514 research outputs found
Anomalous tunneling of bound pairs in crystal lattices
A novel method of solving scattering problems for bound pairs on a lattice is
developed. Two different break ups of the hamiltonian are employed to calculate
the full Green operator and the wave function of the scattered pair. The
calculation converges exponentially in the number of basis states used to
represent the non-translation invariant part of the Green operator. The method
is general and applicable to a variety of scattering and tunneling problems. As
the first application, the problem of pair tunneling through a weak link on a
one-dimensional lattice is solved. It is found that at momenta close to \pi the
pair tunnels much easier than one particle, with the transmission coefficient
approaching unity. This anomalously high transmission is a consequence of the
existence of a two-body resonant state localized at the weak link.Comment: REVTeX, 5 pages, 4 eps figure
Recommended from our members
Natural and anthropogenic rapid changes in the Kara-Bogaz Gol over the last two centuries reconstructed from palynological analyses and a comparison to instrumental records
Palynological analyses (pollen and dinocysts) of a sediment core taken in the Kara-Bogaz Gol have been used to
reconstruct rapid and catastrophic environmental changes over the last two centuries (chronology based on 210Pb). A
natural cyclicity (65 years) of water level changes in the Caspian Sea and in the Kara-Bogaz Gol and anthropogenic
factors (building of a dam separating the CS and the KBG waters) combine to induce rapid changes in water levels of
the KBG, in the salinity of its waters and in vegetation cover of its surroundings. The impact of low water levels on
the dinocysts is marked by a lower diversity and the survival of two species that are typical of the KBG, the Caspian
Sea species present in the KBG having disappeared. During periods of higher water levels (AD 1871 to 1878), the
lake is surrounded by a steppe-like vegetation dominated by Artemisia; whereas during periods of low water levels
(AD 1878 to 1913 and AD 1955-1998), the emerged shore are colonised by Chenopodiaceae. The period of AD 1913
to 1955 corresponding to decreasing water levels has an extremely low pollen concentration and a maximum of
reworking of arboreal taxa. During the last low-level period, humans responded by abandoning the shores of the bay.
What happened to the KBG can be used as an example of what may happen in the future for the Aral Sea.
A problem of reworking of Tertiary dinocysts into modern deposits has been detected owing to the knowledge of the
modern dinoflagellate assemblages recently made available through a water survey. A comparison to modern surface
pollen samples from Central Asia (Anzali, Caspian Sea south and central basins, Aral Sea, Lake Balkhash, Lake
Issyk-Kul and the Chinese Tien-Shan range) allows us to establish the potential reworking of at least five arboreal
pollen taxa possibly by run-off and dust storms
Shear band dynamics from a mesoscopic modeling of plasticity
The ubiquitous appearance of regions of localized deformation (shear bands)
in different kinds of disordered materials under shear is studied in the
context of a mesoscopic model of plasticity. The model may or may not include
relaxational (aging) effects. In the absence of relaxational effects the model
displays a monotonously increasing dependence of stress on strain-rate, and
stationary shear bands do not occur. However, in start up experiments transient
(although long lived) shear bands occur, that widen without bound in time. I
investigate this transient effect in detail, reproducing and explaining a t^1/2
law for the thickness increase of the shear band that has been obtained in
atomistic numerical simulations. Relaxation produces a negative sloped region
in the stress vs. strain-rate curve that stabilizes the formation of shear
bands of a well defined width, which is a function of strain-rate. Simulations
at very low strain-rates reveal a non-trivial stick-slip dynamics of very thin
shear bands that has relevance in the study of seismic phenomena. In addition,
other non-stationary processes, such as stop-and-go, or strain-rate inversion
situations display a phenomenology that matches very well the results of recent
experimental studies.Comment: 10 pages, 10 figure
Microstructural Shear Localization in Plastic Deformation of Amorphous Solids
The shear-transformation-zone (STZ) theory of plastic deformation predicts
that sufficiently soft, non-crystalline solids are linearly unstable against
forming periodic arrays of microstructural shear bands. A limited nonlinear
analysis indicates that this instability may be the mechanism responsible for
strain softening in both constant-stress and constant-strain-rate experiments.
The analysis presented here pertains only to one-dimensional banding patterns
in two-dimensional systems, and only to very low temperatures. It uses the
rudimentary form of the STZ theory in which there is only a single kind of zone
rather than a distribution of them with a range of transformation rates.
Nevertheless, the results are in qualitative agreement with essential features
of the available experimental data. The nonlinear theory also implies that
harder materials, which do not undergo a microstructural instability, may form
isolated shear bands in weak regions or, perhaps, at points of concentrated
stress.Comment: 32 pages, 6 figure
TensorFlow Doing HPC
TensorFlow is a popular emerging open-source programming framework supporting
the execution of distributed applications on heterogeneous hardware. While
TensorFlow has been initially designed for developing Machine Learning (ML)
applications, in fact TensorFlow aims at supporting the development of a much
broader range of application kinds that are outside the ML domain and can
possibly include HPC applications. However, very few experiments have been
conducted to evaluate TensorFlow performance when running HPC workloads on
supercomputers. This work addresses this lack by designing four traditional HPC
benchmark applications: STREAM, matrix-matrix multiply, Conjugate Gradient (CG)
solver and Fast Fourier Transform (FFT). We analyze their performance on two
supercomputers with accelerators and evaluate the potential of TensorFlow for
developing HPC applications. Our tests show that TensorFlow can fully take
advantage of high performance networks and accelerators on supercomputers.
Running our TensorFlow STREAM benchmark, we obtain over 50% of theoretical
communication bandwidth on our testing platform. We find an approximately 2x,
1.7x and 1.8x performance improvement when increasing the number of GPUs from
two to four in the matrix-matrix multiply, CG and FFT applications
respectively. All our performance results demonstrate that TensorFlow has high
potential of emerging also as HPC programming framework for heterogeneous
supercomputers.Comment: Accepted for publication at The Ninth International Workshop on
Accelerators and Hybrid Exascale Systems (AsHES'19
An elasto-visco-plastic model for immortal foams or emulsions
A variety of complex fluids consist in soft, round objects (foams, emulsions,
assemblies of copolymer micelles or of multilamellar vesicles -- also known as
onions). Their dense packing induces a slight deviation from their prefered
circular or spherical shape. As a frustrated assembly of interacting bodies,
such a material evolves from one conformation to another through a succession
of discrete, topological events driven by finite external forces. As a result,
the material exhibits a finite yield threshold. The individual objects usually
evolve spontaneously (colloidal diffusion, object coalescence, molecular
diffusion), and the material properties under low or vanishing stress may alter
with time, a phenomenon known as aging. We neglect such effects to address the
simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully
tensorial, rheological model, equivalent to the (scalar) Bingham model.
Importantly, the model consistently describes the ability of such soft
materials to deform substantially in the elastic regime (be it compressible or
not) before they undergo (incompressible) plastic creep -- or viscous flow
under even higher stresses.Comment: 69 pages, 29 figure
Hyperspherical theory of anisotropic exciton
A new approach to the theory of anisotropic exciton based on Fock
transformation, i.e., on a stereographic projection of the momentum to the unit
4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a
basis of the perturbation theory. The binding energies, wave functions and
oscillator strengths of elongated as well as flattened excitons are obtained
numerically. It is shown that with an increase of the anisotropy degree the
oscillator strengths are markedly redistributed between optically active and
formerly inactive states, making the latter optically active. An approximate
analytical solution of the anisotropic exciton problem taking into account the
angular momentum conserving terms is obtained. This solution gives the binding
energies of moderately anisotropic exciton with a good accuracy and provides a
useful qualitative description of the energy level evolution.Comment: 23 pages, 8 figure
Scaling Transformer to 1M tokens and beyond with RMT
This technical report presents the application of a recurrent memory to
extend the context length of BERT, one of the most effective Transformer-based
models in natural language processing. By leveraging the Recurrent Memory
Transformer architecture, we have successfully increased the model's effective
context length to an unprecedented two million tokens, while maintaining high
memory retrieval accuracy. Our method allows for the storage and processing of
both local and global information and enables information flow between segments
of the input sequence through the use of recurrence. Our experiments
demonstrate the effectiveness of our approach, which holds significant
potential to enhance long-term dependency handling in natural language
understanding and generation tasks as well as enable large-scale context
processing for memory-intensive applications
Recurrent Memory Transformer
Transformer-based models show their effectiveness across multiple domains and
tasks. The self-attention allows to combine information from all sequence
elements into context-aware representations. However, global and local
information has to be stored mostly in the same element-wise representations.
Moreover, the length of an input sequence is limited by quadratic computational
complexity of self-attention.
In this work, we propose and study a memory-augmented segment-level recurrent
Transformer (Recurrent Memory Transformer). Memory allows to store and process
local and global information as well as to pass information between segments of
the long sequence with the help of recurrence. We implement a memory mechanism
with no changes to Transformer model by adding special memory tokens to the
input or output sequence. Then Transformer is trained to control both memory
operations and sequence representations processing.
Results of experiments show that our model performs on par with the
Transformer-XL on language modeling for smaller memory sizes and outperforms it
for tasks that require longer sequence processing. We show that adding memory
tokens to Tr-XL is able to improve it performance. This makes Recurrent Memory
Transformer a promising architecture for applications that require learning of
long-term dependencies and general purpose in memory processing, such as
algorithmic tasks and reasoning
- …