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1. On the propulsion of a rigid body in a viscous liquid under the action of a time-periodic force

   https://doi.org/10.1007/s40687-025-00510-0  

   Galdi, Giovanni P; Karakouzian, Mher M (June 2025, Research in the Mathematical Sciences)

   Arigid body B moves in an otherwise quiescent viscous liquid filling the whole space outside B, under the action of a time-periodic force f of period T applied to a given point of B and of fixed direction. We assume that the average of f over an interval of length T does not vanish, and that the amplitude, δ,off is sufficiently small. Our goal is to investigate when B executes a nonzero net motion; that is, B is able to cover any prescribed distance in a finite time. We show that, at the order δ, this happens if and only if f and B satisfy a certain condition. We also show that this is always the case if B is prevented from spinning. Finally, we provide explicit examples where the condition above is satisfied or not. All our analysis is performed in a general class of weak solutions to the coupled system body-liquid problem. 

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2. Calculating QCD Phase Diagram Trajectories of Nuclear Collisions using a Semi-analytical Model

   https://doi.org/10.1051/epjconf/202327601012  

   Mendenhall, Todd; Lin, Zi-Wei (January 2023, EPJ Web of Conferences)

   Kim, Y.; Moon, D.H. (Ed.)

   At low to moderate collision energies where the parton formation time τ F is not small compared to the nuclear crossing time, the finite nuclear thickness significantly affects the energy density ϵ( t ) and net conserved-charge densities such as the net-baryon density n B ( t ) produced in heavy ion collisions. As a result, at low to moderate energies the trajectory in the QCD phase diagram is also affected by the finite nuclear thickness. Here, we first discuss our semi-analytical model and its results on ϵ( f ), n R ( t ), n Q ( t ), and n s ( t ) in central Au+Au collisions. We then compare the T ( t ), μ B ( t ), μ Q ( t ), and μ S ( t ) extracted with the ideal gas equation of state (EoS) with quantum statistics to those extracted with a lattice QCD-based EoS. We also compare the T -μ B trajectories with the RHIC chemical freezeout data. Finally, we discuss the effect of transverse flow on the trajectories. 

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3. No evidence for pericardial restraint in the snapping turtle ( Chelydra serpentina ) following pharmacologically induced bradycardia at rest or during exercise

   https://doi.org/10.1152/ajpregu.00004.2022  

   Smith, Brandt; Crossley, Dane A.; Wang, Tobias; Joyce, William (May 2022, American Journal of Physiology-Regulatory, Integrative and Comparative Physiology)

   Most animals elevate cardiac output during exercise through a rise in heart rate ( f H ), whereas stroke volume (V S ) remains relatively unchanged. Cardiac pacing reveals that elevating f H alone does not alter cardiac output, which is instead largely regulated by the peripheral vasculature. In terms of myocardial oxygen demand, an increase in f H is more costly than that which would incur if V S instead were to increase. We hypothesized that f H must increase because any substantial rise in V S would be constrained by the pericardium. To investigate this hypothesis, we explored the effects of pharmacologically induced bradycardia, with ivabradine treatment, on V S at rest and during exercise in the common snapping turtle ( Chelydra serpentina) with intact or opened pericardium. We first showed that, in isolated myocardial preparations, ivabradine exerted a pronounced positive inotropic effect on atrial tissue but only minor effects on ventricle. Ivabradine reduced f H in vivo, such that exercise tachycardia was attenuated. Pulmonary and systemic V S rose in response to ivabradine. The rise in pulmonary V S largely compensated for the bradycardia at rest, leaving total pulmonary flow unchanged by ivabradine, although ivabradine reduced pulmonary blood flow during swimming (exercise × ivabradine interaction, P < 0.05). Although systemic V S increased, systemic blood flow was reduced by ivabradine both at rest and during exercise, despite ivabradine’s potential to increase cardiac contractility. Opening the pericardium had no effect on f H , V S , or blood flows before or after ivabradine, indicating that the pericardium does not constrain VS in turtles, even during pharmacologically induced bradycardia. 

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4. A model of d -wave superconductivity, antiferromagnetism, and charge order on the square lattice

   https://doi.org/10.1073/pnas.2302701120  

   Christos, Maine; Luo, Zhu-Xi; Shackleton, Henry; Zhang, Ya-Hui; Scheurer, Mathias_S; Sachdev, Subir (May 2023, Proceedings of the National Academy of Sciences)

   We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory ofN_f= 2 massless Dirac fermions carrying fundamental gauge charges—this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice withπ-flux per plaquette in the ℤ₂center of SU(2). This theory has an emergent SO(5)_fglobal symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsionUat half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving inπℤ₂-flux. At half-filling, the low-energy theory of the Higgs sector hasN_b= 2 relativistic bosons with a possible emergent SO(5)_bglobal symmetry describing rotations between ad-wave superconductor, period-2 charge stripes, and the time-reversal breaking “d-density wave” state. We propose a conformal SU(2) gauge theory withN_f= 2 fundamental fermions,N_b= 2 fundamental bosons, and a SO(5)_f×SO(5)_bglobal symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)_fand a confining state which breaks SO(5)_b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order andd-wave superconductivity. A similar theory applies at nonzero doping and largeU, with longer-range couplings of the chargons leading to charge order with longer periods. 

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5. Stability of a Subcritical Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

   https://doi.org/10.1287/stsy.2019.0058  

   Fu, Yingjia; Williams, Ruth J. (September 2020, Stochastic Systems)

   null (Ed.)

   This work concerns the asymptotic behavior of solutions to a (strictly) subcritical fluid model for a data communication network, where file sizes are generally distributed and the network operates under a fair bandwidth-sharing policy. Here we consider fair bandwidth-sharing policies that are a slight generalization of the [Formula: see text]-fair policies introduced by Mo and Walrand [Mo J, Walrand J (2000) Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networks 8(5):556–567.]. Since the year 2000, it has been a standing problem to prove stability of the data communications network model of Massoulié and Roberts [Massoulié L, Roberts J (2000) Bandwidth sharing and admission control for elastic traffic. Telecommunication Systems 15(1):185–201.], with general file sizes and operating under fair bandwidth sharing policies, when the offered load is less than capacity (subcritical conditions). A crucial step in an approach to this problem is to prove stability of subcritical fluid model solutions. In 2012, Paganini et al. [Paganini F, Tang A, Ferragut A, Andrew LLH (2012) Network stability under alpha fair bandwidth allocation with general file size distribution. IEEE Trans. Automatic Control 57(3):579–591.] introduced a Lyapunov function for this purpose and gave an argument, assuming that fluid model solutions are sufficiently smooth in time and space that they are strong solutions of a partial differential equation and assuming that no fluid level on any route touches zero before all route levels reach zero. The aim of the current paper is to prove stability of the subcritical fluid model without these strong assumptions. Starting with a slight generalization of the Lyapunov function proposed by Paganini et al., assuming that each component of the initial state of a measure-valued fluid model solution, as well as the file size distributions, have no atoms and have finite first moments, we prove absolute continuity in time of the composition of the Lyapunov function with any subcritical fluid model solution and describe the associated density. We use this to prove that the Lyapunov function composed with such a subcritical fluid model solution converges to zero as time goes to infinity. This implies that each component of the measure-valued fluid model solution converges vaguely on [Formula: see text] to the zero measure as time goes to infinity. Under the further assumption that the file size distributions have finite pth moments for some p > 1 and that each component of the initial state of the fluid model solution has finite pth moment, it is proved that the fluid model solution reaches the measure with all components equal to the zero measure in finite time and that the time to reach this zero state has a uniform bound for all fluid model solutions having a uniform bound on the initial total mass and the pth moment of each component of the initial state. In contrast to the analysis of Paganini et al., we do not need their strong smoothness assumptions on fluid model solutions and we rigorously treat the realistic, but singular situation, where the fluid level on some routes becomes zero, whereas other route levels remain positive. 

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