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This broad review summarizes recent advances and "hot"research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25-27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a "snapshot"of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article. The introduction of basic definitions for each topic is followed by an outline of design strategies for the media under consideration, recently developed analysis and implementation techniques, and discussions of current challenges and promising applications. This review, while not comprehensive, will be helpful especially for early-career researchers, among others, as it offers a broad view of the current state-of-the-art and highlights some unique and flourishing research in the mentioned fields, providing insight into multiple exciting research directions., Nanophotonics, 12 (4), ISSN:2192-8614

While resonant modes do not exist within band gaps in infinite periodic materials, they may appear as in-gap localized edge modes once the material is truncated to form a finite periodic structure. Here, we provide an analysis framework that reveals the topological origins of truncation resonances, elucidating formally the conditions that influence their existence and properties. Elastic beams with sinusoidal and step-wise property modulations are considered as classical examples of periodic structures. Their non-trivial topological characteristics stem from the consideration of a phason parameter that produces spatial shifts of the property modulation while continuously varying how the boundaries are truncated. In this context, non-trivial band gaps are characterized by an integer topological invariant, the Chern number, which is equal to the number of truncation resonances that traverse a band gap as the phason is varied. We highlight the existence of multiple chiral edge states that may be localized at opposite boundaries, and illustrate how these can be independently tuned by modified boundary-specific phason parameters. Furthermore, we show that the frequency location of a truncation resonance is influenced by the modulation volume fraction, boundary conditions, and number of cells comprising the finite structure, thus quantifying its robustness to these factors. Non-topological in-gap resonances induced by a defect are also demonstrated, showing that these can be coupled with topological modes when the defect is located at an edge. Finally, experimental investigations on bi-material phononic-crystal beams are conducted to support these findings. The tunability of truncation resonances by material-property modulation may be exploited in applications ranging from vibration attenuation and thermal conductivity reduction to filtering and flow control by phononic subsurfaces.

Phononic crystals (PnC) are spatially periodic materials with band gaps that form by Bragg scattering of elastic waves. Within the frequency range of a band gap, wave propagation is not admitted. A long-standing limitation of this class of materials is that the wavelength for band-gap formation must be on the order of the unit-cell size. This restricts the presence of band gaps to relatively high frequencies for a given lattice spacing. Locally resonant metamaterials, on the other hand, enable the opening of low-frequency, subwavelength band gaps through resonance hybridization. However, their band gaps are characteristically narrow and require large or massive local resonators to form. Here, we break both limitations using beam-based PnCs by (1) locking the rotation degree of freedom at the edges of the primitive unit cell, and (2) coiling the PnC by applying full beam-axis rotations at the locked locations. These respective kinematic and geometric transformations convert a conventional beam PnC from its extended form with a nominal lattice constant to an extremely compact coiled configuration with a greatly reduced lattice constant. With the periodic rotational locking, the band gaps remain intact and are still large, and in fact increase noticeably in size. With the subsequent coiling, the band gaps remain based on Bragg scattering and are quantitatively conserved except now appearing at lower frequencies as dictated by the ratio of the extended-to-coiled lattice constants. This ratio defines a coiling factor, which is a measure of the reduction in the PnC unit-cell length in the direction of wave transmission while maintaining the band structure of its original extended form except for the favorable changes induced by the periodic rotational locking. A coiling factor of ß lowers, by construction, the location of the normalized central frequency of any given band gap by a factor of ß . The only limitation is the need for lateral space to accommodate the coiling of the beam segments. The vibration behavior of a finite version of the coiled structure is experimentally tested demonstrating a matching band-gap response, despite the reduction in length, to that obtained by finite-element analysis of the extended rotationally locked version. This concept creates effectively subwavelength Bragg band gaps. It clears the path for PnCs to serve in applications that are orders-of-magnitude smaller in scale than are currently possible, while featuring band gaps that are significantly larger than those generated by locally resonant metamaterials. This research is funded by the Air Force Office of Scientific Research under grant number 20RXCOR058.

Using the homotopy analysis method, we present an explicit frequency-versus-wavenumber nonlinear dispersion relation for a flexural elastic beam. In our analysis, we employ the Euler–Bernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. As an example, we consider geometric nonlinearity in the form of Green–Lagrange strain. The underlying constitutive relation is formulated by linearly relating the second Piola–Kirchhoff stress to the Green–Lagrange strain, although the method is directly applicable to material nonlinearities as well. The derived analytical solution, for each model, is obtained to Mth-order accuracy and is verified by comparing with a numerical result brought about by laboriously finding the roots of the corresponding travelling-wave implicit relation governing the nonlinear elastodynamics. This is the first derivation of an explicit dispersion relation for an elastic beam undergoing strongly nonlinear finite flexural deformation. The derived relation characterizes the nature of a traveling cosine-like nonlinear wave throughout its stable pre-breaking state.

At the Fermilab Tevatron proton-antiproton ($p\bar{p}$) collider, high-mass electron-neutrino ($e\nu$) pairs are produced predominantly in the process $p \bar{p} \rightarrow W(\rightarrow e\nu) + X$. The asymmetry of the electron and positron yield as a function of their pseudorapidity constrain the slope of the ratio of the $u$- to $d$-quark parton distributions versus the fraction of the proton momentum carried by the quarks. This paper reports on the measurement of the electron-charge asymmetry using the full data set recorded by the Collider Detector at Fermilab in 2001--2011 and corresponding to 9.1~fb$^{-1}$ of integrated luminosity. The measurement significantly improves the precision of the Tevatron constraints on the parton-distribution functions of the proton. Numerical tables of the measurement are provided.

This paper presents a novel metamaterial unit-cell configuration that may exhibit local resonance (LR) band gaps with exceptional properties — e.g., extreme width. The proposed configuration is comprised of a base wave-propagating medium to which a discrete periodic resonating branch — e.g., a branch made of a finite number of repeating diatomic unit cells — is connected. Such periodicity causes waves propagating in the branch to experience attenuation within the branch unit-cell Bragg band gap. The branch may also vibrate in resonance within its Bragg band gap due to the effect of the boundaries introduced upon truncating the nominal periodic medium. Such Bragg band-gap resonances exhibited by the branch are key to the proposed configuration as the metamaterial LR band gaps that form around them may possess exceptional properties. This paper shows that these exceptional LR band gaps are highly tunable and can be systematically designed using a semi-analytical design approach. The design approach is in part based on a recently derived analytical method that predicts, in advance, whether the branch would exhibit resonance and anti-resonance frequencies in its Bragg band-gap. Finally, a numerical case is discussed to showcase the proposed metamaterial configuration and design approach; it presents a metamaterial unit cell that demonstrates an extremely wide LR band gap. These findings open a route towards exploiting discrete, e.g., granular, periodic resonators to realize highly tunable LR band gaps.

Bloch mode synthesis (BMS) techniques enable efficient band-structure calculations of periodic media by forming reduced-order models of the unit cell. Rooted in the framework of the Craig-Bampton component mode synthesis methodology, these techniques decompose the unit cell into interior and boundary degrees-of-freedom that are nominally described, respectively, by sets of normal modes and constraint modes. In this paper, we generalize the BMS approach by state-space transformation to extend its applicability to generally damped periodic materials that violate the Caughey-O’Kelly condition for classical damping. In non-classically damped periodic models, the fixed-interface eigenvalue problem may, in general, produce a mixture of underdamped and overdamped modes. We examine two mode-selection schemes for the reduced order model and demonstrate the underlying accuracy-efficiency trade-offs when qualitatively distinct mixtures of underdamped and overdamped modes are incorporated. The proposed approach provides a highly effective computational tool for analysis of large models of phononic crystals and acoustic/elastic metamaterials with complex damping properties. This investigation does not only extend the applicability of BMS techniques to the most generally damped models of periodic media, it also advances our understanding of the nature of damping modes and the non-trivial manner by which they contribute to the wave propagation properties.

Understanding nanoscale thermal transport is critical for nano-engineered devices such as quantum sensors, thermoelectrics, and nanoelectronics. However, despite overwhelming experimental evidence for nondiffusive heat dissipation from nanoscale heat sources, the underlying mechanisms are still not understood. In this work, we show that for nanoscale heat source spacings that are below the mean free path of the dominant phonons in a substrate, close packing of the heat sources increases in-plane scattering and enhances cross-plane thermal conduction. This leads to directional channeling of thermal transport—a novel phenomenon. By using advanced atomic-level simulations to accurately access the lattice temperature and the phonon scattering and transport properties, we finally explain the counterintuitive experimental observations of enhanced cooling for close-packed heat sources. This represents a distinct fundamental behavior in materials science with far-reaching implications for electronics and future quantum devices.

Bragg scattering in periodic media generates bandgaps, frequency bands where waves attenuate rather than propagate. Yet, a finite periodic structure may exhibit resonance frequencies within these bandgaps. This is caused by boundary effects introduced by the truncation of the nominal infinite medium. Previous studies of discrete systems determined existence conditions for bandgap resonances, although the focus has been limited to mainly periodic chains with free-free boundaries. In this paper, we present closed-form existence conditions for bandgap resonances in discrete diatomic chains with general boundary conditions (free-free, free-fixed, fixed-free, or fixed-fixed), odd or even chain parity (contrasting or identical masses at the ends), and the possibility of attaching a unique component (mass and/or spring) at one or both ends. The derived conditions are consistent with those theoretically presented or experimentally observed in prior studies of structures that can be modeled as linear discrete diatomic chains with free-free boundary conditions. An intriguing case is a free-free chain with even parity and an arbitrary additional mass at one end of the chain. Introducing such an arbitrary mass underscores a transition among a set of distinct existence conditions, depending on the type of chain boundaries and parity. The proposed analysis is applicable to linear periodic chains in the form of lumped-parameter models, examined across the frequency spectrum, as well as continuous granular media models, or similar configurations, examined in the low-frequency regime.

[EN] The finite-element time-domain method for elastic band-structure calculations is presented in this paper. The method is based on discretizing the appropriate equations of motion by finite elements, applying Bloch boundary conditions to reduce the analysis to a single unit cell, and conducting a simulation using a standard time-integration scheme. The unit cell is excited by a wide-band frequency signal designed to enable a large number of modes to be identified from the time-history response. By spanning the desired wave-vector space within the Brillouin zone, the band structure is then robustly generated. Bloch mode shapes are computed using the well-known concept of modal analysis, especially as implemented in an experimental setting. The performance of the method is analyzed in terms of accuracy, convergence, and computation time, and is compared to the finite-difference time-domain method as well as to a direct finite-element (FE) solution of the corresponding eigenvalue problem. The proposed method is advantageous over FD-based methods for unit cells with complex geometries, and over direct FE in situations where the formulation of an eigenvalue problem is not straightforward. For example, the new method makes it possible to accurately solve a time-dependent Bloch problem, such as the case of a complex unit cell model of a topological insulator where an internal fluid flow or other externally controlled physical fields are present. (C) 2018 Elsevier B.V. All rights reserved., A.C. is grateful for the support of Programa de Ayudas de Investigacion y Desarrollo (PAID) and Programa de Movilidad e Internacionalizacion Academica (PMIA-2013) of the UPV. This research was partially funded by the funded by the Ministerio de Economia e Innovacion (MINECO), Spain through project FIS2015-65998-C2-2-P, and partially funded by the National Science Foundation (NSF), USA through grant number 1538596. The authors acknowledge Dr. Noe Jimenez for fruitful discussions.

Metadamping is the phenomenon of either enhanced or diminished intrinsic dissipation in a material stemming from the material's internal structural dynamics. It has been previously shown that a locally resonant elastic metamaterial may be designed to exhibit higher or lower dissipation compared to a statically equivalent phononic crystal with the same amount of prescribed damping. Here we reveal that even further dissipation, or alternatively further reduction of loss, may be reached in an inertially amplified metamaterial that is also statically equivalent and has the same amount of prescribed damping. This is demonstrated by a passive configuration whereby an attenuation peak is generated by the motion of a mass supported by an inclined lever arm. We further show that by coupling this inertially amplified attenuation peak with that of a local resonance attenuation peak, a trade-off between the intensity of spatial attenuation versus temporal attenuation is realized for a range of the inclination angles. Design for performance along this trade-off is therefore possible by adjustment of the lever angle. These findings open the way for highly expanding the Ashby space for stiffness-damping capacity or stiffness-spatial attenuation capacity through design of the internal structure of materials., Comment: 9 pages, 4 figures

The advent of acoustic metamaterials has opened up an emerging frontier in the control of sound transmission. A key limitation, however, is that an acoustic metamaterial based on a single local resonator in the unit cell produces a restricted narrow-band attenuation peak. When multiple local resonators are used, the attenuation peaks that arise—while numerous—are each still narrow and separated by passbands. Here, we present an acoustic metamaterial concept that yields a subwavelength sound transmission loss through two antiresonances—in a single band gap—that are fully coupled and, hence, provide a broadband attenuation range; this is in addition to delivering a high isolation intensity for both peaks that exceeds 100 dB within the 3–5 kHz range or 60 dB around 1 kHz. The underlying coupled-resonance mechanism is triggered by ensuring that two local resonances appear between two coincident frequencies formed by the intersection of the incident acoustic waves sound line with Bragg dispersion curves governing in-plane wave motion orthogonal to the direction of transmission. This phenomenon is nominally realized in the form of a thin single-panel single-material pillared-plate structure with internal contiguous holes, a practical configuration that lends itself to design adjustments and optimization for a frequency range of interest, down to subkilohertz, and to mass fabrication. D.R. acknowledges the financial support received by the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2018-000797-S), and the Spanish Ministry of Education, Professional Training and Universities, for the FPU mobility Grant (EST18/00203).

Inertial amplification has been utilized in phononic media as a mechanism for the generation of large band gaps at low subwavelength frequencies. A unique feature in an inertial-amplification band gap is that it may exhibit two coupled peaks in the imaginary wavenumber portion of its band diagram. This unique double-attenuation band gap has been shown to emerge from a periodic arrangement of a levered mass whose motion is directly connected to that of an independent degree of freedom in the system through the motion of the lever base. Here we demonstrate a double-attenuation band gap emerging specifically from a modal coupling of the levered mass with a conventional local-resonance mass separately attached to the base. This presents a fundamentally distinct mechanical mechanism for the shaping of inertially-amplified band gaps and provides a pathway for realising a combination of strength and breadth in the wave attenuation characteristics. We theoretically present this concept, analytically identify critical conditions for the coupling of the attenuation peaks, and provide a series of parametric sweeps to further highlight the phenomenon and guide design. For example, we find a design with a relatively elevated level of minimum attenuation over practically the entire width of a band gap with a relative size of 130 % , and another design with a smaller band gap but a 15-fold increase in the minimum attenuation strength compared to a pure IA chain.

We present a theory for the dispersion of generated harmonics in a traveling nonlinear wave. The harmonics dispersion relation—derived by the theory—provides direct and exact prediction of the collective harmonics spectrum in the frequency-wavenumber domain and does so without prior knowledge of the spatial-temporal solution. The new relation is applicable to a family of initial wave functions characterized by an initial amplitude and wavenumber. We demonstrate the theory on nonlinear elastic waves in a homogeneous rod and demonstrate its extension to periodic rods. We investigate a thick elastic rod admitting longitudinal motion. In the linear limit, this rod is dispersive due to the effect of lateral inertia. The nonlinearity is introduced through either the stress–strain relation and/or the strain–displacementgradient relation. Using a theory we have developed earlier, we derive an exact general nonlinear dispersion relation for the thick rod. We then derive a special case of this relation and show that it provides an exact prediction of the generated harmonics spectrum, in frequency versus wavenumbers. Both relations are validated by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) for the general nonlinear dispersion relation and short-term, pre-breaking dispersion (by Fourier transformations) for both the general and specialized relation.

International audience; The introduction of engineered resonance phenomena on surfaces has opened a new frontier in surface science and technology. Pillared phononic crystals, metamaterials, and metasurfaces are an emerging class of artificial structured media, featuring surfaces, that consist of pillars–or branching substructures–standing on a plate or a substrate. A pillared phononic crystal exhibits Bragg band gaps while a pillared metamaterial may feature both Bragg band gaps and local-resonance hybridization band gaps. These two band-gap phenomena, along with other unique wave dispersion characteristics, have been exploited for a variety of applications spanning a range of length scales and covering multiple disciplines in applied physics and engineering, particularly in elastodynamics and acoustics. The intrinsic placement of pillars on a semi-infinite surface–yielding a metasurface–has similarly provided new avenues for the control and manipulation of wave propagation. Classical waves are admitted in pillared media, including Lamb waves in plates and Rayleigh and Love waves along the surface of substrates, ranging in frequencies from Hz to several GHz. With the presence of the pillars, these waves couple with surface resonances richly creating new phenomena and properties in the subwavelength regime and in some applications at higher frequencies as well. At the nanoscale, it was shown that atomic-scale resonances–stemming from nanopillars–alter the fundamental nature of conductive thermal transport by reducing the group velocities and generating mode localizations across the entire spectrum of the constituent material well into the THz regime. In this article, we first overview the history and development of pillared materials, then provide a detailed synopsis of a selection of key research topics that involve the utilization of pillars or similar branching substructures in different contexts. Finally, we conclude by providing a short summary and some perspectives on the state of the field and its promise for further future development.

The Bloch mode synthesis (BMS) model-reduction method adapts component mode synthesis techniques to unit-cell problems in order to obtain a reduced-order model that quickly produces band-structure frequencies for any wave vector, or vice versa. Fundamental to BMS is a partitioning of the real-space model into interior and boundary components, and subsequent reduction of the interior via truncated normal mode expansion. In this paper, two enhancements are presented for the BMS method that reduce both computation time and error in band-structure calculations. The first enhancement improves the accuracy of the interior reduction by approximating the participation of the residual modes rather than simply truncating them. The original formulation of BMS includes a modal reduction of the boundary that must be recomputed for every wave vector. This limits computational benefits and prevents the reduced-order model from being useful for the inverse band-structure problem (i.e., the k ( ω ) calculation). The second enhancement is a local boundary reduction that is independent of wave vector and thus does not suffer from the aforementioned limitations.

Elastic metamaterials may exhibit band gaps at wavelengths far exceeding feature sizes. This is attributed to local resonances of embedded or attached substructures. In configurations with attached substructures, such as a pillared plate, waves propagating in the base medium–e.g., the plate portion–experience attenuation at band-gap frequencies. Considering a simplified lumped-parameter model for a waveguide with attached resonating branches, we present a theoretical treatment for a periodic unit cell comprising a base mass-spring chain with a multi-degree-of-freedom, mono-coupled branch. Bloch’s theorem is applied, combined with a sub-structuring approach where the resonating branch is modeled separately and condensed into its effective dynamic stiffness. Thus, the treatment is generally applicable to an arbitrary branch regardless of its size and properties. We provide an analysis–supported by guiding graphical illustrations–that yields an identification of fundamental bounds for the band-gap edges as dictated by the dynamical characteristics of the resonating branch. Analytical sensitivity functions are also derived for the dependence of these bounds on the degree of coupling between the base and the branch. The sensitivity analysis reveals further novel findings including the role of the frequency derivative of the branch dynamic stiffness in providing a direct relation between the band-gap edge locations and variation in the coupling parameters—the mass and stiffness ratios between the base chain and the branch root. In additional analysis, sub-Bragg bounds of an exact model comprising a one-dimensional continuous base–modeled as a rod–and a discrete resonating branch are derived and shown to be tighter than those of the all-discrete model. Finally, the applicability of the derived bounds and sensitivity functions are shown to be valid for a corresponding full two-dimensional finite-element model of a pillared waveguide admitting out-of-plane shear waves.

Over the past three decades, the study of phononic crystals (PCs) has rapidly evolved into a prominent research field offering a versatile platform for the creation of structured materials with salient properties [...]

Vibration energy harvesting is an emerging technology that enables electric power generation using piezoelectric devices. The prevailing approach for characterization of the energy-harvesting capacity in these devices is to consider a finite structure operating under forced vibration conditions. Here, we present an alternative framework whereby the intrinsic energy-harvesting characteristics are formally quantified independent of the forcing and the structure size. In doing so, we consider the notion of a piezoelectric material rather than a finite piezoelectric structure. As an example, we consider a suspended piezoelectric phononic crystal to which we apply Bloch’s theorem and formally quantify the energy-harvesting characteristics within the span of the unit cell’s Brillouin zone (BZ). In the absence of shunted piezoelectric circuits, the wavenumber-dependent dissipation of the phononic crystal is calculated and shown to increase, as expected, with the level of prescribed damping. With the inclusion of the piezoelectric elements, the wavenumber-dependent dissipation rises by an amount proportional to the energy available for harvest which upon integration over the BZ and summing over all branches yields a quantity representative of the net available energy for harvesting. We investigate both monoatomic and diatomic phononic crystals and piezoelectric elements with and without an inductor. The paper concludes with a parametric design study yielding optimal piezoelectric element properties in terms of the proposed intrinsic energy-harvesting availability measure.

The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals consisting of layers with alternating material properties. Considering longitudinal waves and ignoring lateral effects, the exact nonlinear dispersion relation in each homogeneous layer is first obtained and subsequently used within the transfer matrix method to derive an approximate nonlinear dispersion relation for the overall periodic medium. The result is an amplitude-dependent elastic band structure that upon verification by numerical simulations is accurate for up to an amplitude-to-unit-cell length ratio of one-eighth. The derived dispersion relation allows us to interpret the formation of spatial invariance in the wave profile as a balance between hardening and softening effects in the dispersion that emerge due to the nonlinearity and the periodicity, respectively. For example, for a wave amplitude of the order of one-eighth of the unit-cell size in a demonstrative structure, the two effects are practically in balance for wavelengths as small as roughly three times the unit-cell size.

Resonant elastic metamaterials are artificial material systems that exhibit unique dynamical properties shaped by the intrinsic interaction between resonances and traveling dispersive waves. In this chapter, we provide a technical review of the recently proposed concept of dissipation emergence in elastic metamaterials. This concept is termed “metadamping.” Unlike conventional materials used to dampen vibrations where the damping capacity is affected by the atomic configuration, defects, and/or rheological properties, here the level of dissipation is controlled via the dynamics of the metamaterial's resonant substructures. In this manner, it is possible to create a net material system that is both stiff and highly damped, to absorb vehicle vibrations for example. The chapter starts with a motivation and introduction of metadamping, and then presents an in-depth analysis and parametric study of metadamping in the context of both locally and nonlocally resonant elastic metamaterials modeled as mass-spring-dashpot systems. The effect of the core damping model (e.g., viscous vs nonviscous) is also examined. Finally, a review is given of metadamping in a pillared beam that has recently been investigated by experiments, simulations, and theory.

The dispersive behavior of phononic crystals and locally resonant metamaterials is influenced by the type and degree of damping in the unit cell. Dissipation arising from viscoelastic damping is influenced by the past history of motion because the elastic component of the damping mechanism adds a storage capacity. Following a state-space framework, a Bloch eigenvalue problem incorporating general viscoelastic damping based on the Zener model is constructed. In this approach, the conventional Kelvin-Voigt viscous-damping model is recovered as a special case. In a continuous fashion, the influence of the elastic component of the damping mechanism on the band structure of both a phononic crystal and a metamaterial is examined. While viscous damping generally narrows a band gap, the hereditary nature of the viscoelastic conditions reverses this behavior. In the limit of vanishing heredity, the transition between the two regimes is analyzed. The presented theory also allows increases in modal dissipation enhancement (metadamping) to be quantified as the type of damping transitions from viscoelastic to viscous. In conclusion, it is shown that engineering the dissipation allows one to control the dispersion (large versus small band gaps) and, conversely, engineering the dispersion affects the degree of dissipation (high or low metadamping).

A measurement of the inclusive production cross section of isolated prompt photons in proton-antiproton collisions at center-of-mass energy $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ is presented. The results are obtained using the full Run II data sample collected with the Collider Detector at the Fermilab Tevatron, which corresponds to an integrated luminosity of $9.5\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. The cross section is measured as a function of photon transverse energy, ${E}_{T}^{\ensuremath{\gamma}}$, in the range $30l{E}_{T}^{\ensuremath{\gamma}}l500\text{ }\text{ }\mathrm{GeV}$ and in the pseudorapidity region $|{\ensuremath{\eta}}^{\ensuremath{\gamma}}|l1.0$. The results are compared with predictions from parton-shower Monte Carlo models at leading order in QCD and from next-to-leading-order perturbative QCD calculations. The latter show good agreement with the measured cross section.

Author(s): Aaltonen, T; Amerio, S; Amidei, D; Anastassov, A; Annovi, A; Antos, J; Apollinari, G; Appel, JA; Arisawa, T; Artikov, A; Asaadi, J; Ashmanskas, W; Auerbach, B; Aurisano, A; Azfar, F; Badgett, W; Bae, T; Barbaro-Galtieri, A; Barnes, VE; Barnett, BA; Barria, P; Bartos, P; Bauce, M; Bedeschi, F; Behari, S; Bellettini, G; Bellinger, J; Benjamin, D; Beretvas, A; Bhatti, A; Bland, KR; Blumenfeld, B; Bocci, A; Bodek, A; Bortoletto, D; Boudreau, J; Boveia, A; Brigliadori, L; Bromberg, C; Brucken, E; Budagov, J; Budd, HS; Burkett, K; Busetto, G; Bussey, P; Butti, P; Buzatu, A; Calamba, A; Camarda, S; Campanelli, M; Canelli, F; Carls, B; Carlsmith, D; Carosi, R; Carrillo, S; Casal, B; Casarsa, M; Castro, A; Catastini, P; Cauz, D; Cavaliere, V; Cerri, A; Cerrito, L; Chen, YC; Chertok, M; Chiarelli, G; Chlachidze, G; Cho, K; Chokheli, D; Clark, A; Clarke, C; Convery, ME; Conway, J; Corbo, M; Cordelli, M; Cox, CA; Cox, DJ; Cremonesi, M; Cruz, D; Cuevas, J; Culbertson, R; d'Ascenzo, N; Datta, M; de Barbaro, P; Demortier, L | Abstract: We report on a measurement of the $D^{+}$-meson production cross section as a function of transverse momentum ($p_T$) in proton-antiproton ($p\bar{p}$) collisions at 1.96 TeV center-of-mass energy, using the full data set collected by the Collider Detector at Fermilab in Tevatron Run II and corresponding to 10 fb$^{-1}$ of integrated luminosity. We use $D^{+} \to K^-\pi^+\pi^+$ decays fully reconstructed in the central rapidity region $|y|l1$ with transverse momentum down to 1.5 GeV/$c$, a range previously unexplored in $p\bar{p}$ collisions. Inelastic $p\bar{p}$-scattering events are selected online using minimally-biasing requirements followed by an optimized offline selection. The $K^-\pi^+\pi^+$ mass distribution is used to identify the $D^+$ signal, and the $D^+$ transverse impact-parameter distribution is used to separate prompt production, occurring directly in the hard scattering process, from secondary production from $b$-hadron decays. We obtain a prompt $D^+$ signal of 2950 candidates corresponding to a total cross section $\sigma(D^+, 1.5 l p_T l 14.5~\mbox{GeV/}c, |y|l1) = 71.9 \pm 6.8 (\mbox{stat}) \pm 9.3 (\mbox{syst})~\mu$b. While the measured cross sections are consistent with theoretical estimates in each $p_T$ bin, the shape of the observed $p_T$ spectrum is softer than the expectation from quantum chromodynamics. The results are unique in $p\bar{p}$ collisions and can improve the shape and uncertainties of future predictions.

We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. The underlying formulation uses the Cauchy stress and the Green-Lagrange strain. For all models, we consider linear constitutive relations in order to isolate the effect of finite motion. The proposed methodology, however, is applicable to problems that also exhibit material nonlinearity. For the rod model, we obtain the exact analytical explicit solution of the derived finite-deformation dispersion relation, and compare it with data obtained via numerical simulation of nonlinear wave motion in a finite rod. For the beam model, we obtain a solution by numerical root finding. The results allow us to quantify the deviation in the dispersion curves when exact large deformation is considered compared to following the assumption of infinitesimal deformation. We show that incorporation of finite deformation following the chosen definitions of stress and strain raises the frequency branches for both axial and flexural waves above the nominal values associated with linear motion. For the beam problem, only the inextensional planar motion model provides an accurate description of the finite-deformation response for both static deflection and wave dispersion. Our findings, which represent the first derivation of finite-strain, amplitude-dependent dispersion relations for any type of elastic media, draw attention to 1) the tangible effect of finite deformation on wave dispersion and consequently on the speed of sound in an elastic medium and 2) the importance of incorporating longitudinal-transverse motion coupling in nonlinear analysis of thin structures., Comment: Accepted for publication in Wave Motion

et al., A search for a Higgs boson with suppressed couplings to fermions, hf, assumed to be the neutral, lower-mass partner of the Higgs boson discovered at the Large Hadron Collider, is reported. Such a Higgs boson could exist in extensions of the standard model with two Higgs doublets, and could be produced via pp¯→H±hf→W∗hfhf→4γ+X, where H± is a charged Higgs boson. This analysis uses all events with at least three photons in the final state from proton-antiproton collisions at a center-of-mass energy of 1.96 TeV collected by the Collider Detector at Fermilab, corresponding to an integrated luminosity of 9.2 fb−1. No evidence of a signal is observed in the data. Values of Higgs-boson masses between 10 and 100 GeV/c2 are excluded at 95% Bayesian credibility., This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A. P. Sloan Foundation; the Bundesministerium für Bildung und Forschung, Germany; the Korean World Class University Program, the National Research Foundation of Korea; the Science and Technology Facilities Council and the Royal Society, United Kingdom; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovación, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; the Academy of Finland; the Australian Research Council (ARC); and the EU community Marie Curie Fellowship Contract No. 302103.