We prove the uniform solvability of a stationary problem associated to internal waves equation with small viscosity in a two dimensional aquarium with real-analytic boundary, under a Morse--Smale dynamical assumption. This is achieved by using complex deformations of the aquarium, on which the inviscid stationary internal wave operator is invertible.
Advanced tokamak scenarios often feature weak or reversed magnetic shear configurations. In this study, the hybrid kinetic-MHD model implemented in the NIMROD code is used to investigate the effects of reversed magnetic shear on internal kink and fishbone mode in a circular shaped limiter tokamak. In the absence of energetic particles (EPs), the mode growth rate initially increases and then decreases as the magnetic shear changes from positive to negative, indicating stabilizing effects of the reversed magnetic shear on the internal kink mode. In the presence of EPs, when the reversed magnetic shear region is sufficiently narrow, the transition from internal kink/fishbone modes to double kink/fishbone modes takes place, and the stabilizing effects of the reversed magnetic shear can significantly dominate the destabilization of EPs. For non-resonant modes, the EP beta fraction $β_f$ for excitation increases with $q_{min}$, concurrent with progressively lower growth rates in non-resonant fishbone modes. When the equilibrium profile has an internal transport barrier (ITB), broader ITB widths suppress internal kink modes more effectively, whereas steeper temperature gradients strengthen EP stabilization.
Paolo Campana. Andrea Giovannetti, Paolo Pin, Roberto Rozzi
In this work, we provide empirical evidence on organized criminal groups' (OCGs) behavior across the Liverpool area in the U.K. (Merseyside). We find that violent crimes concerning OCGs concentrate in the areas yielding the highest revenue, while OGCs primarily control areas yielding middle or low revenue. We explain and generalize these empirical observations with a theoretical model examining how OCGs strategically select which area to exploit based on expected revenue and the presence of other OCGs. We prove our results for three OCGs analytically and extend them to larger numbers of OCGs through numerical simulations. Both approaches suggest that, when the frequency of OCG activity is sufficiently high, each OCG controls one area, while the violence between OCGs remains low across all areas. When the frequency of OCG activity reduces, violent collisions between OCGs occur in the areas yielding the highest revenue, while some OCGs retain control over the medium-revenue areas. Our results suggest important policy recommendations. Firstly, if interventions are only violence-driven, they might miss critical underlying factors. Secondly, police operations might have unintended negative externalities in other areas of a city when they target criminal property rights, like increased violence in the areas yielding the highest revenue.
We define and study cartesian and cocartesian fibrations between categories internal to an $\infty$-topos and prove a straightening equivalence in this context.
In this paper, we present an impulse response identification scheme that incorporates the internal positivity side-information of the system. The realization theory of positive systems establishes specific criteria for the existence of a positive realization for a given transfer function. These transfer function criteria are translated to a set of suitable conditions on the shape and structure of the impulse responses of positive systems. Utilizing these conditions, the impulse response estimation problem is formulated as a constrained optimization in a reproducing kernel Hilbert space equipped with a stable kernel, and suitable constraints are imposed to encode the internal positivity side-information. The optimization problem is infinite-dimensional with an infinite number of constraints. An equivalent finite-dimensional convex optimization in the form of a convex quadratic program is derived. The resulting equivalent reformulation makes the proposed approach suitable for numerical simulation and practical implementation. A Monte Carlo numerical experiment evaluates the impact of incorporating the internal positivity side-information in the proposed identification scheme. The effectiveness of the proposed method is demonstrated using data from a heating system experiment.
We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collapse of the groupoid in an earlier work of the second author), and relating it to orthogonality, triviality of fibrations, the strong canonical base property, differential Galois theory, and GAGA. We prove that $\mathrm{DCF}_0$ does not have the strong canonical base property, correcting an earlier proof. We also prove that the theory $\mathrm{CCM}$ of compact complex manifolds does not have the strong CBP, and initiate a study of the definable Galois theory of projective bundles. In the rest of the paper we study definable fibrations in $\mathrm{DCF}_0$, where the general fibre is internal to the constants, including differential tangent bundles, and geometric linearizations. We obtain new examples of higher rank types orthogonal to the constants.
Starting with the results obtained in a previous paper in which classical local U(1) gauge invariance in terms of the electromagnetic field strenghts instead of the usual formulation mediated by the four potential was introduced it is shown that using the gauge freedom associated with the third component of the magnetic field, previously obtained spinor equations of motion describe the internal dynamics of a free 1/2 spin particle suggesting a kinematic origin of its rest mass and helicity. The controversial Zitterbewegung (trembling motion) appears in a natural way as internal motion with the velocity of light. Such an interpretation is in contrast with the usual quantum mechanical explanation of transitions between positive and negative energy states.
Product innovation is a risky activity, but when successful, it enables large software companies accrue high profits and leapfrog the competition. Internal startups have been promoted as one way to foster product innovation in large companies, which allows them to innovate as startups do. However, internal startups in large companies are challenging endeavours despite of the promised benefits. How large software companies can leverage internal startups in software product innovation is not fully understood due to the scarcity of the relevant studies. Based on a conceptual framework that combines the elements from the Lean startup approach and an internal corporate venturing model, we conducted a case study of a large software company to examine how a new product was developed through the internal startup effort and struggled to achieve the desired outcomes set by the management. As a result, the conceptual framework was further developed into a Lean startup-enabled new product development model for large software companies.
We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated with a fibration of pointed groupoids. Our generalization consists in replacing pointed groupoids with groupoids internal to a pointed regular category with reflexive coequalizers.
The dynamics of the Goldstino mode of spontaneously broken supersymmetry is universal, being fully determined by the non-linearly realized symmetry. We investigate the small-field limit of this theory. This model non-linearly realizes an alternative supersymmetry algebra with vanishing anti-commutators between the fermionic generators, much like an internal supersymmetry. This Goldstino theory is akin to the Galilean scalar field theory that arises as the small-field limit of Dirac-Born-Infeld theory and non-linearly realizes the Galilean symmetry. Indeed, the small-field Goldstino is the partner of a complex Galilean scalar field under conventional supersymmetry. We close with the generalization to extended internal supersymmetry and a discussion of its higher-dimensional origin.
In this chapter we summarize current knowledge of the internal structure of giant planets. We concentrate on the importance of heavy elements and their role in determining the planetary composition and internal structure, in planet formation, and during the planetary long-term evolution. We briefly discuss how internal structure models are derived, present the possible structures of the outer planets in the Solar System, and summarise giant planet formation and evolution. Finally, we introduce giant exoplanets and discuss how they can be used to better understand giant planets as a class of planetary objects.
The obliquity of the Galilean satellites is small but not yet observed. Studies of cycloidal lineaments and strike-slip fault patterns on Europa suggest that Europa's obliquity is about 1 deg, although theoretical models of the obliquity predict the obliquity to be one order of magnitude smaller for an entirely solid Europa. Here, we investigate the influence of a global liquid layer on the obliquity of the Galilean satellites. Io most likely has a fully liquid core, while Europa, Ganymede, and Callisto are thought to have an internal global liquid water ocean beneath an external ice shell. We use a model for the obliquity based on a Cassini state model extended to the presence of an internal liquid layer and the internal gravitational and pressure torques induced by the presence of this layer. We find that the obliquity of Io only weakly depends on the different internal structure models considered, because of the weak influence of the liquid core which is therefore almost impossible to detect through observations of the obliquity. The obliquity of Europa is almost constant in time and its mean value is smaller (0.033-0.044 deg) with an ocean than without (0.055 deg). An accuracy of 0.004 deg (about 100 m on the spin pole location at the surface) would allow detecting the internal ocean. The obliquity of Ganymede and Callisto depends more on their interior structure because of the possibility of resonant amplifications for some periodic terms of the solution. Their ocean may be easily detected if, at the measuring time, the actual internal structure model lead to a very different value of the obliquity than in the solid case. A long-term monitoring of their shell obliquity would be more helpful to infer information on the shell thickness.
In this paper, the chaotic internal degrees of freedom of a benzene molecule adsorbed on a graphite substrate, their interplay with thermal noise, and their effects on the diffusion and drift are investigated analytically by making use of the presence of two different time scales as well as by molecular-dynamics simulations. The effects of thermal noise are investigated, and it is found that noise does not significantly alter the dynamics of the internal degrees of freedom, yet affects the friction and diffusion of the center of mass. Qualitative and quantitative theoretical predictions for the friction and diffusion of the molecule on the substrate are made and are compared to molecular-dynamics simulations. Contributions to the friction and diffusion from the finite heat bath as well as the slow dynamics of the center of mass are formally identified. It is shown that the torsion in benzene, which dominates the nonlinear coupling, significantly affects the friction of the molecule on the surface. The results compare favorably with recent results from He/neutron spin echo experiments on this system. Based on the analytical and numerical results, some suggestions are made for experimental conditions under which the effects of internal degrees of freedom might be observable.
We consider mechanisms of directed transport in a ratchet model comprising, besides the external freedom where transport occurs, a chemical freedom that replaces the familiar external driving by an autonomous dynamics providing energy input, and an internal freedom representing a functional mode of a motor molecule. The dependence of the current on various parameters is studied in numerical simulations of our model. In particular, we point out the role of the internal freedom as a buffer between energy input and output of mechanical work that allows a temporary storage of injected energy and can contribute to the efficiency of current generation.
On the basis of the entropy of incomplete statistics (IS) and the joint probability factorization condition, two controversial problems existing in IS are investigated, where one is what the correct expression of the internal energy for a composite system is and the other is whether the zeroth law of thermodynamics is true or not. Some new equivalent expressions of the internal energy of a composite system are derived through a precise mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it can't be proven from theory. Finally, it is pointed out that the generalized zeroth law of thermodynamics and the expressions of the internal energy of a composite system derived in literature are incorrect, because two irrational assumptions have been implicitly introduced.
The paper analyses kinematics and dynamics of internal rotations with spin and their effects on the constitutive relations for uniaxial (nematic) liquids and for weakly elastic nematic solids. It is shown that neglecting the internal rotational inertia terms and effects of director gradient made the stress symmetric. This not only highly simplifies the theories but also allows calculating all the kinematic variables of internal rotations without any additional constants, other than those presented in the simplified theory with symmetric stress.
We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating CO oxidation on single crystal surfaces. This stochastic resonance arises directly from the elementary reaction steps of the system without any external input. The lattice gas model is investigated by means of Monte Carlo simulations. It shows oscillation phenomena and mesoscopic pattern formation. Stochastic resonance arises once homogeneous nucleation in the individual surface phases (reconstructed and non-reconstructed) is added. This nucleation is modelled as a noise process. As a result, synchronization of the kinetic oscillations is obtained. Internal stochastic resonance may thus be an internal regulation mechanism of extreme adaptability.
In this paper, I explain how gauge symmetry can be broken in a geometric way, à la Kaluza-Klein. In higher dimensional gravitational theories, one usually considers the extra dimensions to be ``frozen'' in time. However, the internal manifold is actually a dynamic entity. For example, its metric can change even if one expects its topological properties to be invariant. It is conceivable then, that at an earlier epoch the internal manifold made a geometric transition from say a maximally symmetric metric space to a less symmetric one. We know in a Kaluza-Klein reduction scheme, the massless gauge bosons are associated with the Killing vectors of the internal manifold. After the transition of the internal manifold, the gauge bosons associated with the broken Killing isometries will pick up a mass thereby breaking the gauge invariance partially. In this paper, I explore this idea, work out the mass of broken gauge bosons for some simple examples, and also point out how a mechanism similar to that of Higgs may be at work.