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Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration
Mechanical metamaterials present a promising platform for seemingly impossible mechanics. They often require incompatibility of their elementary building blocks, yet a comprehensive understanding of its role remains elusive. Relying on an analogy to ferromagnetic and antiferromagnetic binary spin interactions, we present a universal approach to identify and analyze topological mechanical defects for arbitrary building blocks. We underline differences between two- and three-dimensional metamaterials, and show how topological defects can steer stresses and strains in a controlled and non-trivial manner and can inspire the design of materials with hitherto unknown complex mechanical response.
Topologically protected steady cycles in an icelike mechanical metamaterial
Pushing and pulling on a material’s surface in a steady, periodic way is a common test for characterizing that material’s mechanical properties. Simple materials typically exhibit a single steady state response to a given way of forcing. We proposed a metamaterial made of mechanically bistable elements, which responds with a wide variety of distinct steady state cycles in response to just a single, persistently applied periodic force. This metamaterial could be a step towards building materials that exhibit dynamic forms of memory in their response to periodic driving.
Each unit cell in the metamaterial spontaneously adopts one of two minimum energy deformation modes. As a result, different regions within the material settle into one or the other stable mechanical phases, analogous to competing positive and negative domains in a ferromagnet. The boundary force pattern selects the preferred mechanical phase along a given portion of the boundary. The shape and speed of the internal divisions between mechanical phases can be tuned based on the stiffness of the internal components. Since a wide variety of internal configurations can be compatible with the same chosen phase pattern selected by an applied force along the materials edge, the system is found to settle into many different steady state cycles when the applied force oscillates. The system has a large degree of flexibility and potential for programmability. The observed responses could be tailored by changing the number and distribution of forcing segments along the boundary, testing different system shapes with distinct boundary symmetries, or by forcing different portions of the boundary out of phase or with different amplitudes.
Persistent collective motion of a dispersing membrane domain
We study the Brownian motion of an assembly of mobile inclusions embedded in a fluid membrane. The motion includes the dispersal of the assembly, accompanied by the diffusion of its center of mass. Usually, the former process is much faster than the latter because the diffusion coefficient of the center of mass is inversely proportional to the number of particles. However, in the case of membrane inclusions, we find that the two processes occur on the same timescale, thus significantly prolonging the lifetime of the assembly as a collectively moving object. This effect is caused by the quasi-two-dimensional membrane flows, which couple the motions of even the most remote inclusions in the assembly. The same correlations also cause the diffusion coefficient of the center of mass to decay slowly with time, resulting in weak subdiffusion. We confirm our analytical results by Brownian dynamics simulations with flow-mediated correlations. The effect reported here should have implications for the stability of nanoscale membrane heterogeneities.
Symmetry properties of nonlinear hydrodynamic interactions between responsive particles
Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of a driven suspension consisting of many particles. We consider a pair of particles which, to linear order in the force, do not interact hydrodynamically. If the system possesses an intrinsic property (such as the shape of the particles, their position with respect to a boundary, or the shape of the boundary) which is affected by the external forcing, hydrodynamic interactions that depend nonlinearly on the force may emerge. We study the general properties of such nonlinear response. Analysis of the symmetries under particle exchange and under force reversal leads to general conclusions concerning the appearance of relative translation and the motion's time reversibility. We demonstrate the applicability of the conclusions in three specific examples: (a) two spheres driven parallel to a wall; (b) two deformable objects driven parallel to their connecting line; and (c) two spheres driven along a curved path. The breaking of time reversibility suggests a possible use of nonlinear hydrodynamic interactions to disperse or assemble particles by an alternating force.
Melanin‐Inspired Chromophoric Microparticles Composed of Polymeric Peptide Pigments
Melanin and related polyphenolic pigments are versatile functional polymers that serve diverse aesthetic and protective roles across the living world. These polymeric pigments continue to inspire the development of adhesive, photonic, electronic and radiation‐protective materials and coatings. The properties of these structures are dictated by covalent and non‐covalent interactions in ways that, despite progress, are not fully understood. It remains a major challenge to direct oxidative polymerization of their precursors (amino acids, (poly‐)phenols, thiols) toward specific structures. By taking advantage of supramolecular pre‐organization of tyrosine‐tripeptides and reactive sequestering of selected amino acids during enzymatic oxidation, we demonstrate the spontaneous formation of distinct new chromophores with optical properties that are far beyond the range of those found in biological melanins, in terms of color, UV absorbance and fluorescent emission.
Architectural Change of the Shell-Forming Block from Linear to V-Shaped Accelerates Micellar Disassembly, but Slows the Complete Enzymatic Degradation of the Amphiphiles
Tuning the enzymatic degradation and disassembly rates of polymeric amphiphiles and their assemblies is crucial for designing enzyme-responsive nanocarriers for controlled drug delivery applications. The common methods to control the enzymatic degradation of amphiphilic polymers are to tune the molecular weights and ratios of the hydrophilic and hydrophobic blocks. In addition to these approaches, the architecture of the hydrophilic block can also serve as a tool to tune enzymatic degradation and disassembly. To gain a deeper understanding of the effect of the molecular architecture of the hydrophilic block, we prepared two types of well-defined PEG-dendron amphiphiles bearing linear or V-shaped PEG chains as the hydrophilic blocks. The high molecular precision of these amphiphiles, which emerges from the utilization of dendrons as the hydrophobic blocks, allowed us to study the self-assembly and enzymatic degradation and disassembly of the two types of amphiphiles with high resolution. Interestingly, the micelles of the V-shaped amphiphiles were significantly smaller and disassembled faster than those of the amphiphiles based on linear PEG. However, the complete enzymatic cleavage of the hydrophobic end groups was significantly slower for the V-shaped amphiphiles. Our results show that the V-shaped architecture can stabilize the unimer state and, hence, plays a double role in the enzymatic degradation and the induced disassembly and how it can be utilized to control the release of encapsulated or bound molecular cargo.
Machine-learning iterative calculation of entropy for physical systems
Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding, and more. Current methods for entropy estimation suffer from a high computational cost, lack of generality, or inaccuracy and inability to treat complex, strongly interacting systems. In this paper, we present a method, termed machine-learning iterative calculation of entropy (MICE), for calculating the entropy by iteratively dividing the system into smaller subsystems and estimating the mutual information between each pair of halves. The estimation is performed with a recently proposed machine-learning algorithm which works with arbitrary network architectures that can be chosen to fit the structure and symmetries of the system at hand. We show that our method can calculate the entropy of various systems, both thermal and athermal, with state-of-the-art accuracy. Specifically, we study various classical spin systems and identify the jamming point of a bidisperse mixture of soft disks. Finally, we suggest that besides its role in estimating the entropy, the mutual information itself can provide an insightful diagnostic tool in the study of physical systems.
Target finding in fibrous biological environments
We use a lattice model to study first-passage time distributions of target finding events through complex environments with elongated fibers distributed with different anisotropies and volume occupation fractions. For isotropic systems and for low densities of aligned fibers, the three-dimensional search is a Poisson process with the first-passage time exponentially distributed with the most probable finding time at zero. At high enough densities of aligned fibers, elongated channels emerge, reducing the dynamics dimensionality to one dimension. We show how the shape and size of the channels modify the behavior of the first-passage time distribution and its short, intermediate, and long time scales. We develop an exactly solvable model for synthetic rectangular channels, which captures the effects of the tortuous local structure of the elongated channels that naturally emerge in our system. For arbitrary values of the nematic order parameter of fiber orientations, we develop a mapping to the simpler situation of fully aligned fibers at some other effective volume occupation fraction. Our results shed light on the molecular transport of biomolecules between biological cells in complex fibrous environments.
Experimental Realization of Diffusion with Stochastic Resetting
Stochastic resetting is prevalent in natural and man-made systems, giving rise to a long series of nonequilibrium phenomena. Diffusion with stochastic resetting serves as a paradigmatic model to study these phenomena, but the lack of a well-controlled platform by which this process can be studied experimentally has been a major impediment to research in the field. Here, we report the experimental realization of colloidal particle diffusion and resetting via holographic optical tweezers. We provide the first experimental corroboration of central theoretical results and go on to measure the energetic cost of resetting in steady-state and first-passage scenarios. In both cases, we show that this cost cannot be made arbitrarily small because of fundamental constraints on realistic resetting protocols. The methods developed herein open the door to future experimental study of resetting phenomena beyond diffusion.
Delayed nucleation in lipid particles
Metastable states in first-order phase-transitions have been traditionally described by classical nucleation theory (CNT). However, recently an increasing number of systems displaying such a transition have not been successfully modelled by CNT. The delayed crystallization of phospholipids upon super-cooling is an interesting case, since the extended timescales allow access into the dynamics. Herein, we demonstrate the controllable behavior of the long-lived metastable liquid-crystalline phase of dilauroylphosphatidylethanolamine (DLPE), arranged in multi-lamellar vesicles, and the ensuing cooperative transition to the crystalline state. Experimentally, we find that the delay in crystallization is a bulk phenomenon, which is tunable and can be manipulated to span two orders of magnitude in time by changing the quenching temperature, solution salinity, or adding a secondary phospholipid. Our results reveal the robust persistence of the metastability, and showcase the apparent deviation from CNT. This distinctive suppression of the transition may be explained by the resistance of the multi-lamellar vesicle to deformations caused by nucleated crystalline domains. Since phospholipids are used as a platform for drug-delivery, a programmable design of cargo hold and release can be of great benefit.