In this paper, we study the boundary null-controllability of the compressible Navier-Stokes equations linearized around a positive constant steady state in a bounded interval when the time is sufficiently large. The novelty of this work is that we consider only one Dirichlet boundary control at one end of the interval acting either on the density or velocity part of the concerned system, where the first-order couplings between transport and heat-type equations arise. Moreover, we establish that the null-controllability results are optimal/sharp concerning the regularity of initial states for the velocity case and with respect to time for the density case.The proofs of controllability results rely on a new parabolic-hyperbolic joint Ingham-type inequality, a mixed parabolic-hyperbolic moments method, and some complex analytic arguments. To this end, a careful spectral analysis of the associated non-self-adjoint operator is performed, which is involved due to the effect of boundary conditions.
We investigate lepton number violation (LNV) induced by Delta L 1/4 2 dimension-seven Standard Model effective field theory (SMEFT) operators in the context of same-sign muon colliders. Specifically, we study mu & thorn;mu & thorn; -> W & thorn;W & thorn;=W & thorn;qq0 production at the mu TRISTAN at ffiffisp 1/4 2 TeV with an integrated luminosity of 1 ab-1, using the final-state signature comprising two fat jets. This process is sensitive to eight distinct SMEFT operators, providing a unique avenue for testing LNV beyond the Standard Model. We determine the maximal sensitivity to these operators and compare our results with existing LHC constraints and future projections from the future circular collider. Our findings highlight the potential of same sign muon colliders to serve as powerful probes of LNV and new physics (NP) at the TeV scale.
We study three-dimensional gravity with negative cosmological constant under non-standard boundary conditions where chemical potentials are determined dynamically. Using a boundary Hamiltonian inspired by collective field theory (ColFT), the boundary dynamics reduce to those of a one-dimensional fluid on a circle, with configurations corresponding to bulk geometries such as BTZ black holes. Quantizing the system via bosonization of relativistic fermions, we obtain a microscopic description of black hole states in terms of Young diagrams, whose degeneracies match the Bekenstein-Hawking entropy. We compute the Euclidean canonical partition function and free energy for both the ColFT Hamiltonian and a relativistic free-fermion Hamiltonian. In the ColFT case, the partition function resembles that of chiral U(N) Yang-Mills theory on a torus, with N~1/(βG). This offers a novel way to compute quantum corrections to the partition function. The leading entropy term receives contributions from all genera, while the subleading logarithmic correction is one-loop exact, arising solely from the genus-one sector with coefficient -1/2 . This coefficient remains unchanged in the relativistic fermion case, suggesting the universality of the one-loop correction across different boundary Hamiltonians.
The strong visible photoluminescence (PL) in surface-oxidized nanostructured silicon emerges from the interplay between intrinsic Bloch states and oxide-related interfacial defects, making it difficult to isolate their role. Temperature-dependent (5-350 K) PL measurements on nanostructured silicon with varying crystallite sizes manifest three distinct decay mechanisms involving band-to-band, band-to-trap and trap-to-trap transitions to multiple emission bands appearing in the convoluted broad PL spectrum. At lower temperatures (less than or similar to 225 K), PL peak energy associated with the quantum-confined Bloch states exhibits a nearly linear blue shift, governed by a strong inverse power law dependence of the temperature coefficient on the effective crystallite size, while this trend reverses at higher temperatures. Conversely, the defect-related peak energies increase monotonically at a nearly constant rate throughout the experimental temperature range. A general analytical model for finite systems with a separable pseudo-potential effectively estimates the contributions from different decay channels to the PL emission. Theoretical results align well with the experimentally obtained values of the power-law exponents, offering a novel way to distinguish between the radiative recombination channels involving quantumconfined Bloch states and interfacial defects/trap states in nanostructured silicon.
We study a minimal type-I seesaw framework in which a first-order phase transition, driven by a singlet scalar phi, produces right-handed neutrinos (RHNs) through bubble collisions, realizing a cosmic-scale collider that probes ultrahigh energy scales. The resulting inhomogeneous RHN distribution sources a novel low-frequency gravitational-wave (GW) signal in addition to the standard bubble-collision contribution. A stable lightest RHN can account for the observed dark-matter (DM) relic abundance for masses as low as M1 = mDM >= 106 GeV, with the associated novel GW signal accessible in the Laser Interferometer Space Antenna, Einstein Telescope (ET), and upcoming LIGO-Virgo-KAGRA (LVK) detectors. If the RHNs are unstable, their CP-violating decays generate the baryon asymmetry via leptogenesis for M1 >= 1011 GeV and phase transition temperatures T* >= 106 GeV, yielding the novel GW signatures within the reach of ET, Big Bang Observer (BBO), and upcoming LVK detectors. Part of the parameter space is already constrained by the LVK O(3) data. If RHN decays populate a dark sector fermion chi with mass m chi is an element of [10-4; 104] GeV, successful cogenesis of baryons and asymmetric dark matter is achieved for T* >= 107 GeV and M1 >= 109 GeV, naturally explaining Omega DM similar or equal to 5 Omega B. The corresponding GW signals are testable with Laser Interferometer Space Antenna, ET, and BBO. Finally, we analyze a UV-complete multi-Majoron model based on a global U(1)N & times; U(1)B-L extension of Standard Model, motivated from the hierarchy of lepton masses, in which a distinctive GW signature associated with a cosmic Majoron collider arises from scalar production during U(1)N symmetry breaking, detectable by BBO, ET, and upcoming LVK. Successful leptogenesis is realized for the heaviest RHN mass M3 similar to 1010 GeV and a U(1)N breaking vacuum expectation value v2 similar to O(TeV) that sets the seesaw scale.
