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In the case of binary black hole mergers, the surface of most obvious interest, the Event Horizon, is often computationally difficult to locate. Instead, it is useful to turn to quasi-local characterizations of black hole boundaries, such as Marginally Outer Trapped Surfaces (MOTS), which are defined for a single time slice of the spacetime, and the outer-most of which is the apparent horizon. In this talk, I will describe ongoing work focused on understanding MOTS in the interior of a five-dimensional black hole; both static and rotating. Similar to the four-dimensional Schwarzschild case previously studied, we find examples of self-intersecting MOTS with an arbitrary number of self-intersections. This provides further support that self-intersecting behavior is rather generic. I will also discuss the second stage of our research, which is for a rotating 5D black hole spacetime. These two cases fit into a larger project involving exploration of the generality of self-intersecting behaviour in MOTS, within spacetimes of increasing diversity.

CAP Virtual Congress 2021

Marginally Outer Trapped (Open) Surfaces in 4+1 Dimensional Spacetimes

myers-perry

schwarzschild

binary mergers

mots

black holes

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technical paper

**Introduction:** pHi is a hallmark of altered cellular function in the tumour microenvironment and its response to therapies. One of the main acid-extruding membrane transport proteins in cells is the Na+/H+ exchanger isoform 1 (NHE1). Chemical exchange saturation transfer (CEST) MRI uniquely images pHi. In CEST-MRI, contrast is produced by exciting exchangeable tissue protons at their specific absorption frequency and observing the transfer of magnetization to bulk tissue water. Amine and amide concentration-independent detection (AACID) is a ratiometric approach that uses the distinctive sensitivity of amine and amide protons to CETS contrast. The AACID value inversely relates to tissue pHi. One way to achieve tumour acidification as a therapeutic strategy is by blocking the NHE1 transporter. Cariporide is a potent inhibitor of NHE1. We have shown that cariporide can selectively acidify U87MG glioma in mice. The goal of this study was to determine whether cariporide also selectively acidifies a rat C6 glioma tumour model immediately following injection by mapping tumour pHi.
**Methods:** A 2μL suspension of 10^6 C6 glioma cells were injected into the right frontal lobe of six 8-week-old male rats. To evaluate the effect of cariporide on tumour pHi, rats received an IP injection of the drug (6mg/kg in 2ml) two weeks after tumour implantation. They received the drug inside a 9.4T scanner to measure the change in pHi following injection. 
**Results:** Five minutes after injection we started collecting CEST-MRI for 3 hours. For data analysis, we compared the first maximum change in AACID value post-injection with the pre-injection value. Approximately 60 minutes after injection, the average AACID value in the tumour significantly increased (p<0.05). The average AACID value in tumour post-injection was 5.4% higher compared to pre-injection corresponding to a 0.26 lower pHi. The average AACID value in contralateral tissue also increased in a similar way.
**Conclusion:** We did not observe selective tumour acidification following injection as was observed in the previous study. The reason for this discrepancy is currently unknown but may be related to potential differences in tumour vasculature that may limit the ability of cariporide to infiltrate the tumour. Future work includes increasing cariporide dose and modifying our quantification method to increase the temporal stability of the AACID measurement.

Cariporide Effects on Intracellular pH (pHi) Using CEST-MRI in Rat Model of Glioblastoma

Graphene field effect transistors (GFETs) have an enormous potential for the development of next-generation gas sensors, but more efforts are required to improve their sensitivity and selectivity. In this talk we discuss UV illumination as a promising method to enhance the performance of GFETs for the detection and recognition of analytes such as ethanol, water vapor and dimethyl methylphosphonate (DMMP), a molecule with structural similarities to nerve agents such as sarin. We show that illuminating the devices in operando with a UV LED results in both improved sensitivity and selectivity. By monitoring the sensing response of the GFETs as a function of gate voltage, we directly demonstrate that a shift in the Dirac point due to the optical doping is associated with the increased sensitivity. Moreover, we discuss how the substrate and fabrication residues on the surface of the graphene sensors can play a role in modifying the sensing performance.

Optically enhanced gas sensing performance of graphene field effect transistors

High harmonic generation (HHG) in gasses has become a method of choice among table-top extreme ultraviolet (XUV) sources. In order to generate higher photon energies from this process, many strategies can be implemented, including red-shifting and compressing the driver pulses. Here, we propose a new approach for inducing a red-shift to driver pulses and compressing them to few-cycle durations in a single stage. This method uses the recently discovered multidimensional solitary states (MDSS) pulses that result from the nonlinear Raman process in gas-filled hollow-core fibers. It has a few key advantages: 1) MDSS are created from relatively long pulses, making this method suitable for any laser source offering sub-picosecond pulses. 2) The MDSS pulses can be compressed by simple propagation through glass. 3) In contrast with commonly-used optical parametric amplifiers, the induced red-shift can be modest, allowing to reach a target XUV photon energy while minimizing the detrimental effects of long driver wavelengths on HHG efficiency. 
To produce MDSS pulses, the output pulses of a Titanium-Sapphire system are stretched to 400 fs and coupled to a hollow-core fiber filled with nitrogen. In the fiber, intermodal nonlinear processes occur which lead to the red-shifted MDSS pulses. Then, CaF2 plates inserted into the beam path compress the pulses down to 12 fs and these are sent to an argon-filled cell where HHG occurs. From this simple apparatus, the HHG spectrum is expanded to cover the M$_{2,3}$ edge of cobalt and $10^9$ photons/second are generated at 60 eV. This significant XUV photon flux allows for the implementation of X-ray resonant magnetic scattering measurements on a cobalt/platinum ferromagnet, an example of photon-hungry application. Although such flux has previously been generated in a different gas from the direct output of the same laser system, the conversion efficiency of our approach is one order of magnitude higher as it allows to reach the target photon energy by generating harmonics in argon, a gas that offers a large generation efficiency. Due to its simplicity and versatility, our approach can readily be adapted to different applications and could be particularly interesting for high power Ytterbium laser systems offering sub-picosecond pulses.

Multidimensional Raman Solitons as Drivers of the High Harmonic Generation Process

Seawater spray and precipitation are two main sources of icing and ice accumulation in cold ocean regions, presenting a major challenge for shipping and operating maritime equipment [1]. 
There is a limited number of analytical techniques to study seawater spray ice formation. MRI is known for its non-invasive capabilities in measurements of a solid ice [2,3]. In this work, we investigated the potential of MRI as an analytical measurement technique for studies of the seawater spray ice. 
The signal detected with MRI/NMR comes from pockets of brine in the forming ice, and the unfrozen water, with the 1H NMR signal from the brine decreasing as the temperature drops and the brine freezes further. 3D MRI showed different freezing patterns and temperature gradients depending on the initial freezing temperature and the surface geometry. T1-T2 maps indicated strong changes in relaxation parameters as the freezing progresses, indicating changing environment for the brine in the growing ice [4]. In a separate freezing series using Na NMR, the amount of sodium in the brine remained almost unchanged until the brine reached the eutectic temperature, and the sodium precipitation accelerated.
These measurements were done on an MRI scanner, with the freezing setup designed to fit a 4 cm i.d. RF probe inside a 2.4 T superconducting magnet. To explore a possibility of using NMR for freezing studies in a more open environment, we also used a portable, unilateral NMR device to characterize sea spray freezing on a cold surface. The device consisted of a flat 3-magnet array [5] with the sensitive volume (approx.2 mm x 15 x 15 mm) at 1 cm away from the magnet surface. 1D-resolved 1H NMR measurements provided information on the brine concentration, T2 and diffusion at a range of temperatures.
The results provide information on the changing environment in brine in freezing sea sprays, with a potential for NMR studies both in the lab and in the field.

[1]A.R. Dehghani-Sanij, S.R. Dehghani, G.F. Naterer, Y.S. Muzychka, Ocean Eng. 143 (2017) 1–23.
[2]M.W. Hunter, R. Dykstra, M.H. Lim, T.G. Haskell, P.T. Callaghan, Appl. Magn. Reson. 36 (2009) 1–8.
[3]J.R. Brown, T.I. Brox, S.J. Vogt, J.D. Seymour, M.L. Skidmore, S.L. Codd, J. Magn. Reson. 225 (2012) 17–24. 
[4] G.Wilbur, B.MacMillan, K.M.Bade, I.Mastikhin, J. Magn. Reson. 310 (2020) 106647.
[5] J.C.Garcia-Naranjo, I.Mastikhin, B.J.Colpitts, B.J.Balcom, J. Magn.Reson. 207 (2010) 337-344

Sea spray freezing measurements with MRI and portable NMR

Gravitational Wave (GW) detection from continuous sources such as pulsars is an anticipated discovery. However, due to exceedingly weak signals, detection is challenging. In this presentation, we detail the derivation of a Fourier transform of a continuous wave signal amenable for detection of the GW signal from a pulsar. We also present an easy to implement algorithm for computing peak heights and frequencies from analytical results arising from features in frequency evolution of gravitational wave signals. Our approach can handle gaps in data, allowing longer
coherence lengths. While the presentation focuses on GW detection from pulsar, our results are general and can be applied to any monochromatic signals of this form.

Fourier transform of gravitational wave signals from a pulsar

In optics, caustics are bright, sharp lines and shapes created by the natural focusing of light. Some examples include rainbows, the wavy lines on the bottom of swimming pools and the patterns produced by gravitational lensing. The intensity at a caustic diverges in the classical ray theory, but can be smoothed by taking into account the wave nature of light. In this work we consider a new type of caustic that occurs in quantum systems due to phase singularities; because phase is such a central concept in wave theory, this heralds the breakdown of the wave description and is an example of a quantum caustic. In particular, we consider analogue black holes which can be formed in a flowing Bose-Einstein condensate (BEC) gas. Waves flowing near the event horizon (describing analogue Hawking radiation) appear to suffer a logarithmic phase divergence, which is known as the trans-Planckian problem for gravitational black holes. We describe the regularization procedure required to cure this quantum caustic in our BEC system, and make connections to catastrophe theory.

Hawking radiation as a quantum caustic

Purpose: A quantitative measure of delivered ionizing radiation is recommended for quality assurance and quality control purposes for patients undergoing radiotherapy treatments. Current dosimeters are not well suited for direct measurements due to atomic composition and size limitations. We are developing a fiber optic probe dosimeter based on radiochromic material for in vivo dosimetry. Through measuring the change in optical absorption of the radiochromic sensor, we can quantify the absorbed dose of ionization radiation delivered in real-time. The radiation-sensitive material is composed of lithium-10,12-pentacosa diynoate (LiPCDA), which upon exposure, polymerizes and results in an increased optical density. We observed that monomers of LiPCDA can have two distinct crystalline morphologies, with aspect ratios 10:1 producing hair-like structures and 2:1 resulting in platelets, with polymerized absorbance peaks typically centred at 635 nm and 674 nm, respectively. We aim to characterize and compare the dose-response of the two crystal morphologies achieved through desiccation and Li+ concentration. 

Method: The hair-like LiPCDA in commercial film was desiccated, producing crystals with an absorbance peak at 674 nm. Both materials were exposed to 50-3000 cGy using a clinical linear accelerator with a 6MV X-ray beam; samples of varying Li+ concentration were exposed to 200-400 cGy. Absorbance spectra for all samples were collected and were imaged with a scanning electron microscope to compare their crystal morphology. 

Results: Differences in crystal morphology were not observed when hair-like LiPCDA was desiccated. However, varying the molar ratio of Li+ to PCDA to produce crystals with either 635 nm or 677 nm absorbance peak, differentiable crystal morphologies were observed. The platelet form is ~3x less sensitive to dose but with a more extensive dynamic range relative to hair-like. 

Conclusion: Crystals can be preferentially grown and exhibit differing dose-response. The macrostructure effect on radiation sensitivity in the context of radiotherapy will be explored.

Characterization of modified radiochromic materials for measuring ionizing radiation

In this joint experimental and theoretical work [1], photoelectron emission from excited states of laser-dressed atomic helium is analyzed. We successfully demonstrate a method that is complimentary to transient absorption (e.g. [2]) for the assignment of light-induced states (LIS). The experiment is carried out at DESY in Hamburg and uses the FLASH2 free-electron laser to produce an extreme ultraviolet (XUV) pulse to which the helium atom is subjected along with a temporally overlapping infrared (IR) pulse in the multi-photon ionization regime ($\approx$10$^{12}$ W/cm$^2$). Analysis of the experiment occurs at the reaction microscope (REMI) end station [3] at FLASH2. The XUV pulse is scanned over the energy range 20.4 eV to 24.6 eV, corresponding to excited states of helium. The resonant, electric dipole-allowed $n$P states corresponding to a first step of single XUV photon excitation are shown to lead to ionization, independent of whether or not the lasers temporally overlap. However, dipole-forbidden transitions to $n$S and $n$D states corresponding to multiphoton (XUV $\pm$ $n$IR) excitation are observed during temporal overlap. Studying photo\-electron angular distributions (PADs) in the case where the ionization pathway of a LIS is difficult to resolve energetically allows for an unambiguous determination of the dominant LIS. The IR intensity and relative polarization between the lasers are varied to control the ionization pathway. Numerical solutions of the time-dependent Schr\"odinger equation within a single-active electron model with a local potential completely support the experimental findings in this project.
[1] S. Meister $\textit{et al}$., Phys. Rev. A $\bf{102}$ (2020) 062809; Phys. Rev. A $\bf{103}$ (2021) in press.
[2] S. Chen $\textit{et al}$., Phys. Rev. A $\bf{86}$ (2012) 063408.
[3] S. Meister $\textit{et al}$., Applied Sciences $\bf{10}$ (2020) 2953. 
*work supported by NSERC, NSF, and XSEDE

Emergence of light-induced states in the few-photon ionization of atomic helium*

Lattice gauge theory is an indispensible tool for non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic
ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge
theories.

SU(2) lattice gauge theory on a quantum annealer

We combined information from Fluorescence Correlation Spectroscopy (FCS), Nuclear Magnetic Resonance (NMR), Small-Angle X-ray Scattering (SAXS) and Single-Molecule Förster Energy Transfer (smFRET) to calculate conformational ensembles for the neuronal transcription factor initiation protein 4E-BP2. This is a 120-residue intrinsically disordered protein which toggles between an active, non-phosphorylated (NP) state and an inactive multi-phosphorylated (5P) state. An initial pool of 4E-BP2 structures was generated using Trajectory Directed Ensemble Sampling (TraDES) (Feldman & Hogue, Proteins: Structure, Function, and Bioinformatics, 46, 8-23, 2002). The ENSEMBLE method (Krzeminski et al, Bioinformatics, 29, 398-399, 2013) was used to search and select conformations within the initial pool that are consistent with the experimental data. NMR and SAXS data were used as restraints for the conformational search and FCS and smFRET data were used as validation. 

The NP 4E-BP2 ensemble calculated with SAXS-only restraints showed a bimodal distribution of protein global dimensions such as the radius of gyration and the end-to-end distance. The back-calculated FRET efficiency and the hydrodynamic radius for this ensemble were lower than the respective experimental values. These inconsistencies are likely due to lack of short-range (5-20 Å) distance restraints, which are currently addressed by acquiring Paramagnetic Resonance Enhancement (PRE) data. Such data is available for the phosphorylated state (5P 4E-BP2), however this is partly folded, with a 4-stranded beta domain spanning residues 18-62. To address this challenge, we used the FastFloppyTail (FFT) program (Ferrie & Petersson, The Journal of Physical Chemistry B, 124, 5538-5548, 2020) to generate structures in the initial pool. As such, the folded region was modelled using the 5P 4E-BP2 folds from the Protein Databank, while the disordered tails were generated through the FFT algorithm. By incorporating the more realistic FFT-built prior in ENSEMBLE calculations, more accurate conformational ensembles of both phospho- and non-phospho- variants of 4E-BP2 were obtained. Analysis of these ensembles in terms of polymer physics and contact maps reveal new molecular level details lead to new insights into the biological function of 4E-BP2.

Marginally Outer Trapped (Open) Surfaces in 4+1 Dimensional Spacetimes

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