Variational problems with singular perturbation

In this paper, we construct the local minimum of a certain variational problem which we take in the form $\mathrm{inf}\int_\Omega\left\{\frac{\epsilon}{2}kg^2|\nabla w|^2+\frac{1}{4\epsilon}f^2g^4(1-w^2)^2\right\}\,\mathrm{d}x$, where $\epsilon$ is a small positive parameter and $\Omega\subset\mathbb{R}^n$ is a convex bounded domain with smooth boundary. Here $f,g,k\in C^3(\Omega)$ are strictly positive functions in the closure of the domain $\bar{\Omega}$. If we take the inf over all functions $H^1(\Omega)$, we obtain the (unique) positive solution of the partial differential equation with Neumann boundary conditions (respectively Dirichlet boundary conditions). We wish to restrict the inf to the local (not global) minimum so that we consider solutions of this Neumann problem which take both signs in $\Omega$ and which vanish on $(n-1)$ dimensional hypersurfaces $\Gamma_\epsilon\subset\Omega$. By using a $\Gamma$-convergence method, we find the structure of the limit solutions as $\epsilon\to0$ in terms of the weighted geodesics of the domain $\Omega$

Diffraction efficiency of strong volume holograms

We investigate the diffraction efficiency of strong volume holograms in which the coupling parameter is several times that needed for maximum diffraction efficiency. We discuss the implications of our findings on photorefractive implementations of various neural network systems

Dynamics of grating formation in photovoltaic media

The Kukhtarev equations are solved taking into account the photovoltaic effect and different boundary conditions. In the case of open circuit, the voltage across the crystal is found to vary with a time scale similar to the photorefractive time constant. This effect explains the dynamic behavior observed experimentally

Time-reversal in dynamically-tuned zero-gap periodic systems

We show that short pulses propagating in zero-gap periodic systems can be reversed with 100% efficiency by using weak non-adiabatic tuning of the wave velocity at time-scales that can be much slower than the period. Unlike previous schemes, we demonstrate reversal of {\em broadband} (few cycle) pulses with simple structures. Our scheme may thus open the way to time-reversal in a variety of systems for which it was not accessible before.Comment: Accepted for publication in Phys. Rev. Letter

Mild and Asymptomatic Covid-19 Infections: Implications for Maternal, Fetal and Reproductive Health

The public health implications of the spread of SARS-CoV-2 infection from the initial site of infection to the female reproductive organs, in both pregnant and non-pregnant reproductive age women, are the focus of this paper

Phase-locked sustainment of photorefractive holograms using phase conjugation

A method for sustaining multiply exposed photorefractive holograms, in a phase-locked fashion, by using a pair of phase-conjugating mirrors is described. It is shown that a steady state exists where the overall diffraction efficiency is independent of the number of holographic exposures and the final holograms are exactly in phase with the initial ones. Both analytical and experimental results are presented

The Potential Use of Intrauterine Insemination as a Basic Option for Infertility: A Review for Technology-Limited Medical Settings

Objective. There is an asymmetric allocation of technology and other resources for infertility services. Intrauterine insemination (IUI) is a process of placing washed spermatozoa transcervically into the uterine cavity for treatment of infertility. This is a review of literature for the potential use of IUI as a basic infertility treatment in technology-limited settings. Study design. Review of articles on treatment of infertility using IUI. Results. Aspects regarding the use of IUI are reviewed, including ovarian stimulation, semen parameters associated with good outcomes, methods of sperm preparation, timing of IUI, and number of inseminations. Implications of the finding in light of the needs of low-technology medical settings are summarized. Conclusion. The reviewed evidence suggests that IUI is less expensive, less invasive, and comparably effective for selected patients as a first-line treatment for couples with unexplained or male factor infertility. Those couples may be offered three to six IUI cycles in technology-limited settings

Building Qutrit Diagonal Gates from Phase Gadgets

Phase gadgets have proved to be an indispensable tool for reasoning about ZX-diagrams, being used in optimisation and simulation of quantum circuits and the theory of measurement-based quantum computation. In this paper we study phase gadgets for qutrits. We present the flexsymmetric variant of the original qutrit ZX-calculus, which allows for rewriting that is closer in spirit to the original (qubit) ZX-calculus. In this calculus phase gadgets look as you would expect, but there are non-trivial differences in their properties. We devise new qutrit-specific tricks to extend the graphical Fourier theory of qubits, resulting in a translation between the 'additive' phase gadgets and a 'multiplicative' counterpart we dub phase multipliers. This enables us to generalise the qubit notion of multiple-control to qutrits in two ways. The first type is controlling on a single tritstring, while the second type applies the gate a number of times equal to the tritwise multiplication modulo 3 of the control qutrits.We show how both types of control can be implemented for any qutrit Z or X phase gate, ancilla-free, and using only Clifford and phase gates. The first requires a polynomial number of gates and exponentially small phases, while the second requires an exponential number of gates, but constant sized phases. This is interesting, because such a construction is not possible in the qubit setting. As an application of these results we find a construction for emulating arbitrary qubit diagonal unitaries, and specifically find an ancilla-free emulation for the qubit CCZ gate that only requires three single-qutrit non-Clifford gates, provably lower than the four T gates needed for qubits with ancilla.Comment: In Proceedings QPL 2022, arXiv:2311.0837

Constructing all qutrit controlled Clifford+T gates in Clifford+T

For a number of useful quantum circuits, qudit constructions have been found which reduce resource requirements compared to the best known or best possible qubit construction. However, many of the necessary qutrit gates in these constructions have never been explicitly and efficiently constructed in a fault-tolerant manner. We show how to exactly and unitarily construct any qutrit multiple-controlled Clifford+T unitary using just Clifford+T gates and without using ancillae. The T-count to do so is polynomial in the number of controls $k$, scaling as $O(k^{3.585})$. With our results we can construct ancilla-free Clifford+T implementations of multiple-controlled T gates as well as all versions of the qutrit multiple-controlled Toffoli, while the analogous results for qubits are impossible. As an application of our results, we provide a procedure to implement any ternary classical reversible function on $n$ trits as an ancilla-free qutrit unitary using $O(3^n n^{3.585})$ T gates.Comment: 14 page