We study long-time dynamics of small even perturbations of the soliton in 1D quadratic Klein-Gordon equation. The soliton possesses both an internal mode and the unstable mode. On a codimension-one manifold of fine-tuned initial data the instability is suppressed and the internal mode decays slowly by transferring energy into the continuum. We show that this decay and the associated nonlinear frequency shift are accurately captured by a cubic resonant approximation, with the damping rate determined by a Fermi golde rule-type coefficient. This provides a quantitative description of irreversible energy transfer from the internal mode to dispersive radiation.
The program of internal type theory seeks to develop the categorical model theory of dependent type theory using the language of dependent type theory itself. In the present work we study internal homotopical type theory by relaxing the notion of a category with families (cwf) to that of a wild, or precoherent higher cwf, and determine coherence conditions that suffice to recover properties expected of models of dependent type theory. The result is a definition of a split 2-coherent wild cwf, which admits as instances both the syntax and the "standard model" given by a universe type. This will allow us to give a straightforward internalization of the notion of a 2-coherent reflection of homotopical type theory in itself: namely as a 2-coherent wild cwf morphism from the syntax to the standard model. Our theory also easily specializes to give definitions of "low-dimensional" higher cwfs, and conjecturally includes the container higher model as a further instance.
Reinforcement learning has emerged as a powerful paradigm for post-training large language models (LLMs) to improve reasoning. Approaches like Reinforcement Learning from Human Feedback (RLHF) and Reinforcement Learning with Verifiable Rewards (RLVR) have shown strong results, but they require extensive external supervision. We investigate an alternative class of methods, Reinforcement Learning from Internal Feedback (RLIF), which relies solely on intrinsic model-derived signals instead of external rewards. In particular, we leverage unsupervised reward proxies such as token-level entropy, trajectory-level entropy, and self-certainty. Our theoretical analysis shows these internal objectives are partially equivalent, and we empirically evaluate various RLIF strategies on challenging math reasoning benchmarks. Experimental results demonstrate that RLIF can boost the reasoning performance of base LLMs at the beginning phase of the training, matching or surpassing RLVR techniques on these tasks. However, when training progresses, performance degrades even below the model before training. Moreover, we find that RLIF yields little improvement for instruction-tuned models, indicating diminishing returns of intrinsic feedback once an LLM is already instruction-tuned. We further analyze this limitation by mixing model weights and explain the reason of RLIF's training behaviors, providing practical guidelines for integrating internal feedback signals into LLM training. We hope our analysis of internal feedback will inform more principled and effective strategies for LLM post-training.
Recurring auctions are ubiquitous for selling durable assets like artworks and homes, with follow-up auctions held for unsold items. We investigate such auctions theoretically and empirically. Theoretical analysis demonstrates that recurring auctions outperform single-round auctions when buyers face entry costs, enhancing efficiency and revenue due to sorted entry of potential buyers. Optimal reserve price sequences are characterized. Empirical findings from home foreclosure auctions in China reveal significant annual gains in efficiency (3.40 billion USD, 16.60%) and revenue (2.97 billion USD, 15.92%) using recurring auctions compared to single-round auctions. Implementing optimal reserve prices can further improve efficiency (3.35%) and revenue (3.06%).
The present work studies the gravitational radiation of a non abelian vortex with a non compact internal moduli describing its excitations. This situation may be realised by semi-local supersymmetric vortices \cite{novedad1}-\cite{reviewshifman}, although supersymmetry is not necessary for this to happen. In the situation considered along this work, the internal space has infinite volume, and a largely energetic perturbation propagates along the object, even though the vortex line may not be moving. A specific configuration is presented, in which the internal space is the resolved conifold with its Ricci flat metric. The curious feature about it is that it corresponds to a static vortex, that is, the perturbation is only due to the internal modes. Even being static, the emission of gravitational radiation is in the present case of considerable order. This suggest that the presence of slowly moving objects that can emit a large amount of gravitational radiation is a hint of non abelianity.
The article reflects the author's point of view on the disasters that occurred with American atomic submarines Thresher and Scorpion in 1960th and Indonesian diesel submarine Nanggala-420 in April 2021. A possible role of giant internal waves in such tragic events is discussed. Parameters of large-amplitude internal solitary waves, their shapes and speeds of propagation are presented. The author's reconstruction of the disasters is given.
In recent electron-positron angular correlation measurements the observed significant enhancements relative to the internal pair creation at large angles was interpreted as indication of the creation of $J^{π}=1^{+}$ boson called X17 particle. In this paper it is brought up that such enhancements can be generated by higher order processes. It is found that nuclear transitions, the transition energy of which is significantly lower than the whole transition energy, can cause peaked angle dependence in electron-positron angular correlation.
We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, 2D parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics,emphasize the role of boundary conditions and reveal the phase shifting in the transversal direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.
This study employs an improved volume of fluid method and adaptive mesh refinement algorithm to numerically investigate the internal jet-like mixing upon the coalescence of two initially stationary droplets of unequal sizes. The emergence of the internal jet is attributed to the formation of a main vortex ring, as the jet-like structure shows a strong correlation with the main vortex ring inside the merged droplet. By tracking the evolution of the main vortex ring together with its circulation, we identified two mechanisms that are essential to the internal-jet formation: the vortex-ring growth and the vortex-ring detachment. Recognizing that the manifestation of the vortex-ring-induced jet physically relies on the competition between the convection and viscous dissipation of the vortex ring, we further developed and substantiated a vortex-ring-based Reynolds number criterion to interpret the occurrence of the internal jet at various Ohnesorge numbers and size ratios. For the merged droplet with apparent jet formation, the average mixing rate after jet formation increases monotonically with the vortex-ring Reynolds number, which therefore serves as an approximate measure of the jet strength. In this respect, stronger internal jet is responsible for enhanced mixing of the merged droplet.
This work is devoted to prove the pointwise controllability of the Bernoulli-Euler beam equation. It is obtained as a limit of internal controllability of the same type of equation.
The agreement between the fragments' internal and kinetic temperatures with the breakup temperature is investigated using a Statistical Multifragmentation Model which makes no a priori as- sumption on the relationship between them. We thus examine the conditions for obtaining such agreement and find that, in the framework of our model, this holds only in a relatively narrow range of excitation energy. The role played by the qualitative shape of the fragments' state densities is also examined. Our results suggest that the internal temperature of the light fragments may be affected by this quantity, whose behavior may lead to constant internal temperatures over a wide excitation energy range. It thus suggests that the nuclear thermometry may provide valuable information on the nuclear state density.
Jean-Baptiste Minne, Lionel Desgranges, Virgil Optasanu
et al.
In PWR, the Zircaloy based clad is the first safety barrier of the fuel rod, it must prevent the dispersion of the radioactive elements, which are formed by fission inside the UO2 pellets filling the clad. We focus here on internal corrosion that occurs when the clad is in tight contact with the UO2 pellet. In this situation, with temperature of 400^{\circ}C on the internal surface of the clad, a layer of oxidised Zircaloy is formed with a thickness ranging from 5 to 15 $μ$m. In this paper, we will underline the specific behaviour of this internal corrosion layer compared to wet corrosion of Zircaloy. Simulations will underline the differences of stress field and their influences on corresponding dissolved oxygen profiles. The reasons for these differences will be discussed as function of the mechanical state at inner surface of the clad which is highly compressed. Differences between mechanical conditions generated by an inner or outer corrosion of the clad are studied and their influences on the diffusion phenomena are highlighted.
Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter
et al.
We consider several types of internal queries, that is, questions about fragments of a given text $T$ specified in constant space by their locations in $T$. Our main result is an optimal data structure for Internal Pattern Matching (IPM) queries which, given two fragments $x$ and $y$, ask for a representation of all fragments contained in $y$ and matching $x$ exactly; this problem can be viewed as an internal version of the Exact Pattern Matching problem. Our data structure answers IPM queries in time proportional to the quotient $|y|/|x|$ of fragments' lengths, which is required due to the information content of the output. If $T$ is a text of length $n$ over an integer alphabet of size $σ$, then our data structure occupies $O(n/ \log_σn)$ machine words (that is, $O(n\log σ)$ bits) and admits an $O(n/ \log_σn)$-time construction algorithm. We show the applicability of IPM queries for answering internal queries corresponding to other classic string processing problems. Among others, we derive optimal data structures reporting the periods of a fragment and testing the cyclic equivalence of two fragments. IPM queries have already found numerous further applications, following the path paved by the classic Longest Common Extension (LCE) queries of Landau and Vishkin (JCSS, 1988). In particular, IPM queries have been implemented in grammar-compressed and dynamic settings and, along with LCE queries, constitute elementary operations of the PILLAR model, developed by Charalampopoulos, Kociumaka, and Wellnitz (FOCS 2020). On the way to our main result, we provide a novel construction of string synchronizing sets of Kempa and Kociumaka (STOC 2019). Our method, based on a new restricted version of the recompression technique of Jeż (J. ACM, 2016), yields a hierarchy of $O(\log n)$ string synchronizing sets covering the whole spectrum of fragments' lengths.