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This paper is concerned with an analysis of the near-tip region of a fluid-driven fracture propagating in a permeable saturated rock. The analysis is carried out by considering the stationary problem of a semi-infinite fracture moving at constant speed V. Two basic dissipative processes are taken into account: fracturing of the rock and viscous flow in the fracture, and two fluid balance mechanisms are considered – leak-off and storage of the fracturing fluid in the fracture. It is shown that the solution is characterized by a multiscale singular behaviour at the tip, and that the nature of the dominant singularity depends both on the relative importance of the dissipative processes and on the scale of reference. This solution provides a framework to understand the interaction of representative physical processes near the fracture tip, as well as to track the changing nature of the dominant tip process(es) with the tip velocity and its impact on the global fracture response. Furthermore, it gives a universal scaling of the near-tip processes on the scale of the entire fracture and sets the foundation for developing efficient numerical algorithms relying on accurate modelling of the tip region.

Abstract The Aerogel Ring Imaging Cherenkov (ARICH) counter serves as a particle identification device in the forward end-cap region of the Belle II spectrometer. It is capable of identifying pions and kaons with momenta up to $4\\>$GeV$\\>$c$^{-1}$ by detecting Cherenkov photons emitted in the silica aerogel radiator. After the detector alignment and calibration of the probability density function, we evaluate the performance of the ARICH counter using early beam collision data. Event samples of $D^{\\ast +} \\to D^0 \\pi^+ (D^0 \\to K^-\\pi^+)$ were used to determine the $\\pi(K)$ efficiency and the $K(\\pi)$ misidentification probability. We found that the ARICH counter is capable of separating kaons from pions with an identification efficiency of $93.5 \\pm 0.6 \\, \\%$ at a pion misidentification probability of $10.9 \\pm 0.9 \\, \\%$. This paper describes the identification method of the counter and the evaluation of the performance during its early operation.

We derive a novel integral equation relating the fluid pressure in a finger-like hydraulic fracture to the fracture width. By means of an asymptotic analysis in the small height to length ratio limit we are able to establish the action of the integral operator for receiving points that lie within three distinct regions: (1) an outer expansion region in which the dimensionless pressure is shown to be equal to the dimensionless width plus a small correction term that involves the second derivative of the width, which accounts for the nonlocal effects of the integral operator. The leading order term in this expansion is the classic local elasticity equation in the PKN model that is widely used in the oil and gas industry; (2) an inner expansion region close to the fracture tip within which the action of the elastic integral operator is shown to be the same as that of a finite Hilbert transform associated with a state of plane strain. This result will enable pressure singularities and stress intensity factors to be incorporated into analytic models of these finger-like fractures in order to model the effect of material toughness; (3) an intermediate region within which the action of the Fredholm integral operator of the first kind is reduced to a second kind operator in which the integral term appears as a small perturbation which is associated with a convergent Neumann series. These results are important for deriving analytic models of finger-like hydraulic fractures that are consistent with linear elastic fracture mechanics.

The field of mechanical circulatory support has made great strides in the preceding 2 decades. Although pediatric mechanical circulatory support has lagged behind that of adults, the gap between them is expected to close soon. The only device currently approved by the US Food and Drug Administration for use in children is the Berlin Heart EXCOR ventricular assist device (VAD). The prospective Berlin Heart Investigational Device Exemption Trial demonstrated good outcomes, such as bridge to transplantation or recovery, in ~90% of children supported with this device. However, a high incidence of hemorrhagic and thrombotic complications was also noted. As a result, pediatric centers have just started implanting adult intracorporeal continuous-flow devices in children. This paradigm shift has opened a new era in pediatric mechanical circulatory support. Whereas children on VAD were previously managed exclusively in hospital, therapeutic options such as outpatient management and even destination therapy have been becoming a reality. With continued miniaturization and technological refinements, devices currently in development will broaden the range of options available to children. The HeartMate 3 and HeartWare MVAD are two such compact VADs, which are anticipated to have great potential for pediatric use. Additionally, a pediatric-specific continuous-flow VAD, the newly redesigned Jarvik Infant 2015, is currently undergoing preclinical testing and is expected to undergo a randomized clinical trial in the near future. This review aims to discuss the challenges posed by the use of intracorporeal adult continuous-flow devices in children, as well as to provide our perspective on the future prospects of the field of pediatric VADs.

We have developed a new type of particle identification device, called an aerogel ring imaging Cherenkov (ARICH) counter, for the Belle II experiment. It uses silica aerogel tiles as Cherenkov radiators. For detection of Cherenkov photons, hybrid avalanche photo-detectors (HAPDs) are used. The designed HAPD has a high sensitivity to single photons under a strong magnetic field. We have confirmed that the HAPD provides high efficiency for single-photon detection even after exposure to neutron and $\\gamma $-ray radiation that exceeds the levels expected in the 10-year Belle II operation. In order to confirm the basic performance of the ARICH counter system, we carried out a beam test at the using a prototype of the ARICH counter with six HAPD modules. The results are in agreement with our expectations and confirm the suitability of the ARICH counter for the Belle II experiment. Based on the in-beam performance of the device, we expect that the identification efficiency at $3.5\\,{\\rm GeV}/c$ is 97.4% and 4.9% for pions and kaons, respectively. This paper summarizes the development of the HAPD for the ARICH and the evaluation of the performance of the prototype ARICH counter built with the final design components.

We present measurements ofB → K^(*)(892)γdecays using365 \\rm fb⁻¹of data collected from 2019 to 2022 by the Belle II experiment at the SuperKEKB asymmetric-energye⁺e⁻collider. The data sample contains(387 ± 6) × 10⁶Υ(4S)events. We measure branching fractions ( 𝓑 ) andC\\!{P}{}{a}symmetries ( 𝓐_(C\\!P) ) for bothB⁰→ K^(*0)γandB⁺→ K^(*+)γdecays. The difference inC\\!{P}{}{a}symmetries ( Δ𝓐_(C\\!P) ) and the isospin asymmetry ( Δ₀₊ ) between these neutral and charged channels are also measured. We obtain the following branching fractions andC\\!{P}{}{a}symmetries:𝓑 (B⁰ → K^(*0)γ) = (4.14 ± 0.10 ± 0.11 ) × 10⁻⁵ ,𝓑 (B⁺ → K^(*+)γ) = (4.04 ± 0.13 ^(+0.13)_(-0.15) )× 10⁻⁵ ,𝓐_(C\\!P) (B⁰ → K^(*0)γ) = (-3.3 ± 2.3 ± 0.4 )% , and𝓐_(C\\!P) (B⁺ → K^(*+)γ) = (-0.7 ± 2.9 ± 0.5 )% . The measured difference inC\\!{P}{}{a}symmetries isΔ𝓐_(C\\!P) = (+2.6 ± 3.8 ± 0.6 )% , and the measured isospin asymmetry isΔ₀₊ = (+4.8 ± 2.0 ± 1.8 )% . The first uncertainties listed are statistical and the second are systematic. These results are consistent with world-average values and theory predictions.

We present the results of a search for the charged-lepton-flavor violating decays B ⁰→ K ^(*0) τ ^(±) ℓ ^(∓) , where ℓ ^(∓)is either an electron or a muon. The results are based on 365 fb ⁻¹and 711 fb ⁻¹datasets collected with the Belle II and Belle detectors, respectively. We use an exclusive hadronic B-tagging technique, and search for a signal decay in the system recoiling against a fully reconstructed B meson. We find no evidence for B ⁰→ K ^(*0) τ ^(±) ℓ ^(∓)decays and set upper limits on the branching fractions in the range of (2.9–6.4)×10 ⁻⁵at 90% confidence level. 19 pages, 4 figures

We report measurements of the absolute branching fractions𝓑(B_(s)⁰ → D_(s)^(±) X) ,𝓑(B_(s)⁰ → D⁰/D̄⁰ X) , and𝓑(B_(s)⁰ → D^(±) X) , where the latter is measured for the first time. The results are based on a 121.4 fb ⁻¹data sample collected at theΥ(10860)resonance by the Belle detector at the KEKB asymmetric-energye⁺ e⁻collider. We reconstruct oneB_(s)⁰meson ine⁺e⁻ → Υ(10860) → B_(s)^(*) B̄_(s)^(*)events and measure yields ofD_(s)⁺ ,D⁰ , andD⁺mesons in the rest of the event. We obtain𝓑(B_(s)⁰ → D_(s)^(±) X) = (68.6 ± 7.2 ± 4.0)% ,𝓑(B_(s)⁰ → D⁰/D̄⁰ X) = (21.5 ± 6.1 ± 1.8)% , and𝓑(B_(s)⁰ → D^(±) X) = (12.6 ± 4.6 ± 1.3)% , where the first uncertainty is statistical and the second is systematic. Averaging with previous Belle measurements gives𝓑(B_(s)⁰ → D_(s)^(±) X) = (63.4 ± 4.5 ± 2.2)%and𝓑(B_(s)⁰ → D⁰/D̄⁰ X) = (23.9 ± 4.1 ± 1.8)% . For theB_(s)⁰production fraction at theΥ(10860) , we findf_(s) = (21.4^(+1.5)_(-1.7))% .

Using data samples of 983.0 fb − 1 and 427.9 fb − 1 accumulated with the Belle and Belle II detectors operating at the KEKB and SuperKEKB asymmetric-energy e + e − colliders, singly Cabibbo-suppressed decays$ {\\Xi}_c^{+}\\to p{K}_S^0 $Ξ c + → p K S 0 ,$ {\\Xi}_c^{+}\\to \\Lambda {\\pi}^{+} $Ξ c + → Λ π + , and$ {\\Xi}_c^{+}\\to {\\Sigma}^0{\\pi}^{+} $Ξ c + → Σ 0 π + are observed for the first time. The ratios of branching fractions of$ {\\Xi}_c^{+}\\to p{K}_S^0 $Ξ c + → p K S 0 ,$ {\\Xi}_c^{+}\\to \\Lambda {\\pi}^{+} $Ξ c + → Λ π + , and$ {\\Xi}_c^{+}\\to {\\Sigma}^0{\\pi}^{+} $Ξ c + → Σ 0 π + relative to that of$ {\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+} $Ξ c + → Ξ − π + π + are measured to be$ {\\displaystyle \\begin{array}{c}\\frac{\\mathcal{B}\\left({\\Xi}_c^{+}\\to p{K}_S^0\\right)}{\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+}\\right)}=\\left(2.47\\pm 0.16\\pm 0.07\\right)\\%,\\\ {}\\frac{\\mathcal{B}\\left({\\Xi}_c^{+}\\to \\Lambda {\\pi}^{+}\\right)}{\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+}\\right)}=\\left(1.56\\pm 0.14\\pm 0.09\\right)\\%,\\\ {}\\frac{\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Sigma}^0{\\pi}^{+}\\right)}{\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+}\\right)}=\\left(4.13\\pm 0.26\\pm 0.22\\right)\\%.\\end{array}} $B Ξ c + → p K S 0 B Ξ c + → Ξ − π + π + = 2.47 ± 0.16 ± 0.07 % , B Ξ c + → Λ π + B Ξ c + → Ξ − π + π + = 1.56 ± 0.14 ± 0.09 % , B Ξ c + → Σ 0 π + B Ξ c + → Ξ − π + π + = 4.13 ± 0.26 ± 0.22 % . Multiplying these values by the branching fraction of the normalization channel,$ \\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+}\\right)=\\left(2.9\\pm 1.3\\right)\\% $B Ξ c + → Ξ − π + π + = 2.9 ± 1.3 % , the absolute branching fractions are determined to be$ {\\displaystyle \\begin{array}{c}\\mathcal{B}\\left({\\Xi}_c^{+}\\to p{K}_S^0\\right)=\\left(7.16\\pm 0.46\\pm 0.20\\pm 3.21\\right)\\times {10}^{-4},\\\ {}\\mathcal{B}\\left({\\Xi}_c^{+}\\to \\Lambda {\\pi}^{+}\\right)=\\left(4.52\\pm 0.41\\pm 0.26\\pm 2.03\\right)\\times {10}^{-4},\\\ {}\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Sigma}^0{\\pi}^{+}\\right)=\\left(1.20\\pm 0.08\\pm 0.07\\pm 0.54\\right)\\times {10}^{-3}.\\end{array}} $B Ξ c + → p K S 0 = 7.16 ± 0.46 ± 0.20 ± 3.21 × 10 − 4 , B Ξ c + → Λ π + = 4.52 ± 0.41 ± 0.26 ± 2.03 × 10 − 4 , B Ξ c + → Σ 0 π + = 1.20 ± 0.08 ± 0.07 ± 0.54 × 10 − 3 . The first and second uncertainties above are statistical and systematic, respectively, while the third ones arise from the uncertainty in$ \\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+}\\right) $B Ξ c + → Ξ − π + π + .

We report measurements of thee⁺e⁻ → BB̄ ,BB̄^(*) , andB^(*)B̄^(*)cross sections at four energies, 10653, 10701, 10746 and 10805 MeV, using data collected by the Belle II experiment. We reconstruct oneBmeson in a large number of hadronic final states and use its momentum to identify the production process. In the first2-5MeV aboveB^(*)B̄^(*)threshold, thee⁺e⁻ → B^(*)B̄^(*)cross section increases rapidly. This may indicate the presence of a pole close to the threshold.