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Stringy canonical forms

Canonical forms of positive geometries play an important role in revealing hidden structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we introduce “stringy canonical forms”, which provide a natural definition and extension of canonical forms for general polytopes, deformed by a parameter α'. They are defined by real or complex integrals regulated with polynomials with exponents, and are meromorphic functions of the exponents, sharing various properties of string amplitudes. As α'→ 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. At finite α', they have simple poles corresponding to the facets of the polytope, with the residue on the pole given by the stringy canonical form of the facet. There is the remarkable connection between the α'→ 0 limit of tree-level string amplitudes, and scattering equations that appear when studying the α'→ ∞ limit. We show that there is a simple conceptual understanding of this phenomenon for any stringy canonical form: the saddle-point equations provide a diffeomorphism from the integration domain to the interior of the polytope, and thus the canonical form can be obtained as a pushforward via summing over saddle points. When the stringy canonical form is applied to the ABHY associahedron in kinematic space, it produces the usual Koba-Nielsen string integral, giving a direct path from particle to string amplitudes without an a priori reference to the string worldsheet. We also discuss a number of other examples, including stringy canonical forms for finite-type cluster algebras (with type A corresponding to usual string amplitudes), and other natural integrals over the positive Grassmannian.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Understanding the Impacts of Stellar Companions on Planet Formation and Evolution: A Survey of Stellar and Planetary Companions within 25 pc

We explore the impact of outer stellar companions on the occurrence rate of giant planets detected with radial velocities. We searched for stellar and planetary companions to a volume-limited sample of solar-type stars within 25 pc. Using adaptive optics imaging observations from the Lick 3 m and Palomar 200″ Telescopes, we characterized the multiplicity of our sample stars, down to the bottom of the main sequence. With these data, we confirm field star multiplicity statistics from previous surveys. We additionally combined three decades of radial velocity (RV) data from the California Planet Search with newly collected RV data from Keck/HIRES and the Automated Planet Finder/Levy Spectrometer to search for planetary companions in these same systems. Using an updated catalog of both stellar and planetary companions, as well as detailed injection/recovery tests to determine our sensitivity and completeness, we measured the occurrence rate of planets among the single- and multiple-star systems. We found that planets with masses in the range of 0.1–10 M {sub J} and with semimajor axes of 0.1–10 au have an occurrence rate of 0.18{sub −0.03}{sup +0.04} planets per star when they orbit single stars and an occurrence rate of 0.12 ± 0.04 planets per star when they orbit a star in a binary system. Breaking the sample down by the binary separation, we found that only one planet-hosting binary system had a binary separation <100 au, and none had a separation <50 au. These numbers yielded planet occurrence rates of 0.20{sub −0.06}{sup +0.07} planets per star for binaries with separation a {sub B} > 100 au and 0.04{sub −0.02}{sup +0.04} planets per star for binaries with separation a {sub B} < 100 au. The similarity in the planet occurrence rate around single stars and wide primaries implies that wide binary systems should actually host more planets than single-star systems, since they have more potential host stars. We estimated a system-wide planet occurrence rate of 0.3 planets per wide binary system for binaries with separations a {sub B} > 100 au. Finally, we found evidence that giant planets in binary systems have a different semimajor-axis distribution than their counterparts in single-star systems. The planets in the single-star sample had a significantly higher occurrence rate outside of 1 au than inside 1 au by nearly 4σ, in line with expectations that giant planets are most common near the snow line. However, the planets in the wide binary systems did not follow this distribution, but rather had equivalent occurrence rates interior and exterior to 1 au. This may point to binary-mediated planet migration acting on our sample, even in binaries wider than 100 au.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Geometric secret sharing in a model of Hawking radiation

We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This “inception black hole” can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER=EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed “island formula”. We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraining solar electron number density via neutrino flavor data at Borexino

Understanding the physics of the deep solar interior, and the more exotic environs of core-collapse supernovae (CCSN) and binary neutron-star (NS) mergers, is of keen interest in many avenues of research. To date, this physics is based largely on simulations via forward integration. While these simulations provide valuable constraints, it could be insightful to adopt the "inverse approach" as a point of comparison. Within this paradigm, parameters of the solar interior are not output based on an assumed model, but rather are inferred based on real data. Here, we take the specific case of solar electron number density, which historically is taken as output from the standard solar model. We show how one may arrive at an independent constraint on that density profile based on available neutrino flavor data from the Earth-based Borexino experiment. The inference technique's ability to offer a unique lens on physics can be extended to other datasets, and to analogous questions for CCSN and NS mergers, albeit with simulated data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Adsorption of furan, hexanoic acid, and alkanes in a hierarchical zeolite at reaction conditions: Insights from molecular simulations

Hierarchical zeolites containing both micropores and mesopores are valuable catalysts for facilitating reactions of large molecules. Furan acylation by fatty acids is a promising reaction for valorizing biomass, and the self-pillared pentasil (SPP) zeolite was found to perform particularly well for this reaction. To better understand the distribution of molecules in hierarchical zeolites at the elevated temperature (T = 523 K) and the elevated pressure (p >1 bar) associated with typical reaction conditions, unary and binary adsorption were predicted using Monte Carlo simulations in the isothermal–isobaric Gibbs ensemble. Adsorption of six species (furan, hexanoic acid, -hexane, -decane, -tetradecane, and 3,6-diethyloctane) was investigated from vapor, liquid, and supercritical phases, and loadings into the micropores, onto the mesopore surface, and in the mesopore interior of SPP were obtained. As pressure increases, -alkanes fill the micropores before loading the surface and then the interior of the mesopore, while furan and hexanoic acid adsorb strongly to the mesopore surface due to hydrogen bonding interactions with surface silanols. Hydrogen bonding interactions also draw hexanoic acid molecules in the micropore region toward the pore mouths, so their carboxylic acid group forms H-bonds with silanols, while the alkyl tails interact with the micropore walls. Mesopore condensation is observed for molecules below their critical point, and occurs when the Gibbs free energy of transfer into the mesopore interior and onto the mesopore surface converge. When hexanoic acid adsorption occurs in the presence of alkane solvents, then the selectivity and spatial distribution of hexanoic acid in the micropores and on the surface can be tuned by adjusting the fluid pressure and the alkane length and/or branching.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

LiDAR-Aided Interior Orientation Parameters Refinement Strategy for Consumer-Grade Cameras Onboard UAV Remote Sensing Systems

Unmanned aerial vehicles (UAVs) are quickly emerging as a popular platform for 3D reconstruction/modeling in various applications such as precision agriculture, coastal monitoring, and emergency management. For such applications, LiDAR and frame cameras are the two most commonly used sensors for 3D mapping of the object space. For example, point clouds for the area of interest can be directly derived from LiDAR sensors onboard UAVs equipped with integrated global navigation satellite systems and inertial navigation systems (GNSS/INS). Imagery-based mapping, on the other hand, is considered to be a cost-effective and practical option and is often conducted by generating point clouds and orthophotos using structure from motion (SfM) techniques. Mapping with photogrammetric approaches requires accurate camera interior orientation parameters (IOPs), especially when direct georeferencing is utilized. Most state-of-the-art approaches for determining/refining camera IOPs depend on ground control points (GCPs). However, establishing GCPs is expensive and labor-intensive, and more importantly, the distribution and number of GCPs are usually less than optimal to provide adequate control for determining and/or refining camera IOPs. Moreover, consumer-grade cameras with unstable IOPs have been widely used for mapping applications. Therefore, in such scenarios, where frequent camera calibration or IOP refinement is required, GCP-based approaches are impractical. To eliminate the need for GCPs, this study uses LiDAR data as a reference surface to perform in situ refinement of camera IOPs. The proposed refinement strategy is conducted in three main steps. An image-based sparse point cloud is first generated via a GNSS/INS-assisted SfM strategy. Then, LiDAR points corresponding to the resultant image-based sparse point cloud are identified through an iterative plane fitting approach and are referred to as LiDAR control points (LCPs). Finally, IOPs of the utilized camera are refined through a GNSS/INS-assisted bundle adjustment procedure using LCPs. Seven datasets over two study sites with a variety of geomorphic features are used to evaluate the performance of the developed strategy. The results illustrate the ability of the proposed approach to achieve an object space absolute accuracy of 3–5 cm (i.e., 5–10 times the ground sampling distance) at a 41 m flying height.

47 OTHER INSTRUMENTATION↗

Area 6 Control Point: An Architectural Survey of the Area 6 Control Point, Nevada National Security Site, Nye County, Nevada

The U.S. Department of Energy (DOE), National Nuclear Security Administration Nevada Field Office (NNSA/NFO) proposes to demolish five buildings and five accessory resources in the Area 6 Control Point at the Nevada National Security Site (NNSS) in Nye County, Nevada. The demolition and removal of the buildings and accessories constitute an undertaking subject to review under Section 106 of the National Historic Preservation Act (NHPA) (54 United States Code [USC] § 306101) and its implementing regulations, 36 Code of Federal Regulations (CFR) Part 800. The buildings and accessories were recorded in Identification and Evaluation of 14 Architectural Resources Scheduled for Demolition, Area 6 Control Point and Vicinity, Nevada National Security Site, Nye County, Nevada (Menocal et al. 2020). The report found that the five buildings were not individually eligible for listing in the National Register of Historic Places (NRHP, National Register) but were potentially eligible as contributing elements to an unrecorded Area 6 Control Point district. The report also found that the five accessory resources were not individually eligible for the NRHP but they contributed to other historic properties, including the contributing elements to the unrecorded district. Finally, the report found that the undertaking would result in an adverse effect to historic properties. The State Historic Preservation Office (SHPO) concurred with the report’s findings regarding the eligibility of the buildings and structures in the Area of Potential Effect (APE) and that the undertaking would result in an adverse effect (Reed 2020). The NNSA/NFO, in consultation with the SHPO, then developed the Memorandum of Agreement DE-GM58-21NA25543 Between the U.S. Department of Energy and the Nevada State Historic Preservation Officer Regarding Demolition of Fourteen Buildings and Structures in Area 6 of the Nevada National Security Site, Nye County, hereafter referred to as the MOA. The MOA stipulates that a district boundary be delineated with an accompanying boundary report and supporting photographs (Stipulation III.A) followed by an architectural survey of the potential historic district (Stipulation III.B). The SHPO reviewed and concurred with the proposed district boundary and accompanying boundary report and photographs (O’Neill et al. 2021) on August 23, 2021, in fulfillment of Stipulation III.A (Reed 2021). This architectural survey report has been prepared in accordance with Stipulation III.B. It includes an NRHP evaluation of the district, identifies contributing and non-contributing elements, and is accompanied by Architectural Resource Assessment (ARA) forms. The NRHP evaluation concludes that the Area 6 Control Point is recommended eligible as a historic district under the Secretary of the Interior’s Significance Criterion A at the national level as the location of the command center and various support facilities directly related to timing and firing operations for nuclear testing on the NNSS from 1951 to 1992. It is also recommended eligible under Significance Criterion C for embodying the distinctive characteristics of a nuclear command center in the context of the Cold War and as a significant and distinguishable entity. There are a total of 29 primary resources within the district boundary. Of these, 28 are recommended as contributing elements to the Area 6 Control Point Historic District and one is recommended as non-contributing.

54 ENVIRONMENTAL SCIENCES↗

Phase transitions in high-purity zirconium under dynamic compression

In this work, we present results from ramp compression experiments on high-purity Zr that show the α → ω, ω → β, as well as reverse β → ω phase transitions. Simulations with a multi-phase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic α ! ! transition occurs ~ 9 GPa above the equilibrium phase boundary, the ω → β transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium ω – β line at P = 29:2 GPa, and T = 490 K. The thermodynamic path in the interior of the sample lies ~ 100 K above the isentrope at the point of the ω → β transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the non-equilibrium α → ω transition. The inferred rate of the α → ω transition is several orders of magnitude higher than that measured in dynamic diamond anvil cell (DDAC) experiments in an overlapping pressure range. We discuss a model for the influence of shear stress on the nucleation rate. We find that the shear stress s ji has the same effect on the nucleation rate as a pressure increase δP = cϵ ij s ji /(ΔV/V); where c is a geometric constant ~ 1 and, ϵ ij are the transformation shear strains. The small fractional volume change ΔV/V ≈ 0:1 at the α → ω transition amplifies the effect of shear stress, and we estimate that for this case δP is in the range of several GPa. Correcting our transition rate to a hydrostatic rate brings it approximately into line with the DDAC results, suggesting that shear stress plays a significant role in the transformation rate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Automatic Digitization and Orientation of Scanned Mesh Data for Floor Plan and 3D Model Generation

This paper describes a novel approach for generating accurate floor plans and 3D models of building interiors using scanned mesh data. Unlike previous methods, which begin with a high resolution point cloud from a laser range-finder, our approach begins with triangle mesh data, as from a Microsoft HoloLens. It generates two types of floor plans, a “pen-and-ink” style that preserves details and a drafting-style that reduces clutter. It processes the 3D model for use in applications by aligning it with coordinate axes, annotating important objects, dividing it into stories, and removing the ceiling. Its performance is evaluated on commercial and residential buildings, with experiments to assess quality and dimensional accuracy. Our approach demonstrates promising potential for automatic digitization and orientation of scanned mesh data, enabling floor plan and 3D model generation in various applications such as navigation, interior design, furniture placement, facilities management, building construction, and HVAC design.

Sharma, Ritesh↗

Development and experimental evaluation of new building air leakage measurement methods: measurement of interior air leaks and comparison to conventional methods

Building air leaks (both through exterior and interior surfaces) can have a significant impact on energy consumption, indoor air quality, fire safety, and moisture accumulation affecting structural durability. Blower door testing has been used to measure leaks in buildings, but commonly used testing methods do not directly measure interior leaks. In this paper, new testing methods (guarded interior test and zonal multipoint pressure testing method) are presented that directly measure these interior leaks, utilizing common blower door equipment for both single and multi-point testing. Furthermore, these new methods are compared to conventional methods in terms of the information provided, limitations and time/effort needed. In addition, building leak measurement results are analyzed to reveal a) coupling between power law model values (exponent and coefficient) for an ensemble of buildings, b) the error in using single point testing when estimating low pressure leakage, and c) how building power law models vary from low to high pressure ranges.

99 GENERAL AND MISCELLANEOUS↗

Computational Methods to Characterize Panel Loading Conditions for Accelerated Testing

Panel cracking and degradation due to wind loading are known to have a detrimental effect on power output. Recreating these damaging conditions in a controlled experimental setting requires an understanding of the loads being generated at the panel surface as a function of both wind speed, wind direction, and panel orientation. To better understand these relationships, a computational fluid dynamics (CFD) simulation package was constructed using an open-source Python library for solving partial differential equations with the finite element method. This CFD package allows the simulated wind speed and panel orientation of a multi-panel array to be easily changed and provides the capability to measure the traction forces at discrete points along the sun-facing and ground-facing surface of an interior panel residing in the wake of one or more upstream panels. A parameter exploration was performed in which the panel angle was varied in even increments from -70 deg to 70 deg and the wind speed was varied from 2 to 30 m/s. During post processing, the measured traction along the panel surface was averaged spatially and interpreted as a time-varying signal, where further processing of this signal yielded the root mean square amplitude and a characteristic frequency associated with the loading. This study found that higher wind speeds are generally associated with increased amplitude of loading and that the panel orientation angle can significantly exacerbate or mitigate this loading. These outcomes are presented along with current work on higher-fidelity verification simulations and recommendations for performing accelerated experimental testing.

loading↗

An Accelerated Clip Algorithm for Unstructured Meshes: A Batch-Driven Approach

The clip technique is a popular method for visualizing complex structures and phenomena within 3D unstructured meshes. Meshes can be clipped by specifying a scalar isovalue to produce an output unstructured mesh with its external surface as the isovalue. Similar to isocontouring, the clipping process relies on scalar data associated with the mesh points, including scalar data generated by implicit functions such as planes, boxes, and spheres, which facilitates the visualization of results interior to the grid. In this paper, we introduce a novel batch-driven parallel algorithm based on a sequential clip algorithm designed for high-quality results in partial volume extraction. Our algorithm comprises five passes, each progressively processing data to generate the resulting clipped unstructured mesh. The novelty lies in the use of fixed-size batches of points and cells, which enable rapid workload trimming and parallel processing, leading to a significantly improved memory footprint and run-time performance compared to the original version. On a 32-core CPU, the proposed batch-driven parallel algorithm demonstrates a run-time speed-up of up to 32.6x and a memory footprint reduction of up to 4.37x compared to the existing sequential algorithm. The software is currently available under an open-source license in the VTK visualization system.

Tsalikis, Spiros↗

Vacancy and interstitial interactions with crystal/amorphous, metal/covalent interfaces

In this work, we use atomistic simulations to investigate the interaction of vacancies and interstitials with interfaces between a crystalline metal and an amorphous, covalently-bonded solid. We select the gold (Au)/silicon (Si) binary system as a model material and construct interface models along two different facets of crystalline Au and with amorphous Si (a-Si) created at three different quench rates. We compute formation energies of vacancies, self-interstitials, and interstitial impurities as a function of position relative to the interface and find that they have markedly lower values near the interface than in the interior of the adjoining phases. We conclude that crystal/amorphous, metal/covalent interfaces may be as effective at removing radiation-induced point defects as interfaces in polycrystalline metals composites. Moreover, irrespective of interface character, the average formation energies of all point defects at all the Au/a-Si interfaces we investigated are comparable. Thus, unlike in polycrystalline metals, where an interface’s crystallographic character has a marked effect on its interactions with point defects, all interface types in crystal/amorphous, metal/covalent composites may be equally effective at absorbing all radiation-induced defects.

36 MATERIALS SCIENCE↗

How deep is your soil? Quantifying and spatially analyzing understudied deep soil in the United States

Deep soil is largely understudied and important in understanding biogeochemical processes in soil. Here, understudied soil is defined as the difference between soil studied to a known depth and the estimated bedrock depth. To understand more about deep soil, the understudied soil in the US was quantified and spatially analyzed using soil survey data and model estimates of bedrock depth. An equation was derived to find understudied soil using the dataset parameters “max lower depth studied”, “depth to bedrock”, and “likelihood of bedrock in the top 200 cm”. The survey data and bedrock model revealed that soil has been studied to an average depth of 1-2 meters, and the average depth to bedrock is 20 meters. Soil data density in the soil surveys was greatest in the West Coast, Midwest, and areas historically managed for agricultural, while the non-contiguous US and interior West were underrepresented. The soil had been studied deeper than the estimated soil depth in 455 out of 56,889 observation points concentrated in Alaska, California, Texas, Florida, Puerto Rico, and the US Virgin Islands. To understand the diversity and any taxonomic bias of the global soil data available, soil order was compared to US-based National Resource Conservation Service percentages and it was found that Oxisols, Alfisols, Ultisols, Andisols, and Histosols were overrepresented while Gelisols, Aridisols, Vertisols, Entisols, and Spodosols are underrepresented. Soil depth is important in exploring the complexity of biogeochemical processes that take place in soil.

Bedrock↗

Compositional zoning of the Otowi Member of the Bandelier Tuff, Valles caldera, New Mexico, USA

The Otowi Member of the Bandelier Tuff erupted at ca. 1.60 Ma from the Valles caldera (New Mexico, USA). It consists of as much as 400 km 3 (dense rock equivalent) of strongly differentiated high-silica rhyolite and shows systematic upward variations in crystallinity, mineral chemistry, and trace element concentrations through its thickness, but the major element composition is almost constant and is near the low-pressure granite minimum. Incompatible trace elements in whole pumice fragments and glasses show well-correlated linear covariations. Upward zoning to lower abundances of incompatible trace elements is accompanied by development of overgrowths on quartz and alkali feldspar, although earlier-formed interiors of quartz and feldspar have near-constant compositions throughout the tuff, modified by cation diffusion in the case of feldspar. Melt inclusions in remnant quartz cores show diverse Pb isotope ratios, pointing to a wide range of distinct protoliths that contributed rhyolitic melt to the Otowi magma. Mineral thermometers suggest a modest temperature gradient through the melt body, perhaps of 40 °C, at the time of eruption. Chemical, textural, and mineralogical variations and volume-composition relations through the tuff are consistent with an origin for zoning by melting of a high-crystallinity cumulate layer beneath cognate supernatant liquid to produce denser, remobilized liquid of accumulative composition (i.e., the “modified mush model”). Melting may have occurred in several episodes. The latest of these episodes, probably thousands of years prior to eruption, introduced new rhyolitic liquid into the system and was associated with a thermal excursion, recorded in core compositions of pyroxene, during which much of the earlier crystal mass was dissolved. This left inherited cores and interiors of accumulated quartz and feldspar mantled with new growth having less-evolved compositions (higher Ti, Sr, and Ba). Changing solubility of zircon during cumulate melting produced a reversal of Zr concentrations. There is no clear petrologic evidence of a recharge eruption trigger; nonetheless, compositional zoning resulted mainly from repeated recharge-induced remobilization of quartz-feldspar cumulate. The Otowi system was built, evolved, and modified by several events over the course of a few hundred thousand years.

Wolff, J. A.↗

Analysis of the Stable Interphase Responsible for the Excellent Electrochemical Performance of Graphite Electrodes in Sodium-Ion Batteries

Considerable efforts have been exerted to understand the formation and properties of the solid electrolyte interphase (SEI) in sodium ion batteries. However, the puzzling existence and role of SEI behind the huge volume changes of the graphite electrodes need to be answered. Herein, the reason of how ether-derived SEI maintains excellent reversibility despite the huge volume changes during cycling is unraveled. Theoretical simulations and Fourier-transform infrared spectroscopy demonstrate the formation mechanism of an SEI between the graphite anode and electrolyte. Furthermore, the high mechanical tolerance of the ether-derived SEI is confirmed in atomic force microscopy. A depth profile of X-ray photoelectron spectroscopy points to a multilayer structure of the ether-derived SEI. The outer layer comprises organics (sodium alkoxide), while the inorganics (Na 2 CO 3 , NaF) in interior region are mixed with some organics. Notably, the presence of organics ensures the adaptability of the SEI to the volume expansion of graphite during cycling, and the concentrated distribution of inorganics improves the Young's modulus (resistance to deformation). Therefore, the graphite anode exhibits high cycle stability (96.6% capacity retention ratio at 1 A g –1 over 860 cycles) and efficiency (≈99.5%).

25 ENERGY STORAGE↗

Revisiting the refined Distance Conjecture

The Distance Conjecture of Ooguri and Vafa holds that any infinite-distance limit in the moduli space of a quantum gravity theory must be accompanied by a tower of exponentially light particles, which places tight constraints on the low-energy effective field theories in these limits. One attempt to extend these constraints to the interior of moduli space is the refined Distance Conjecture, which holds that the towers of light particles predicted by the Distance Conjecture must appear any time a modulus makes a super-Planckian excursion in moduli space. In this note, however, we point out that a tower which satisfies the Distance Conjecture in an infinite-distance limit of moduli space may be parametrically heavier than the Planck scale for an arbitrarily long geodesic distance. This means that the refined Distance Conjecture, in its most naive form, does not place meaningful constraints on low-energy effective field theory. This motivates alternative refinements of the Distance Conjecture, which place an absolute upper bound on the tower mass scale in the interior of moduli space. We explore two possibilities, providing evidence for them and briefly discussing their implications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. So our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

42 ENGINEERING↗