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Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an infinite rooted directed $k$-ary tree, where we place $k^\ell$ chips on the root for some positive integer $\ell$, and we say a vertex $v$ can fire if it has at least $k$ chips. A vertex fires by dispersing one chip to each out-neighbor. Once every vertex has less than $k$ chips, we reach a stable configuration since no vertex can fire. We determine the exact number and properties of the possible stable configurations of chips in the setting where chips are distinguishable., Comment: 21 pages, 6 Figures

Chip-firing is a combinatorial game played on an undirected graph in which we place chips on vertices. We study chip-firing on an infinite binary tree in which we add a self-loop to the root to ensure each vertex has degree 3. A vertex can fire if the number of chips placed on it is at least its degree. In our case, a vertex can fire if it has at least 3 chips, and it fires by dispersing $1$ chip to each neighbor. Motivated by a 2023 paper by Musiker and Nguyen on this setting of chip-firing, we give an upper bound for the number of stable configurations when we place $2^\ell - 1$ labeled chips at the root. When starting with $N$ chips at the root where $N$ is a positive integer, we determine the number of times each vertex fires when $N$ is not necessarily of the form $2^\ell - 1$. We also calculate the total number of fires in this case., Comment: 24 pages, 8 figures

Nearly constant mean angular momentum profiles are widely observed in curved turbulent flows, including the bulk region of Taylor--Couette (TC) flows, where the inner and outer cylinders have weakly counter-rotating and co-rotating conditions. For high-Reynolds-number TC flows under these conditions, both the bulk and boundary layers become turbulent without Taylor rolls, referred to as the featureless ultimate regime (UR). In this study, we examine Reynolds-averaged Navier--Stokes (RANS) models to predict the nearly constant mean angular velocity as a one-dimensional problem in the featureless UR of TC turbulence. High-Reynolds-number experiments of TC turbulence are performed for reference, where the radius ratio is $\eta = r_\mathrm{in}/r_\mathrm{out} = 0.732$ and angular velocity ratio $a = -\omega_\mathrm{out}/\omega_\mathrm{in}$ is in the range $-0.5 \le a \le 0.1$. Verification of the RANS model using the algebraic Reynolds stress model (ARSM) suggests that convection of the Reynolds stress is essential for predicting the angular momentum profile. We introduce the Jaumann derivative as a covariant time derivative to develop ARSMs that incorporate the convection effect in a covariant manner. The proposed ARSM using the Jaumann derivative of the term composed of the strain and vorticity tensors successfully predicts the nearly constant mean angular momentum for a wide range of angular velocity ratios in the co-rotating case. The modelling approach incorporating time-derivative terms is a candidate for expressing curvature effects while satisfying the covariance of the Reynolds stress tensor., Comment: 27 pages, 8 figures

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional space while preserving important relationships. TopoMap is another technique that excels at preserving the underlying structure of the data, leading to interpretable visualizations. In particular, TopoMap maps the high-dimensional data into a visual space, guaranteeing that the 0-dimensional persistence diagram of the Rips filtration of the visual space matches the one from the high-dimensional data. However, the original TopoMap algorithm can be slow and its layout can be too sparse for large and complex datasets. In this paper, we propose three improvements to TopoMap: 1) a more space-efficient layout, 2) a significantly faster implementation, and 3) a novel TreeMap-based representation that makes use of the topological hierarchy to aid the exploration of the projections. These advancements make TopoMap, now referred to as TopoMap++, a more powerful tool for visualizing high-dimensional data which we demonstrate through different use case scenarios., Comment: This is the author's version of the article that has been accepted for publication in IEEE Transactions on Visualization and Computer Graphics (TVCG)

In transition-metal compounds, the transition-metal d electrons play an important role in their physical properties; however, the effects of the electron correlation between the ligand p electrons have not been clear yet. In this Letter, the Ru 4d and O 2p partial density of states (PDOS) in transition-metal oxide SrRuO$_3$ involving Weyl fermions are investigated by resonant photoemission spectroscopy. The observations demonstrate that the O 2p PDOS is distorted from that predicted by first-principles calculations than the Ru 4d PDOS. The results indicate that the electron correlation in the ligand orbitals will be important to understand the electronic structure of the p-d hybridized state in strongly correlated electron systems, even with topological states., Comment: 24 pages, 7 figures

NanoTerasu, a new 3 GeV synchrotron light source in Japan, began user operation in April 2024. It provides high-brilliance soft to tender X-rays and covers a wide spectral range from ultraviolet to tender X-rays. Its compact storage ring with a circumference of 349 m is based on a four-bend achromat lattice to provide two straight sections in each cell for insertion devices with a natural horizontal emittance of 1.14 nm rad, which is small enough for soft X-rays users. The NanoTerasu accelerator incorporates several innovative technologies, including a full-energy injector C-band linear accelerator with a length of 110 m, an in-vacuum off-axis injection system, a four-bend achromat with B-Q combined bending magnets, and a TM020 mode accelerating cavity with built-in higher-order-mode dampers in the storage ring. This paper presents the accelerator machine commissioning over a half-year period and our model-consistent ring optics correction. The first user operation with a stored beam current of 160 mA is also reported. We summarize the storage ring parameters obtained from the commissioning. This is helpful for estimating the effective optical properties of synchrotron radiation at NanoTerasu., Comment: 30 pages, 24 figures, submitted to the journal

Assuming static and spherically symmetric stars with perfect fluid matter, we used realistic equations of state to study neutron stars in covariant $f(Q)$ gravity. The structure profiles and properties of neutron stars such as mass, radius and compactness are obtained through numerical methods using quadratic, exponential, and logarithmic $f(Q)$ models. The results indicate that nonmetricity affects the interior profile deviations of the star, which in turn influence the properties of stars, as illustrated in the mass-radius relation diagram. This effect allows the star to accommodate either more or less matter compared to GR, resulting in a different total mass. For the quadratic model, we cannot generate larger masses, whereas the other two models can give consistent results for both smaller and larger masses of the observed stars. By tuning model parameters, we obtain $\mathcal{M}-\mathcal{R}$ diagrams that are compatible with observational constraints from NICER and LIGO., Comment: 29 pages, 36 figures

Non-thermal fermionic particle production is investigated in Einstein-Cartan modified gravity with a modified Holst term and non-minimal couplings between the spin connection and a fermion. By using the auxiliary field method, the theory is rewritten into a pseudoscalar-tensor theory with Einstein-Hilbert action and canonical kinetic and potential terms for a pseudoscalar field. The introduced field is called Einstein-Cartan pseudoscalaron. If the potential energy of the Einstein-Cartan pseudoscalaron dominates the energy density of the early universe, it causes inflationary expansion. After the end of inflation, the pseudoscalaron develops a large value and the non-minimal couplings destabilize the vacuum. Evaluating the non-thermal fermionic particle production process, we obtain the mass and the helicity dependences of the produced particle number density. We show the model parameters to enhance the preheating and reheating processes., Comment: 13 pages, 9 figures

The nonlinear massive plane wave solution of the classical scalar field in the Higgs potential is revisited to study the mass generation and particle creation. In particular, by assuming that the Higgs system is in the slightly excited state in early universe and it is described by the nonlinear solution, we study the mass generation mechanism for massive vector bosons and a heavy fermion in the quantum field theory around the nonlinear massive classical field. The nonlinear massive classical solution gives the transition from the vacuum to a pair of vector bosons and fermions. We present the new formulae of the probability density of the production process for particles in the standard model of elementary particle physics. The probability densities of the particle productions vanish when the nonlinear massive solution reduces to the constant solution (the classical vacuum expectation value); while the probability densities are expressed as the function of the free parameter in the classical solution in general case. We discuss the behavior of the probability densities for the three oscillating modes in the classical solution., Comment: 19 pages, 10 figures

Gauge theory compactified on an orbifold is defined by gauge symmetry, matter contents, and boundary conditions. There are equivalence classes (ECs), each of which consists of physically equivalent boundary conditions. We propose the powerful necessary conditions, trace conservation laws (TCLs), which achieve a sufficient classification of ECs in U(N) and SU(N) gauge theories on $T^2/Z_m$ orbifolds $(m=2,3,4,6)$. The TCLs yield the equivalent relations between the diagonal boundary conditions without relying on an explicit form of gauge transformations. The TCLs also show the existence of off-diagonal ECs, which consist only of off-diagonal matrices, on $T^2/Z_4$ and $T^2/Z_6$. After the sufficient classification, the exact numbers of ECs are obtained., Comment: 32 pages, 2 figures

New measurements of photofission and photoneutron reactions on $^{238}$U and $^{232}$Th in the Giant Dipole Resonance (GDR) energy region have been performed at the laser Compton-scattering $\gamma$-ray source of the NewSUBARU synchrotron radiation facility using a high-and-flat efficiency moderated $^3$He detection array. The neutron-multiplicity sorting of high-multiplicity fission neutron coincidence events has been performed using a dedicated energy dependent, multiple firing statistical treatment. The photoneutron $(\gamma,\,in)$ with $i$~=~1~--~3 and photofission $(\gamma,\,F)$ reactions have been discriminated by considering a Gaussian distribution of prompt-fission-neutron (PFN) multiplicities predicted by the theory of evaporation in sequential neutron emission from excited fission fragments. We report experimental $(\gamma,\,n)$, $(\gamma,\,2n)$, $(\gamma,\,3n)$ and $(\gamma,\,F)$ cross sections, average energies of PFNs and of $(\gamma,\,in)$ photoneutrons, as well as the mean number of PFNs per fission act and the width of the PFNs multiplicity distribution. Based on these primary experimental results and combined with reasonable assumptions, we extract also the first- and second-chance fission contributions. The new experimental results are compared with statistical-model calculations performed with the EMPIRE-3.2 Malta and TALYS-1.964 codes on the present data and with prompt fission emission calculations obtained with the Los Alamos model in the frame of the most probable fragmentation approach with and without sequential emission.

In five- and six-dimensional $U(N)$ and $SU(N)$ gauge theories compactified on $S^1/Z_2$ and $T^2/Z_3$ orbifolds, we propose a new method to classify the equivalence classes (ECs) of boundary conditions (BCs) wihtout depending on the structure of gauge transformations. Some of the BCs are connected through gauge transformations and constitute ECs, each of which contains physically equivalent BCs. Previous methods for classifying ECs have been used specific gauge transformations. In this paper, we show that a geometric property of orbifolds significantly narrows down the possibilities of connecting BCs and completes the classification of ECs., Comment: 22 pages, 2 figures

We investigate the quintessential inflation in the logarithmic Cartan $F(R)$ gravity. A small logarithmic modification of the general relativity has the potential to introduce both inflation and dark energy. We evaluate the time evolution of the Universe such as inflation, reheating, and dark energy. The parameters in the model are fixed to introduce the inflation and the dark energy scales. We show that the CMB fluctuations induced by the inflation are consistent with the current observations. In the reheating process, it is possible to achieve the reheating temperature required for nucleosynthesis in Big Bang scenario. It can be seen that by choosing an appropriate value for the scalaron field after reheating, the scalaron field again dominates the energy of the Universe and causes the current accelerating expansion as dark energy., Comment: 16pages, 13figures

A singular foliation $\mathcal{F}$ on a complete Riemannian manifold $M$ is called Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g., the partition of $M$ into orbits of an isometric action. In this paper, we investigate variational problems in compact Riemannian manifolds equipped with SRF with special properties, e.g. isoparametric foliations, SRF on fibers bundles with Sasaki metric, and orbit-like foliations. More precisely, we prove two results analogous to Palais' Principle of Symmetric Criticality, one is a general principle for $\mathcal{F}$ symmetric operators on the Hilbert space $W^{1,2}(M)$, the other one is for $\mathcal{F}$ symmetric integral operators on the Banach spaces $W^{1,p}(M)$. These results together with a $\mathcal{F}$ version of Rellich Kondrachov Hebey Vaugon Embedding Theorem allow us to circumvent difficulties with Sobolev's critical exponents when considering applications of Calculus of Variations to find solutions to PDEs. To exemplify this we prove the existence of weak solutions to a class of variational problems which includes $p$-Kirschoff problems., Comment: 54 pages

We probe the magnetic field-induced Tomonaga-Luttinger liquid (TLL) state in the bond-alternating spin-$1/2$ antiferromagnetic (AFM) chain compound NaVOPO$_4$ using thermodynamic as well as local $\mu$SR and $^{31}$P NMR probes down to milli-K temperatures in magnetic fields up to 14~T. The $\mu$SR and NMR relaxation rates in the gapless TLL regime decay slowly following characteristic power-law behaviour, enabling us to directly determine the interaction parameter $K$ as a function of the magnetic field. These estimates are cross-checked using magnetization and specific heat data. The field-dependent $K$ lies in the range of $0.4 < K < 1$ and indicates repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders NaVOPO$_4$ the first experimental realization of TLL with repulsive fermionic interactions in hitherto studied $S=1/2$ bond-alternating AFM-AFM chain compounds., Comment: 7 pages, 2 figures, 47 references

A magnetic phase diagram of the non-Heisenberg Tsai-type 1/1 Au-Ga-Tb approximant crystal (AC) has been established across a wide electron-per-atom (e/a) range via magnetization and powder neutron diffraction measurements. The diagram revealed exotic ferromagnetic (FM) and antiferromagnetic (AFM) orders that originate from the unique local spin icosahedron common to icosahedral quasicrystals (iQCs) and ACs; The noncoplanar whirling AFM order is stabilized as the ground state at the e/a of 1.72 or less whereas a noncoplanar whirling FM order was found at the larger e/a of 1.80, with magnetic moments tangential to the Tb icosahedron in both cases. Moreover, the FM/AFM phase selection rule was unveiled in terms of the nearest neighbour (J1) and next nearest neighbour (J2) interactions by numerical calculations on a non-Heisenberg single icosahedron. The present findings will pave the way for understanding the intriguing magnetic orders of not only non-Heisenberg FM/AFM ACs but also non-Heisenberg FM/AFM iQCs, the latter of which are yet to be discovered.

Diamond-type structure allotrope {\alpha}-Sn is attracting much attention as a topological Dirac semimetal (TDS). In this study, we demonstrate that {\alpha}-Sn undergoes a phase transition to another allotrope {\beta}-Sn with superconductivity at low temperature by irradiating with a focused Ga ion beam (FIB). To clarify the transition mechanism, we performed X-ray photoemission spectroscopy (XPS) measurements on an {\alpha}-Sn thin film irradiated with FIB and an as-grown {\alpha}-Sn thin film. The XPS results suggest that the local annealing, which is one of the side effects of FIB, causes the transformation from {\alpha}-Sn into {\beta}-Sn. Furthermore, the difference in the chemical states between {\alpha}-Sn and {\beta}-Sn can be quantitatively explained by the crystal structures rather than the degree of metallicity reflecting the conductivity. These results propose a new way of fabricating TDS/superconductor in-plane heterostructures based on {\alpha}-Sn and {\beta}-Sn., Comment: 18 pages, 5 figures