θ, φ) for an orthorhombic ferromagnetic superconductor with transition temperatures TCurie > Tc. We assume the FS is split by strong spin-orbit coupling, with a single parallel-spin (↑↑) pairing interaction of the p-wave polar state form locked onto theê3 crystal axis normal to the spontaneous magnetization M0 ⊥ê3 due to the ferromagnetism. The orbital harmonic oscillator eigenvalues are modified according to B → Bα, where α(θ, φ) = m3/m cos 2 θ + γ −2 (φ) sin 2 θ, γ 2 (φ) = m3/(m1 cos 2 φ + m2 sin 2 φ) and m = (m1m2m3) 1/3 . At fixed φ, the order parameter anisotropy causes Bc2 to exhibit a novel θ-dependence, which for γ 2 (φ) > 3 becomes a double peak at 0 • < θ * < 90 • and at 180 • − θ * , providing a sensitive bulk test of the order parameter orbital symmetry in both phases of URhGe and in similar compounds still to be discovered.

We calculate the angular and temperature T dependencies of the upper critical field Hc2(θ, φ, T ) for the C4v point group helical p-wave states, assuming a single uniaxial ellipsoidal Fermi surface, Pauli limiting, and strong spin-orbit coupling that locks the spin-triplet d-vectors onto the layers. Good fits to the Sr2RuO4 Hc2,a(θ, T )

We study polymer translocation through a nanopore subject to conformational differences created by putting two different solvents at the cis and trans compartments using Langevin dynamics in three dimensions (3D). Initially a fraction of the chain is placed in a good solvent at the cis side and the rest of the chain at the trans side is immersed in a bad solvent where it forms a globule. We study several aspects of the translocating chain as a function of the strength of the interaction ɛ/k(B)T for the bad solvent, where the temperature T is kept below the Θ temperature for the specific bead-spring model that we have used to describe the chain. For ɛ/k(B)T≥1 we find the mean first passage time (τ)~(ɛ/k(B)T)(-1) and (τ)~N(1.1±0.05). In that regard, translocation under solvent asymmetry is similar to the case of driven translocation under a bias inside the pore. However, the globule formed at the trans in the immediate vicinity of the pore readily absorbs the incoming particles making the translocation process faster than the driven translocation. Our simulation results for long chains and ɛ/k(B)T≥1 agree well with a theoretical prediction by Muthukumar [M. Muthukumar, J. Chem. Phys. 111, 10371 (1999).].

We calculate the temperature T and angular (θ, φ) dependence of the upper critical induction Bc2(θ, φ, T ) for parallel-spin superconductors with an axially symmetric p-wave pairing interaction pinned to the lattice and a dominant ellipsoidal Fermi surface (FS). For all FS anisotropies, the chiral Scharnberg-Klemm state Bc2(θ, φ, T ) exceeds that of the chiral Anderson-Brinkman-Morel state, and exhibits a kink at θ = θ * (T, φ), indicative of a first-order transition from its chiral, nodal-direction behavior to its non-chiral, antinodal-direction behavior. Applicability to Sr2RuO4, UCoGe, and topological superconductors such as CuxBi2Se3 is discussed.

We extended the Scharnberg-Klemm theory of Hc2(T ) in p-wave superconductors with broken symmetry to cases of partially broken symmetry in an orthorhombic crystal, as is appropriate for the more exotic ferromagnetic superconductor UCoGe in strong magnetic fields. For some partially broken symmetry cases, Hc2(T ) can mimic upward curvature in all three crystal axis directions, and reasonably good fits to some of the UCoGe data are obtained.

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