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The phase diagram and symmetry breaking patterns of a holographic CFT with U(1)$\times$SU(2) symmetry are analyzed using the simplest holographic action, namely Einstein-Yang-Mills (YM) theory with a negative cosmological constant. This is relevant for both condensed matter and QCD applications. With a U(1) and an "isospin" chemical potential turned on, we determine all possible symmetry breaking patterns, which are associated to the condensation of spin-one order parameters. The possible IR asymptotics of the Einstein-YM solutions are derived analytically, both for 2+1 and 3+1 boundary dimensions. The competing solutions are then computed numerically, both at zero and non-zero temperature, from which the full three-dimensional phase diagram is determined. We find a surface of second order phase transitions that separate uncondensed and condensed phases. In some regions with a large fraction of charged to neutral degrees of freedom, the phase transition becomes first order., Comment: 45 pages + appendix, 18 figures; v2: added some references, cleaned up sections 2 and 3

Holographic quantum field theories that confine in flat space, are considered on a fixed AdS space. The space of holographic solutions for such theories is constructed and three types of regular solutions are found. Theories with two AdS boundaries provide interfaces between two confining theories. Theories with a single AdS boundary correspond to ground states of a single confining theory on AdS. We find solutions without a boundary, whose interpretation is not obvious. There is also a special limiting solution that oscillates an infinite number of times around the UV fixed point. We analyze in detail the holographic dictionary for the one-boundary solutions and compute the free energy. No (quantum) phase transitions are found when we change the curvature. We find an infinite number of pure vev solutions, but no CFT solution without a vev. We also compute the free energy of the interface solutions. We find that the product saddle points have always lower free energy than the connected solutions. This implies that in such interfaces, normalized cross-correlators vanish exponentially in $N_c^2$., Comment: 118 pages

We consider the p-system in Eulerian coordinates on a star-shaped network. Under suitable transmission conditions at the junction and dissipative boundary conditions in the exterior vertices, we show that the entropy solutions of the system are exponentially stabilizable. Our proof extends the strategy by Coron et al. (2017) and is based on a front-tracking algorithm used to construct approximate piecewise constant solutions whose BV norms are controlled through a suitable exponentially-weighted Glimm-type Lyapunov functional.

We study a fractional cross-diffusion system that describes the evolution of multi-species populations in the regime of large-distance interactions in a bounded domain. We prove existence and weak-strong uniqueness results for the initial-boundary value problem and analyze the convergence of the solutions to equilibrium via relative entropy methods.

Flow-Induced Vibrations (FIV) of an elastically mounted circular cylinder are investigated by means of two-dimensional simulations. A mechanical coupling between cross-flow translation and rotation provides a single degree-of-freedom system in which the coupled rotational oscillations affect the fluid-structure dynamics. The structural response of this system is investigated exploring the design space spanned by reduced velocity, coupling radius, and phase density ratio. The kinematic coupling introduces the rotation-induced shear layer modifications, as well as an equivalent inertia effect connected to the coupling force. Such a computational campaign is carried out by means of direct numerical simulations with immersed boundary forcing at a Reynolds number equal to 100. The investigated system exhibits the wake-body synchronisation features typical of lock-in for non-rotating cylinders. However, the kinematic coupling provides a novel FIV scenario, in which the oscillation amplitude is magnified in the locked configurations with respect to the forced rotation case. Furthermore, it is found a significant widening of the reduced velocity domain where the lock-in condition takes place. In view of the proposed analyses, it is determined that the coupled rotation guarantees the phase alignment between lift and displacement necessary to sustain the lock-in condition, making the oscillation amplitude grow indefinitely with the reduced velocity. This is inherently achieved due to the rotational shear layer and the added mass contribution, which prevent the exact match between oscillation frequency and system natural frequency in vacuum. The outcomes of this study might potentially lead to innovative water energy harvesters offering larger power outputs and extended optimal operating regions.

We study the viscous Burgers equation with a family of initial data having infinite mass. After rescaling, the solution converges toward a bounded discontinuous profile in the long-time limit. Moreover, by changing the scale near the discontinuity point again, we find a new profile that is also discontinuous. This process can be repeated an arbitrary number of times.

We propose an isogeometric approach to model the deformation of active thin films using layered, nonlinear, Kirchhoff Love shells. Isogeometric Collocation and Galerkin formulations are employed to discretize the electrophysiological and mechanical sub-problems, respectively, with the possibility to adopt different element and time-step sizes. Numerical tests illustrate the capabilities of the active stress based approach to effectively simulate the contraction of thin films in both quasi-static and dynamic conditions.

We study the problem of transporting one probability measure to another via an autonomous velocity field. We rely on tools from the theory of optimal transport. In one space-dimension, we solve a linear homogeneous functional equation to construct a suitable autonomous vector field that realizes the (unique) monotone transport map as the time-$1$ map of its flow. Generically, this vector field can be chosen to be Lipschitz continuous. We then use Sudakov's disintegration approach to deal with the multi-dimensional case by reducing it to a family of one-dimensional problems.

In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bounded domain in $\mathbb{R}^d$. The nonlocal operator we consider is the spectral fractional Laplacian with Neumann boundary conditions. In the case of a "strong slippage" regime with "complete wetting" interfacial conditions, we prove local entropy estimates that entail finite speed of propagation of the support and a lower bound for the waiting time phenomenon.

We analyze the optimal regularity that is exactly propagated by a transport equation driven by a velocity field with BMO gradient. As an application, we study the 2D Euler equations in case the initial vorticity is bounded. The sharpness of our result for the Euler equations follows from a variation of Bahouri and Chemin's vortex patch example.

The fractional Caffarelli-Kohn-Nirenberg inequality states that $$ \int_{\mathbb{R}^n}\int_{\mathbb{R}^n} \frac{(u(x)-u(y))^2}{|x|^\alpha |x-y|^{n+2s} |y|^\alpha} \mathrm{d} x \, \mathrm{d} y \geq \Lambda_{n, s, p, \alpha,\beta} \|u |x|^{-\beta}\|_{L^p}^2, $$ for $0

Observables in quantum gravity are famously defined asymptotically, at the boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate system or suitably dressing the field operators, an approximate, "quasi-local" approach is also possible, that can give account of the measurements performed by a set of observers living inside the spacetime. In particular, one can attach spatial coordinates to the worldlines of these observers and use their proper times as a time coordinate. Here we highlight that any such local formulation has to face the relativity of the event, in that changing frame (= set of observers) implies a reshuffling of the point-events and the way they are identified. As a consequence, coordinate transformations between different frames become probabilistic in quantum gravity. We give a concrete realization of this mechanism in Jackiw-Teitelboim gravity, where a point in the bulk can be defined operationally with geodesics anchored to the boundary. We describe different ways to do so, each corresponding to a different frame, and compute the variances of the transformations relating some of these frames. In particular, we compute the variance of the location of the black hole horizon, which appears smeared in most frames. We then suggest how to calculate this effect in Einstein gravity, assuming knowledge of the wavefunction of the metric. The idea is to expand the latter on a basis of semiclassical states. Each element of this basis enjoys standard/deterministic coordinate transformations and the result is thus obtained by superposition. As a divertissement, we sabotage the familiar Lorentz boosts by adding to Minkoswki spacetime a quantum superposition of gravitational waves and compute the probabilistic transformation to a boosted frame in linearized gravity. Finally, we attempt to translate the relativity of the event in the language of dressed operators., Comment: 40 pages, 10 Figures. Comments welcome. v2: improved discussion, references added. v3: minor changes. Matches published version

We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key feature of of the problem is that the interplay between the nonlinear force and the boundary conditions allows for a continuous set of equilibrium points. We prove an exponential rate of convergence for the solution towards a (uniquely determined) equilibrium point.

We consider ($d+n+1$)-dimensional solutions of Einstein gravity with constant negative curvature. Regular solutions of this type are expected to be dual to the ground states of ($d+n$)-dimensional holographic CFTs on $AdS_d\times S^n$. Their only dimensionless parameter is the ratio of radii of curvatures of $AdS_d$ and $S^n$. The same solutions may also be dual to $(d-1)$-dimensional conformal defects in holographic QFT$_{d+n}$. We solve the gravity equations with an associated conifold ansatz, and we classify all solutions both singular and regular by a combination of analytical and numerical techniques. There are no solutions, regular or singular, with two boundaries along the holographic direction. Out of the infinite class of regular solutions, only one is diffeomorphic to $AdS_{d+n+1}$ and another to $AdS_d\times AdS_{n+1}$. For the regular solutions, we compute the on-shell action as a function of the relevant parameters., Comment: 75 pages, 23 figures

We prove sharp bounds on the enstrophy growth in viscous scalar conservation laws. The upper bound is, up to a prefactor, the enstrophy created by the steepest viscous shock admissible by the $L^\infty$ and total variation bounds and viscosity. This answers a conjecture by D. Ayala and B. Protas (\emph{Physica D}, 2011), based on numerical evidence, for the viscous Burgers equation., Comment: 7 pages

We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem under the overdetermination that the interface serves as a level surface of the solution. The first proof avoids the method of moving planes; instead, it leverages the comparison principle and the fact that the solution of the obstacle problem is superharmonic within its domain. The second proof utilizes a suitable version of Serrin's method of moving planes., Comment: 10 pages, 2 figures

A (toy) model for cold and luke-warm strongly-coupled nuclear matter at finite baryon density is used to study neutrino transport. The complete charged current two-point correlators are computed in the strongly-coupled medium and their impact on neutrino transport is analyzed. The full result is compared with various approximations for the current correlators and the distributions, including the degenerate approximation, the hydrodynamic approximation as well as the diffusive approximation and we comment on their successes. Further improvements are discussed., Comment: 67 pages + Appendix; 27 figures. Accepted for publication in JHEP. The treatment of isospin asymmetry was not correct in the previous version, so the isospin chemical potential is set to zero in this new version. Most of our results are qualitatively unchanged. We are planning to study the isospin asymmetric case in a future work

We prove a fractional Hardy-Rellich inequality with an explicit constant in bounded domains of class $C^{1,1}$. The strategy of the proof generalizes an approach pioneered by E. Mitidieri (Mat. Zametki, 2000) by relying on a Pohozaev-type identity.

We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast \rho$ satisfy an Ole\u{\i}nik-type entropy condition. More precisely, under different sets of assumptions on the velocity function $V$, we prove that $W$ satisfies a one-sided Lipschitz condition and that $V'(W) W \partial_x W$ satisfies a one-sided bound, respectively. As a byproduct, we deduce that, as the exponential kernel is rescaled to converge to a Dirac delta distribution, the weak solution of the nonlocal problem converges to the unique entropy-admissible solution of the corresponding local conservation law, under the only assumption that the initial datum is essentially bounded and not necessarily of bounded variation.

Classical gravity coupled to a CFT$_4$ (matter) is considered. The effect of the quantum dynamics of matter on gravity is studied around maximally symmetric spaces (flat, de Sitter and Anti de Sitter). The structure of the graviton propagator is modified and non-trivial poles appear due to matter quantum effects. The position and residues of such poles are mapped as a function of the relevant parameters, the central charge of the CFT$_4$, the two $R^2$ couplings of gravity as well as the curvature of the background space-time. The instabilities induced are determined. Such instabilities can be important in cosmology as they trigger the departure from de Sitter space and in some regions of parameters are more important than the well-known scalar instabilities. It is also determined when the presence of such instabilities is unreliable if the associated scales are larger than the ``species" cutoff of the gravitational theory., Comment: 99 pages + appendix, 24 figures + appendix

This work is concerned with fractional Gaussian fields, i.e. Gaussian fields whose covariance operator is given by the inverse fractional Laplacian $(-\Delta)^{-s}$ (where, in particular, we include the case $s >1$). We define a lattice discretization of these fields and show that their scaling limits -- with respect to the optimal Besov space topology (up to an endpoint case) -- are the original continuous fields. As a byproduct, in dimension $d<2s$, we prove the convergence in distribution of the maximum of the fields. A key tool in the proof is a sharp error estimate for the natural finite difference scheme for $(-\Delta)^s$ under minimal regularity assumptions, which is also of independent interest., Comment: v2: minor corrections, additional references; v3: further minor corrections, expanded introduction

The single baryon solution of V-QCD is numerically computed. The spectrum of spin and isospin modes is also computed by quantizing the light fluctuations around the baryon. It is shown that there is a partial restoration of chiral symmetry at the baryon center., Comment: 46 pages + Appendix, 13 figures

We study the spatial critical points of the solutions $u=u(x,t)$ of the fractional heat equation. For the Cauchy problem, we show that the origin $0$ satisfies $\nabla_x u(0,t) = 0$ for $t>0$ if and only if the initial data satisfy a balance law of the form $\int_{\mathbb{S}^{N-1}} \omega u_0(r\omega) \, \mathrm{d} \omega=0$ for a. e. $r \ge 0$. Moreover, for the Dirichlet initial-boundary value problem, we prove two symmetry results: $\Omega$ is a ball centered at the origin if and only if $\nabla_x u(0,t) = 0$ for $t>0$ provided that the initial data satisfies the above-mentioned balance law; $\Omega$ is centrosymmetric if and only if $\nabla_x u(0,t) = 0$ for $t>0$ provided that the initial data is centrosymmetric. These results extend some theorems obtained by Magnanini and Sakaguchi in 1997-1999 for the (local) heat equation to the fractional context. These extensions are nontrivial because of the nonlocal nature of the fractional Laplacian. Among others, the proof of the characterization of a ball in the Dirichlet initial-boundary value problem for the fractional heat flow not only works for the classical heat flow but also gives a new insight into the problem., Comment: 19 pages

Coronal holes (CHs) are the source of high-speed streams (HSSs) in the solar wind, whose interaction with the slow solar wind creates corotating interaction regions (CIRs) in the heliosphere. Whenever the CIRs hit the Earth, they can cause geomagnetic storms. We develop a method to predict the strength of CIR/HSS-driven geomagnetic storms directly from solar observations using the CH areas and associated magnetic field polarity. First, we build a dataset comprising the properties of CHs on the Sun, the associated HSSs, CIRs, and orientation of the interplanetary magnetic field (IMF) at L1, and the strength of the associated geomagnetic storms by the geomagnetic indices Dst and Kp. Then, we predict the Dst and Kp indices using a Gaussian Process model, which accounts for the annual variation of the orientation of Earth's magnetic field axis. We demonstrate that the polarity of the IMF at L1 associated with CIRs is preserved in around 83% of cases when compared to the polarity of their CH sources. Testing our model over the period 2010-2020, we obtained a correlation coefficient between the predicted and observed Dst index of R = 0.63/0.73, and Kp index of R = 0.65/0.67, for HSSs having a polarity towards/away from the Sun. These findings demonstrate the possibility of predicting CIR/HSS-driven geomagnetic storms directly from solar observations and extending the forecasting lead time up to several days, which is relevant for enhancing space weather predictions., Comment: 13 pages, 11 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

We study the quantitative stability of critical points of the fractional Sobolev inequality. We show that, for a non-negative function $u \in \dot H^s(\mathbb R^N)$ whose energy satisfies $$\tfrac{1}{2} S^\frac{N}{2s}_{N,s} \le \|u\|_{\dot H^s(\mathbb R^N)} \le \tfrac{3}{2}S_{N,s}^\frac{N}{2s},$$ where $S_{N,s}$ is the optimal Sobolev constant, the bound $$ \|u -U[z,\lambda]\|_{\dot{H}^s(\mathbb R^N)} \lesssim \|(-\Delta)^s u - u^{2^*_s-1}\|_{\dot{H}^{-s}(\mathbb R^N)}, $$ holds for a suitable fractional Talenti bubble $U[z,\lambda]$. {For functions $u$ which are close to Talenti bubbles, we give the sharp asymptotic value of the implied constant in this inequality.} As an application {of this}, we derive an explicit polynomial extinction rate for positive solutions to a fractional fast diffusion equation., Comment: Corrected typos, added some remarks and explanations. To appear in J. Funct. Anal

We consider three related topics: (a) Holographic quantum field theories on AdS spaces. (b) Holographic interfaces of flat space QFTs. (c) Wormholes connecting generically different QFTs. We investigate in a concrete example how the related classical solutions explore the space of QFTs and we construct the general solutions that interpolate between the same or different CFTs with arbitrary couplings. The solution space contains many exotic RG flow solutions that realize unusual asymptotics, as boundaries of different regions in the space of solutions. We find phenomena like "walking" flows and the generation of extra boundaries via "flow fragmentation"., Comment: 97 pages, 52 figures

The structure of the five-dimensional Tachyon-Chern-Simons action and its relevance to single-baryon states in the context of the V-QCD models for holographic QCD with backreacting flavor are analyzed. The most general form of the Tachyon-Chern-Simons 5-form, compatible with symmetries and flavor anomalies is determined. It is the sum of a non-trivial gauge-invariant 5-dimensional form and a non-invariant closed 5-form that reproduces the flavor anomalies. Single-baryon solutions of the gravity theory, arising from the DBI plus Tachyon-Chern-Simons actions are considered. The baryon is realised as a bulk axial instanton. The baryon ansatz and the field equations are derived and the boundary conditions are determined, which ensure that the solution has finite boundary energy and unit baryon charge. The boundary baryon number, which is computed from the universal (closed) part of the Tachyon-Chern-Simons action, is shown to coincide with the bulk axial instanton number., Comment: 42 pages + Appendix, 2 figures, Accepted for publication in JHEP

We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the classical decay rates of partially dissipative systems satisfying the stability condition (SK) with a time-delay depending only on the velocity of each component and the size of the undamped region. To quantify this delay, we assume that the undamped region is a bounded space-interval and that the system without space-restriction on the dissipation satisfies the stability condition (SK). The former assumption ensures that the time spent by the characteristics of the system in the undamped region is finite and the latter that whenever the damping is active the solutions decay. Our approach consists in reformulating the system into n coupled transport equations and showing that the time-decay estimates are delayed by the sum of the times each characteristics spend in the undamped region.

Among the strategies to fight cancer, multi-therapeutic approaches are considered as a wise choice to put in place multiple weapons to suppress tumors. In this work, to combine chemotherapeutic effects to magnetic hyperthermia when using biocompatible scaffolds, we have established an electrospinning method to produce nanofibers of polycaprolactone loaded with magnetic nanoparticles as heat mediators to be selectively activated under alternating magnetic field and doxorubicin as a chemotherapeutic drug. Production of the fibers was investigated with iron oxide nanoparticles of peculiar cubic shape (at 15 and 23 nm in cube edges) as they provide benchmark heat performance under clinical magnetic hyperthermia conditions. With 23 nm nanocubes when included into the fibers, an arrangement in chains was obtained. This linear configuration of magnetic nanoparticles resemble that of the magnetosomes, produced by magnetotactic bacteria, and our magnetic fibers exhibited remarkable heating effects as the magnetosomes. Magnetic fiber scaffolds showed excellent biocompatibility on fibroblast cells when missing the chemotherapeutic agent and when not exposed to magnetic hyperthermia as shown by viability assays. On the contrary, the fibers containing both magnetic nanocubes and doxorubicin showed significant cytotoxic effects on cervical cancer cells following the exposure to magnetic hyperthermia. Notably, these tests were conducted at magnetic hyperthermia field conditions of clinical use. As here shown, on the doxorubicin sensitive cervical cancer cells, the combination of heat damage by magnetic hyperthermia with enhanced diffusion of doxorubicin at therapeutic temperature are responsible for a more effective oncotherapy., Comment: 10 pages, 7 figures

The International Fusion Materials Irradiation Facility (IFMIF), presently in its Engineering Validation and Engineering Design Activities (EVEDA) phase under the frame of the Broader Approach Agreement between Europe and Japan, accomplished in summer 2013, on schedule, its EDA phase with the release of the engineering design report of the IFMIF plant, which is here described. Many improvements of the design from former phases are implemented, particularly a reduction of beam losses and operational costs thanks to the superconducting accelerator concept, the re-location of the quench tank outside the test cell (TC) with a reduction of tritium inventory and a simplification on its replacement in case of failure, the separation of the irradiation modules from the shielding block gaining irradiation flexibility and enhancement of the remote handling equipment reliability and cost reduction, and the water cooling of the liner and biological shielding of the TC, enhancing the efficiency and economy of the related sub-systems. In addition, the maintenance strategy has been modified to allow a shorter yearly stop of the irradiation operations and a more careful management of the irradiated samples. The design of the IFMIF plant is intimately linked with the EVA phase carried out since the entry into force of IFMIF/EVEDA in June 2007.

We study strongly coupled ABJM theory on the 3-sphere with massive quenched flavor using the AdS/CFT correspondence. The holographic dual consists of type IIA supergravity with probe D6-branes. The flavor mass is a relevant deformation driving an RG flow whose IR endpoint is pure ABJM theory. At non-zero mass, we find that the theory on the 3-sphere exhibits a quantum phase transition at a critical value of the sphere radius. The transition corresponds to a topology change in the D6-brane embeddings whose dual interpretation is the meson-melting transition. We perform the holographic computation of the free energy on 3-sphere and we use it to construct various candidate F-functions. These were recently proposed in the context of Einstein-scalar gravity to interpolate monotonically between the values of the sphere free energies of the UV and IR CFTs. We find that while the F-functions of the flavored ABJM theory have the correct UV and IR limits, they are not monotonic. We surmise that the non-monotonicity is related to the presence of the phase transition., Comment: 52 pages, 9 figures, v3 includes three new references and small corrections, matches the published version

For $s \in (0,1)$ and a bounded open set $\Omega \subset \mathbb R^N$ with $N > 2s$, we study the fractional Brezis--Nirenberg type minimization problem of finding $$ S(a) := \inf \frac{\int_{\mathbb R^N} |(-\Delta)^{s/2} u|^2 + \int_\Omega a u^2}{\left( \int_\Omega u^\frac{2N}{N-2s} \right)^\frac{N-2s}{N}}, $$ where the infimum is taken over all functions $u \in H^s(\mathbb R^N)$ that vanish outside $\Omega$. The function $a$ is assumed to be critical in the sense of Hebey and Vaugon. For low dimensions $N \in (2s, 4s)$, we prove that the Robin function $\phi_a$ satisfies $\inf_{x \in \Omega} \phi_a(x) = 0$, which extends a result obtained by Druet for $s = 1$. In dimensions $N \in (8s/3, 4s)$, we then study the asymptotics of the fractional Brezis--Nirenberg energy $S(a + \varepsilon V)$ for some $V \in L^\infty(\Omega)$ as $\varepsilon \to 0+$. We give a precise description of the blow-up profile of (almost) minimizing sequences and characterize the concentration speed and the location of concentration points.